I think it might be useful for you to distinguish the two principal senses of "time", as Aristotle did.

First, "time" is primarily used to signify a measurement. So we say how long something takes by referring to a unit of measurement, hours, minutes, seconds, etc., In this sense, "time" refers to a measurement of duration, and from this usage we derive "velocity" and all sorts of concepts of physics.

In a secondary sense, "time" refers to the thing measured. This use of "time" is a little bit more difficult to grasp, but to give substance to our measurements of duration, we must assume that there is actually something being measured. We might call this the passing of time, or something like that.,

What's not true? You said: "(sets) can be assigned any possible order (in the sense of humanly created order), with absolutely no regard for truth or falsity." I asked what it means for the possibility (of the order) to have "absolutely no regard for truth or falsity". — Luke

I said, the assignment of possibility is done without regard for order.

Sorry Luke, your interpretation is so bad (no wonder you see contradiction in everything I say) , I have extreme difficulty communicating with you. I don't see how any reasonable mind could interpret the way you do, therefore I can only conclude that you make these unreasonable interpretations intentionally.

A set is not a bag of items, it's an abstraction, that's the point fishfry has been stressing. A bag of items has an inherent order, as I've spent months describing to you. If we want to represent that bag of items as a thing called "a set" we cannot truthfully predicate of that subject, the property of "no inherent order" because the thing being represented necessarily does have an inherent order. No inherent order is a false representation.

Fishfry claims that a pure abstraction is an imaginary fiction, so it doesn't matter that it's not a true representation, and claimed that the imaginary fiction is useful toward a "higher truth". However, fishfry insisted on using a map analogy for explaining abstractions, and a map is a representation, so there is inconsistency in what fishfry was presenting. Furthermore, fishfry could not explain how an imaginary fiction could be useful toward obtain a higher truth.

Has that been the basis of your argument from the start? Funny, since I've seen you argue against the eternalist block universe in other threads. You really are a troll. — Luke

Going through this thread, and taking statements out of context isn't enough for you, so now you have to refer to other threads. You bring "taking things out of context" to a whole new level. I really am a troll but you're just an ass hole.

Possibility has "no regard for truth or falsity"? What does that mean? — Luke

That's not true. Possibilities are limited by the actual state of the world. Anything claimed to be possible, which is not allowed for by the present state, is actually impossible.

You can't have impossibility without possibility. — Luke

And this is not even true. If determinism is the true description of reality, then true possibility is actually impossible, such that we would have the impossibility of changing the eternalist block universe, without any real possibility.

I've spent the last couple of posts saying that math is a lie, math is fiction, math is untruth in the service of higher truth, and you put words in my mouth. It's not fun and there's no point. — fishfry

I didn't see any mention of "higher truth". And I really don't think you've provided any explanation as to how lies, fictions, and untruths could be "in the service of higher truth". That sounds similar to Plato's "noble lie", where the rulers of the State lie to the common people for the sake of their own good. The proposal that such lies and deception are for the sake of a "higher truth" is extremely doubtful.

The problem we have here is that you seem to believe that mathematics give us idealized exactness, when really it fails at this. So this is a self-deception on your part. It all seems to stem from your idea that you can separate a "pure mathematics" as pure abstraction, away from applied mathematics, so that this pure mathematics deals with idealized exactness, while applied mathematics deals with the imprecision of real world measurement. You do not seem to understand that those who engage in so called "pure mathematics" are actually working on ways to solve the problems of imprecision in real world measurement, not trying to create pure abstractions. The problems of real world imprecision are not solved by axioms of idealized exactness, because of the fundamental incompatibility between the two.

Here's a proposal for you to consider. Imagine that human beings, when they first came out with mathematics many thousands of years ago, believed that mathematics provided them with ideal exactness. So we go way back, before Pythagoreans, Egyptians, or even Babylonians, and see that the people knew things from math, such as the example that they could derive a perfect right angle all the time, and they believed that mathematics gave to them idealized exactness. However, there were slight problems in applying numbers to spatial projections, such as the irrational nature of the square root of two, and pi.

Spatial projections are a creation based in real world appearances. I do not think you would deny this. So if we say that numbers are based in this idealized exactness, then when they are applied to real world problems, spatial projects, an incompatibility appears. The mathematician is faced with the problem of solving this incompatibility. But the mathematician is incapable of altering the reality of our spatial temporal existence, so there is no choice but to alter that lofty "idealized exactness" of the fundamental mathematical principles, numbers, if that incompatibility is to be resolved. The mathematician therefore is attempting to produce axioms which will bring numbers away from idealized exactness.

What I propose for you to consider then, is that mathematics may have been based in the idea of idealized exactness, many thousands of years ago, just like religion might have been based in the idea of an eternal immortal soul, but the progress which is made in mathematics, by mathematicians, is to bring us down from this idea, bring us away from it, to make mathematics something more compatible with the real world. For mathematicians to be working in some lofty world of ideal exactness, while this is completely incompatible with the real world, is pointless. So what the mathematicians are really doing is finding ways to bring the principles down out of that pointless realm of ideal exactness, compromise them in a way which makes them applicable, while maintaining as much exactness as possible.

You do need to understand the concept of the necessary approximateness of all physical measurement. I can't imagine why you would take a stance so fundamentally wrong. — fishfry

You see, my stance is directionally opposed to yours. Which one is fundamentally wrong is debatable. You seem to think that the way to "higher truth" is for the mathematician to work with "pure abstractions", of ideal exactness, which have no correlation to anything in the real world. I think the way to "higher truth" is to rid mathematics of such "pure abstractions", (because they are based in nothing but imagination), and to find "higher truth" we need to replace these principles with principles that correlate with the real world, even if this means to forfeit "ideal exactness". We both know that ideal exactness is impossible in the real world, therefore it cannot be a good principle upon which to judge mathematical principles which have the sole purpose of real world measurements.

You strongly imply that the inherent order is able to be apprehended in these quotes. We must be able to apprehend the inherent order if it is "describable" and we are able to see it. — Luke

You are not respecting the difference I described between what "order" refers to, and what "inherent order" refers to. The former we can apprehend, the latter we cannot, though they are both fundamentally intelligible. That's why I said, ultimately they can both be placed in the same category, I'll call it "intelligible".

I explained those differences already, and you are simply taking things out of context. The "inherent order" is fundamentally intelligible, but not by us, due to deficient capacity. Earlier I used the analogy of the way theologians speak of God. God is fundamentally intelligible, but not intelligible to use. Also, as Kant describes, noumena is fundamentally intelligible, but not by us.

That's right, and then you forced upon the conversation your idiosyncratic idea of "the inherent order" that is unrelated to sets or ordering in mathematics. Fishfry and Tones tried telling you this, but you weren't interested. — Luke

In this entire thread, no one but jgill has offered any sort of alternative explanation as to what "inherent order" could refer to. Clearly it refers to an order which inheres within something. Jgill proposed that it is the order which inheres within a biological organism. But I see no reason to restrict this term to living things, as inanimate things also display reason to believe they have an inherent order. Until you bring forth another idea for "inherent order", it appears like you have no reason to say that mine is idiosyncratic, it really seems to be the only coherent understanding of "inherent order" possible.

You seem to be missing the point of my argument. By removing "inherent order" from the things called sets, as fishfry did, with the assumption of "no inherent order", these things (sets) can be assigned any possible order (in the sense of humanly created order), with absolutely no regard for truth or falsity, because it is stipulated that the set has no inherent order. My point of contention is that there is no such thing as something with no inherent order, it is an impossibility as self-contradictory, a unity of parts without any order to those parts. So this concept of a set, as a thing with no inherent order, is fundamentally wrong, and ought to be rejected.

Thanks? I guess. But this does not answer the question of how your concept of "the inherent order" relates to "order" more generally. You could start with your own ideas of "order" and "the inherent order" and explain how these relate to each other. Why is "the inherent order" not a type of "order"? — Luke

What is referred to by "inherent order" is not a type of what is referred to as "order" because of the separation between them. This is described by Kant as noumenal and phenomenal. Inherent order is within the thing, as essential to the existence of the thing being the precise thing that it is. This is associated with the law of identity, which refers to the uniqueness of a thing. It has a unique inherent order, which makes it fundamentally intelligible as the unique thing which it is, and discernible from other unique things. However, the human mind does not grasp and understand the uniqueness of the thing, it grasps the thing relative to others, by similarities of universals, abstractions.

So the "order" understood by the human mind, created by the human mind as universal, is fundamentally different from the order inhering within the particular individual. If we said inherent order is a type of order (as conceive by humans), we'd dissolve the distinction between universal and particular, in a category mistake, making a particular into a universal. The law of identity prevents us from doing this.

How what is referred to as "inherent order" (within the particular) is related to what is referred to as "order" (a universal created by the human mind), is that they are both fundamentally intelligible. The former is not intelligible to the human being though. We could switch to the Aristotelian term "form" here. Aristotle distinguished two principal senses of the word "form", the form which inheres within the particular object, making it the unique object which it is, and the "form" which we assign, in describing the object, which involves universal abstractions. The latter, the form we assign to the object, neglects, or leaves out, the object's matter. "Matter" is assigned to the particular object to account for its accidents, the parts which are not grasped by the human mind, and this accounts for the object's uniqueness. Under this structure, the form of the particular, its inherent order, complete with accidents, is fundamentally intelligible, but not intelligible to the human intellect which understands through universal forms (orders), leaving the particular, inherent order, incomprehensible.

Have you considered that what you say might appear to be contradictory because it is contradictory, and that the problem is with your metaphysical edifice rather than with my understanding? — Luke

You haven't given me any real evidence that this might be the case, so no. I'll continue to wait for you to produce some substance, and indication that you understand, rather than demonstrating that you can search keywords throughout a lengthy thread, and take quotes out of context to produce the appearance of contradiction.

The Pythagorean theorem in the real world is literally false. It's close but no cigar. It's approximately true, that's the best you can say. But the point here is that you are on record claiming the Pythagorean theorem is "very true." So you are not in a position to deny saying that. — fishfry

"Idealized exactness" is not "truth". The Pythagorean theorem is very true in the real world. Where we disagree is on what constitutes being true. That has been obvious all along, you allow that fictions like "no inherent order", may be a part of your idealized exactness, thereby compromising your supposed truth with falsity.

Idealized mathematics (as opposed to say, numerical methods or engineering math, etc.) is perfectly exact. That's its supreme virtue. — fishfry

No fishfry, "infinity" is in no way perfectly exact. You did not address this, and there are a multitude of other examples of the imprecision of mathematics, such as the mathematician's ability to choose between incompatible axioms, and the various different roles which "zero" plays, as evidenced by imaginary numbers.

Now it seems to me that the starting point for an interesting discussion is to note that the Pythagorean theorem is literally false in the world, and perfectly exactly true in idealized math; and from there, to meditate on the nature of mathematical abstraction. How we can literally tell a lie about the world, that the theorem is true, and yet that lie is so valuable and comes to represent or model an idealized form or representation of the world. — fishfry

You keep insisting that the Pythagorean theorem is false in the world, but it is used many times every day, and every time it is used it proves itself. Where's your evidence that it's false? And if you produce competing mathematical principles as your evidence, you are only proving the inexactness of mathematics, not the falsity of that particular theorem..

But if you deny both these premises, one, that the P theorem is false in the world (close though it may be) and perfectly true in idealized math, then there is no conversation to be had. And for what it's worth, your opinions on these two statements are dramatically at odds with the overwhelming majority of informed opinion. — fishfry

Of course I deny those premises. They are both false. But we have different ideas of what constitute truth. I think truth is correspondence with reality, you think truth is some form of idealized exactness. But "idealized exactness" does not even describe mathematics in a true way. How can justify your claim that the Pythagorean theorem has idealized exactness when the square root of two is irrational? What defines an irrational ratio is that it is lacking in perfect exactitude. So both you premises are false. The Pythagorean theorem is not false in the real world, it gives us the right angle every single time, and there is no perfection to its truth in idealized math, because it gives us irrational ratios. See both your premises need to be rejected.

The fact that Moby Dick changed the name of the ship from the Essex to the Pequod, changed the names of the characters, and invented episodes and stories that never really happened, does not detract from the novel in the least. A representation or abstraction stands alone. — fishfry

You still do not seem to have any respect for the difference between a creative work of the imagination, and a representation. A "representation" cannot stand alone, because it necessarily represents something, that's why it's called a representation. If it stood alone it could not be called a representation. An imaginary fiction, like Moby Dick, stands alone as a creative piece of art, not meant to represent anything. It is not a representation.

This problem appears to deeply affect the way that you think about truth. You seem to think that a representation can be true without any rules of correspondence, simply by standing alone. Of course this is not true because it is the rules of correspondence which provide for the truth or falsity of any representation. Consider your map analogy, the key, or legend, tells you what the symbols stand for, allowing for the truth or falsity of the map.

Your map analogy fails because of your desire to extend it into the artistic world of fictitious creations which are not meant to represent anything, and therefore not similar to maps. Here, we have works of art, created by imaginative power, which are enjoyed for aesthetic beauty, This is where you place your "idealized exactness" striven for by mathematicians in their acts of imaginative creation, as a high form of beauty. If mathematicians could obtain to that highest level, ideal exactness, they might create the highest form of beauty, "truth". However, idealized exactness is not a part of the real world, just like "no inherent order" is not a part of the real world, nor is infinity part of the world, while mathematicians and mathematics are parts of the real world. So these beautiful works of art produced by the mathematicians, which have great aesthetic beauty, but do not represent anything, are simply beautiful works of art, which, as any other part of the world, contain imperfections.

Now, you present these works of art to me as "representations", and claim that there is truth within them, as "idealized exactness". However, they very clearly do not obtain to that level of "ideal exactness" so if ideal exactness is supposed to be truth for you, then these works of the mathematicians are obviously not true.

It obtains it every day of the week. It obtained idealized exactness in the time of Euclid. — fishfry

I think Euclid's parallel postulate is somewhat questionable in some modern geometry. You've just given me more proof that idealized exactness has not been obtained. If it had been obtained, there would be no need for new forms of geometry which cast doubt on the old. Geometry works in the field, in real world situations it gives us truth, but it clearly does not give us the ideal (absolutely perfect) exactness, which you seem to believe it does.

There are no dimensionless points, lines made up of points, and planes made up of lines in the world. — fishfry

Hmm, an infinity of dimensionless points could not produce a line with dimension, more evidence that ideal exactness has not been obtained.

The mathematical theory of infinity is a classic example of an abstraction that has nothing at all to do with the real world. And yet, without the mathematical theory of infinity we can't get calculus off the ground, and then there's no physics, no biology, no probability theory, no economics. So THAT is the start of an interesting philosophical conversation. How does such a massive fiction as transfinite set theory turn out to be so darn useful in the physical sciences? Where's Eugene Wigner now that we need him? — fishfry

I had no doubt that you'd have good things to say about infinity in mathematics, but you didn't address the point. The use of infinity in mathematics is clear evidence that mathematics does not not consist of idealized exactness. And now that you mention it, calculus itself is based in principles of allowing less than perfect exactness, with notions like infinitesimals.

Is this a reference to what you've been trying to talk to me about from time to time? Universals, and how they bear on mathematical abstraction? What does it mean, exactly? After all I frequently point out to you that mathematical ontology posits the existence of certain abstract entities, and this is exactly what you deny. If I understood this point about universals better (or at all, actually) I'd better understand where you're coming from. — fishfry

Yes, well maybe we'll continue this discussion for a few more years.

This was before you let anyone know that the inherent order was noumenal and invisible, which is right around the time I believe you changed your position. You started from this position: — Luke

I didn't change my position. We've been through this already. You misunderstood my use of words. I went back and explained how the position was consistent, but the choice of words was difficult.

That is, you started out telling us that the actual/inherent order can be perceived with the senses and apprehended, then you changed your position to say that the inherent order cannot be perceived with the senses or apprehended, and now you're saying that the inherent order is invisible but it can (again) be perceived with the senses. At least, that's your latest position. — Luke

This is false, I never said inherent order is apprehended. I've remained consistent and I've clarified this already.

If inherent order is not a type of order, then I don't understand what you have been arguing about regarding mathematical order. Why did you previously allow for other types of order, such as best-to-worst? — Luke

If you recall fishfry introduced "inherent order" by claiming that a set has no inherent order. I haven't been using "mathematical order" so I don't even know what you're talking about here. Near the beginning of the thread there was no consensus between the participants in the thread as to what "order" referred to. I developed the distinction between inherent order, and the order created by the mind as the thread moved on.

You previously spoke of "perceive" and "apprehend" as opposing concepts, but now you consider them synonymous? For a long stretch of the discussion, you repeated in various forms that we perceive with the senses, as distinct from apprehending with the mind: — Luke

OK, so I should have used "apprehend" then, and "perceive" was not a good option. As I said the choice of words is difficult, that is the nature of ontology. Just one little mistake after weeks or months of trying to explain the same thing to you over and over again, in as many different ways as possible, day after day, I think that's pretty good. You know, trying to explain the same thing in many different ways, so that a person who is having trouble understanding might have a better chance to understand, requires saying the same thing with different words. The appearance of contradiction is inevitable, to the person who refuses to look beyond the appearance, and try to understand what the other person is trying to say.

Your response to my last post makes it overwhelmingly clear that you are trying to see contradiction in my words, and not trying to understand. What a surprise!

Meta, I'm going to withdraw from this phase of our ongoing conversation. Perhaps we'll pick it up at some time in the future. If you can't agree that real world measurement is necessarily imprecise and that mathematical abstraction deals in idealized exactness, we are not using words the same way and there is no conversation to be had. I don't think you would be able to cite another thinker anywhere ever who would claim that physical measurement is exact. That's just factually wrong. — fishfry

I did not claim that physical measurement is exact. We agree that real world measurement is necessarily imprecise. Where I disagreed is with your claim that mathematics has obtained ideal exactness. That is what is factually wrong. Some mathematicians might strive for such perfection, and I would not deny that, but they have not obtained it, for the reasons I described.

Principally, mathematics has a relationship of dependency on physical world measurements which I described. This has ensured that the imprecision of physical world measurements has been accepted into the principles of mathematics. The lofty goal of idealized exactness has always been, and will continue to be, compromised by the need for principles to practise physical measurement, where idealized exactness is not a requirement. Therefore mathematics will never obtain idealized exactness. Look at the role of infinity in modern mathematics for a clear example of straying from that goal of idealized exactness.

Right. Sorry for assuming that we're talking about humans. Once we meet aliens or once we evolve to the point where we classify as a different species then yes, we may see more. — khaled

As I said, knowledge is a cumulative thing. Do you not agree that human beings have knowledge within themselves, instinctual knowledge, which was acquired by earlier life forms? If so, then you ought not define "what can and cannot be known" by the limitations of the human life form.

It is justified by definition. You have access to the reason in your mind. You don't have access to "the reason that orders the world". — khaled

This is completely untrue. Human beings communicate. Through communication we have access to what is in the minds of others. And we only have access to the minds of others through the medium which is the physical world. Therefore we must have access to the physical world. You can deny that this is "access", but what's the point to restricting the use of "access" in this way? You might as well say that we don't have access to anything and we know nothing. What good is such a claim?

Any theory about "the reason that orders the world" is just that, a theory. As long as it accounts for own reasoning and perceptions the only thing separating it from any other theory is Occam's razor. — khaled

So, what's wrong with having theories? Remember, you claimed that talking about "the reason that orders the world" is pointless. Are you now claiming that theories, in general, are useless? That's not true, theories are very useful.

If you do believe in evolution then you ought to believe that it is more likely than not that our reasoning and perceptions are incomplete. Not only is this supported by experimental evidence (Hoffman) but also we can easily find scenarios where there are things we cannot detect that affect us, such as UV light. — khaled

I'm sorry Khaled, but I cannot see your reasoning. You are claiming that because our reasoning and perceptions are incomplete, we ought not make any effort toward completion. How is such a defeatism ('because I don't have it I ought not try to get it') the approach of a rational being?

That you don't understand that all physical measurement is approximate, and that math deals in idealized exactness that does not correlate or hold true in the real world, is an issue I would have no patience to argue with you. You are simply wrong. Physical measurements are limited by the imprecision of our instruments. This is not up for debate. But I do see a relation between your misunderstanding of this point, and your general failure to comprehend mathematical equality. — fishfry

The fact that you believe that mathematics deals with "idealized exactness", is the real problem. Look at the role of things like irrational numbers and infinities in conventional mathematics, these are very clear evidence that the dream of "idealized exactness" for mathematics is just that, a dream, and not reality at all, it's an illusion only. Idealized exactness never has been there, and probably never will be there.

You seem to deny this brute fact concerning mathematics, to insist on a separation between real world measurement (deficient in exactness) and ideal mathematics (consisting of perfect exactitude). You hide behind this denial, to completely ignore the reality that the principles of mathematics have been created from the acts of, and for the purpose of, real world measurements.

These are two facts you need to recognize, 1) Mathematical principles have been derived from acts of measurement, and 2) Mathematical principles are created for the purpose of measurement. Since this separation which you espouse cannot be accomplished, due to the fact that the principles of mathematics have been derived from the practise of measurement (1), as I explained with the example of the Pythagorean theorem, you ought to dismiss that intent to separate, altogether. And, because measurement is the purpose of mathematics in its practise (2), it is itself an instrument of measurement. So your observations that physical measurements are limited by "the imprecision of our instruments" ought to inspire you to a recognition of the imprecision of our mathematics.

Inherent order is only one type of order (you also allow for other types such as best-to-worst). How is it that we do not perceive order with the senses in general, but that we do perceive inherent order with the senses specifically? — Luke

I can't answer the how, but I have answered the why. The two types of order are completely distinct and different.

It was not until recently that you began arguing that we do perceive inherent order with the senses and can "see" or otherwise "sense" invisible physical entities such as molecules, ultraviolet light, and the inherent order. — Luke

Go way back, to when I said "see" the inherent order in the dots on the plain in the diagram.

You will note I maintain the distinction here between order and inherent order. You must have been aware of this distinction in your own response when you contradicted your latest argument and affirmed that: "1) We do not perceive order with the senses". It is therefore a complete fabrication to attribute your own contradiction to my misunderstanding or lack of awareness of the distinction between order and inherent order. — Luke

Right, that's a good quote, showing context. I think I generally indicated inherent order with the word "inherent", or "inheres within", indicating order within the object itself, (noumenal if that helps). If I just said "order", I likely was referring to the type of order created within the mind.

You need to recognize the complete separation between what is referred to with "inherent order" and what is referred to with "order". Inherent order, as inhering within the object, is not a type of order, as created by the mind, like the description indicates, this is impossible. The complete separation is required by their contradictory natures. However, there may be similarities by which we could place both, order and inherent order, into one category, but we haven't approached that yet.

In the quoted passage you seem to be looking at what is referred to by "inherent order", as a type of what is referred to as "order". This would constitute a misunderstanding, they are completely distinct and one is not a type of the other.

In other words, you explicitly state here that we do not sense the inherent order specifically. — Luke

Sorry, that was a mistaken statement, instead of "sense" I should have used a better expression, like "perceive" or "apprehend". I was flustered by your ridiculous claim that I had earlier implied that sense was not involved at all. This is the complete context:

Of course sense perception is involved! Where have you been? We've been talking about seeing things and inferring an order. My point was that we do not sense the order which inheres within the thing, we produce an order in the mind. I never said anything ridiculous like we do not use the senses to see the thing, when we produce a representation of order for the thing. — Metaphysician Undercover

I should have said "my point was that we do not receive, from the senses into the mind (apprehend), the order which inheres within the thing, we produce an order within the mind". This would allow clearly that the inherent order is present to the senses (is that a better way to say it?), as I had been describing. The intent was to establish the complete separation between the order constructed, and the order inherent in the object, described above. To clarify, the inherent order is present to the senses, but not present to the mind, when the mind produces a representation. "Present to the senses" I have been arguing qualifies as being sensed, but in the quoted passage I mistakenly said that this is not a case of being sensed

Again, I apologize, that was a sloppy post. I was a little rushed. and extremely put off by your claim that I was saying sense was not at all involved in the act of showing, so my reply was a reflex, consisting of a poorly chosen word, rather than clearly thought out. If you understand what I have presented in this post, you'll see that the senses are the medium which separate the order produced in the mind, from the inherent order which exists within the object. And this is why the order produced by the mind is completely distinct from the order which inheres within the object, though it is very true that the senses, and sensation have a relation to both of these distinct things.

In this particular case, there is no direction towards the answer. Rather, every direction is as good as any other. — khaled

I see no reason to agree with you. And I did read your statements. You stated a personal opinion; "there is no use in talking about 'the reason that orders the world'". And you made a further statement about your personal resignation; "I don't have access to 'the reason that orders the world' so I don't care about it."

Nowhere have I seen the claim that a human being has no direct access to the independent ordering of the world justified. Plato argued that the philosopher does have access to it through the means of apprehending "the good". This is the point of the cave allegory. And, it is the described responsibility of the philosopher to turn around, and go back to the others to assist them in their enlightenment.

So the statement, "no human being can have access to the reason that orders the world" is absolutely unsupported, as far as I can tell, yet the statement "it is possible for a human being to access the reason that orders the world" is flimsily supported. Flimsy support out weighs no support by an infinitely large magnitude, so I choose the flimsy support for my opinion; while your opinion ought to be banished from the philosophical mind as that held by those who are satisfied to be trapped in the cave of illusion for all eternity.

And this is true of everyone. It's not about the limitations of the individual but the limitations of being human. — khaled

It appears like you do not believe in evolution then. If these limitations are truly the limitations of being human, as you believe, they are still not the limitations of being alive.

Only a fool would want to know something they know they can’t know. — khaled

Even if you know that you will never know the answer to a specific question, you can proceed in the direction toward finding the answer, and potentially help others, who are not so helpless as you, to find that answer. That the answer will not be found by you does not mean that it will not be found, so this ought not prevent you from working toward finding it. There's an interesting aspect of knowledge, it's cumulative, and not restricted by the limitations of the individual.

You have stated both that we do and do not perceive (i.e. see) order with the senses. This is not a failing on my part. — Luke

It suddenly occurred to me today, why you are having so much trouble understanding. It's not so much the ambiguous use of "see" which is throwing you off, but I now see that you are not respecting the distinction between the two completely different referents for "order", which I thoroughly explained to you.

In the case of "inherent order" the order is within the thing sensed. It is sensed (in the manner I described), but not apprehended by the mind due to the deficient capacity of the sensing being. I've also used "order" to refer to orders created by the mind, within the mind, sometimes intended to represent the inherent order, as a model does. This order is apprehended by the mind, being created within the mind, but it is in no way sensed, because it is created within the mind and is therefore not part of the thing sensed.

You can see that in one context the referent of the word "order" is sensed but not apprehended by the mind, while in the other context the referent order is apprehended by the mind, but not sensed. Without adhering to the particulars of the context, and maintaining the differentiation between the two very distinct things referred to with the word "order", it would appear like "order" is used in a contradictory way; both sensed and not sensed, apprehended by the mind and not apprehended by the mind This is what you have been doing, taking my statements concerning "order" out of their context, failing to respect the described difference between the two distinct types of order, and claiming that I have contradicted myself

This is an important point for you to recognize. It's not in the real world, (where truth and falsity is determined by correspondence), where the Pythagorean theorem is false, it's tried and tested in the real world, and very true. It's only in you imaginary world, of so-called pure abstraction, where the only test for truth is logical consistency, or coherency, that it appears to be false. All this indicates is that your imaginary world is not to be trusted, as it does not give us coherency between even the most simple mathematical principles. On the other hand the Pythagorean theorem alone, can be trusted, because it does give us the right angle. So the quest for logical consistency, or coherency, is not a quest for truth..

It's not complicated; you contradicted yourself. I think you see that now, which is why you have given up. — Luke

So, your failure to recognize the distinct ways that I used "see", which I explained over and over again, constitutes contradiction on my part. OK, I must have contradicted myself then, according to the way that you use "contradicted", therefore I give up.

As such, I don't care about "the reason that orders the world". Maybe it is the same as the reason in my mind, or maybe the reason in my mind is just an "evolutionary shortcut", a hack, a parody of the real thing optimized for survival. Either way, I don't have access to "the reason that orders the world" so I don't care about it. — khaled

The philosophical mind has the desire to know. So such statements are very unphilosophical.

That is the point that I was trying to make. I think it calls into question Kenosha Kid’s view that there is ‘one objective reality’ which all interpretations try to approximate or interpret. I agree that reality may be one, but that unity must necessarily transcend subject-object dualism, meaning that it’s out of scope for naturalism as such. — Wayfarer

What I find is the biggest problem with the materialist view is that it inevitably leads to determinism. The determinist perspective is "that there is 'one objective reality'", and this objective reality encompasses all of the past and future, in an eternalist sort of way.

This perspective completely ignores the very real, important and significant, difference between past and future, which we know very well through our experience. Ignoring this difference, and the fact that the undetermined nature of the future gives us the capacity for freely willed actions, while the fixed nature of the past renders us helpless in any desire to change what has already occurred, presents us with a very skewed conception of "one objective reality". The difficulty in understanding "objective reality" is the need to know how the undetermined becomes determined at the moment of the present.

Say, did you know that the Pythagorean theorem is false in the real world? — fishfry

No, you've got that wrong. The Pythagorean theorem is true in the real world, because it works well and has been proven. Where it is false is in your imaginary world. It works very well for me. I use it regularly. That you think my right angle is a wrong angle is a bit of a problem though. We know induction is not perfect, it just describes what is experienced or practised. (Am I spelling practise wrong?) That the Pythagorean theorem is false in your imaginary world which you call "abstraction", is just more evidence that what you call "abstraction" is not abstraction at all, but fiction.

Do you think that we can see infrared and ultraviolet light just because it exists in the world? — Luke

Yes, I think the eyes most likely do sense infrared and ultraviolet in some way: https://www.sciencedaily.com/releases/2014/12/141201161116.htm

I have not misunderstood. — Luke

Yes, you are very clearly misunderstanding, and I'm tired of trying to explain. You don't seem to have a mind which is inclined toward trying to understand complicated ontological problems, instead thinking that everything can be described simply by is or is not, because otherwise would be contradiction.

No middle 'e' in judgment. I can't take anyone seriously who can't spell. — fishfry

What kind of petty bullshit is this? Fuck you fishfry, I thought we were trying to be civil with one another. I see you've gone off the deep end already, and it's only Monday.

The point is that the process of abstraction necessarily, by its very nature, must omit many important aspects of the thing it's intended to model. You prefer not to engage with this point. — fishfry

I've engage with this point, explaining that I think it is wrong. If it's an important aspect, an essential feature, then if the abstraction processes "misses" it, the abstraction is wrong. If it is something which can be left out of the abstraction, it is in Aristotelian terms "accidental" or "an accident", and is not an important aspect. Abstraction separates the important from the unimportant, and if it omits important aspects it is faulty.

That's fantastic. The Pythagorean theorem is a beautiful, gorgeous, striking, brilliant, dazzling, elegant, sumptuous, and opulent example of an abstraction that is not based on ANYTHING in the real world and that has NO INDUCTIVE CORRELATE WHATSOEVER. I am thrilled that you brought up such an example that so thoroughly refutes your own point.

The Pythagorean theorem posits and contemplates a purely abstract, hypothetical, mathematical right triangle such that the sum of the squares on the legs is equal to the square on the hypotenuse. No such right triangle has ever, nor will ever, exist in the real world. — fishfry

That's amazingly wrong, to think that the Pythagorean theorem is not based in anything from the real world. It's based in the method used to produced parallel lines for marking out plots of land. Check into the history of "the right angle", and you will learn this. Clearly this is something in the real world.

Your own example falsifies this. I can never confirm the Pythagorean theorem in by observation of the world. I can only prove it deductively and never inductively. — fishfry

Huh? Construction workers prove the Pythagorean theorem in the real world, many times every day. Make a 3,4,5 triangle, tt never fails to produce the desired angle. How is this not proof? Try it yourself. Mark two points to produce a line. Use the Pythagorean theorem to make a right angle at each of the two points, and make two new points on those right angles, at equal distances from the original points. Measure the distance between the two new points, and you will see that it is the same as the distance between the two original points, and you have proven the Pythagorean theorem because you have used it to produce right angles, and have proven that the angles produced are in fact right angles by producing two more equivalent angles.

This is the complete opposite of induction. — fishfry

What you seem to not grasp, is that people were producing right angles long before the Pythagorean theorem was formalized. The Pythagorean theorem came into existence as a formalized description of what those people were doing. Therefore it is a generalization of what people were doing when they succeeded in producing the right angle, so it is an inductive conclusion. Try and see if you can apprehend pi as an inductive conclusion? It is a generalization, what all circles have in common, just like the Pythagorean theorem is a generalization, what all instances of "the right angle" have in common. If you produce an angle which is not consistent with what the Pythagorean theorem says, you have not produced the right angle.

But getting back to the larger point: A map is a formalization of certain aspects of reality that necessarily falsifies many other things. Just as a set is a formalization of the idea of a collection, that necessarily leaves out many other things. I have a bag of groceries. I formalize it as a set. The set doesn't have order, the grocery bag does. The set doesn't have milk, eggs, bowling balls, and rutabagas, the grocery bag does. — fishfry

As explained above, if an abstraction, or formalization, leaves out important aspects, then it is faulty. And if you insist on using the map analogy after I've explained why it is unacceptable, I will insist that if a map leaves out important things, then it is obviously a faulty map.

One reason why the map analogy is faulty, is because the map maker can decide, based on the purpose for which the map is being made, which aspects are important, and which are not. In the case of abstraction, formalizing, or generalizing, we have no choice but to adhere to the facts of reality, or else the formalizations will be incorrect.

I think what you are saying is that an abstraction faithfully represents some aspects of the thing, and leaves out others. — fishfry

An abstraction is a generalization. It does not represent "the thing" in any way, nor does it represent aspects of the thing. It represents a multitude of things, by creating a category or type, by which we can classify things. Again, another reason why the map analogy is misleading. It appears to make you think that an abstraction represents a thing, like a map does. That is incorrect, the abstraction is a generalization, a universal, which represents a multitude of things.

The essence of your argument is that "inherent order" is so tightly bound to the thing, that it can not be separated by an abstraction. I believe that's the core of our difference. Do I have that right? — fishfry

This is not really a good representation of my argument, because you don't seem to understand what abstraction is in anyway near to the way that I do. It's a good start anyway. But let me put it in another way. Let's suppose a category, or type called "thing". The abstraction, generalization, or formalization, would be a statement of definition, what it means to be a thing. This would be a statement as to what all things have in common, which makes it correct to call each of them a "thing". To be an acceptable definition, would be to be a good inductive conclusion. My argument is that the good inductive conclusion is that all things have inherent order therefore it would be a bad formalization, generalization, or abstraction, to posit a thing without inherent order because this is contrary to good inductive reasoning. Furthermore, I've argued that since such a principle, is not based in any inductive reasoning, it cannot truthfully be called an abstraction, generalization, or formalization, it is simply an imaginary fiction.

For purposes of the conversation, yes, I'll stipulate that. So what? It's how mathematical abstraction works. Just like the Pythagorean theorem does the same thing. — fishfry

As I've explained, it is false to call this an abstraction. To make up a purely imaginary, fictitious principle, is not abstraction. And, the Pythagorean theorem is not at all like this. Creating the Pythagorean theorem was a matter of taking what people had been doing on the ground, producing the right angle and parallel lines, and using inductive reasoning to determine what all these cases of producing the right angle had in common. Therefore it is not a purely imaginary and fictitious principle, it is a truthful inductive statement about what all instances of the producing the right angle have in common.

Well now you're just arguing about my semantics. If I don't use the word generalization (which by the way I have not -- please note); nor have I used the phrase inductive conclusion. I have not used those phrases, you are putting words in my mouth. I said mathematical models are formalized abstractions, or formal abstractions. Or formal representations. That's what they are. The need not and generally don't conform to the particulars of the thing they are intended to represent. Just as an idealized right triangle satisfies the Pythagorean theorem, and no actual triangle ever has or ever will. Oh what a great example, I wish I had thought of it. Thank you! — fishfry

Remember, you claimed a difference between a formalization, and an inductive conclusion. I did not accept such a difference, and asked you to validate this claim. You have not yet done so, but continue to speak as if your proposed distinction is a true distinction, while I have demonstrated that it is not. Therefore I suggest that you give up, as false, this claim to a difference.

You say that like it's a bad thing! Ok, imaginary fiction then. But a useful one! — fishfry

Yes, fictions are useful. The principal use of these is to mislead and deceive. A secondary use is entertainment, but this requires consent to the fact that what is presented is fiction.

So if you have a problem, it's your problem and not mine, and not math's. — fishfry

Of course, deception is a problem for the one being deceived, not the deceiver. Or maybe I'm just not entertained by your proposed entertainment. Again, still my problem, but perhaps you have made a poor presentation.

Well a set isn't actually a collection. A set is an undefined term whose meaning is derived from the way it behaves under a given axiom system. And there is more than one axiom system. So set is a very fuzzy term. Of course sets are inspired by collections, but sets are not collections. Only in high school math are sets collections. In actual math, sets are no longer collections, and it's not clear what sets are. Many mathematicians have expressed the idea that sets are not a coherent idea. It would be great to have a more sophisticated discussion of this point. I'm not even disagreeing with you about this. Sets are very murky. — fishfry

It was you who called a set a collection, and referred to some sort of mystical process of collecting, which allows for your proposed "no inherent order".

So therefore perhaps I should stop wasting my time trying to argue that math is inspired by reality, or that math is an abstraction of reality, and simply concede your point that it's utter fiction, and put the onus on you to deal with that. I could in fact argue the abstraction and inspired-by route, but you bog me down in semantics when I do that and it's tedious. — fishfry

I dealt with this. Most math is not fiction, as evident in the example of the Pythagorean theorem. I differentiated the types of mathematical principles which are imaginary fictions though, things like "no inherent order", and "infinity".

If I see 100 bowling balls fall down, "bowling balls always fall down" is an inductive conclusion. But F = ma and the law of Newtonian gravity are mathematical models from which you can derive the fact that bowling balls fall down. It's a physical law, meaning that if you assume it, you can explain (within the limits of observational technology) the thing you observe. — fishfry

The law of gravity is the more general statement, saying all things with mass will fall down. The statement that bowling balls will fall down is more specific. Inductive reasoning is to produce a general statement from empirical observations of particular instances. So, the law of gravity as a general statement, is an inductive conclusion. And, bowling balls may or may not have been observed in producing that inductive law, but the law extends to cover things not observed, due to the nature of inductive reasoning, and the generality of what is produced. This is why inductive reasoning gives us predictive capacity. That mathematics is used to enhance the predictive capacity of inductive reasoning is not relevant to this point.

But this is not an important point in the overall discussion. — fishfry

It is important, because induction, by its nature, requires observation of particular instances. And you seem to be arguing that there is a type of abstraction, pure abstraction, which does not require any inductive principles. So it is important that you understand exactly what induction is, and how it brings principles derived from observations of particular instances, into abstract formulae. Do you see that the Pythagorean theorem for example, as something produced from practice, is derived from induction?

Ok. I don't think the definition of induction versus a formal model is super important here. But "bowling balls always fall down" is simply a generalization of an inductive observation, whereas the law of gravity lets you derive the fact that bowling balls fall down; and that in fact on the Moon, they'd weigh less. The latter is not evident from "bowling balls always fall down," but it is evident from the equation for gravitational force. — fishfry

It is the inductive conclusion, which allows for the derivation, the prediction, which you refer to. As it is a general statement, it can be applied to things not yet observed. It is not the mathematics which provides the capacity for prediction. mathematics enhances the capacity

This point is not central to the main point, which is that models must necessarily omit key aspects of the thing being modeled. — fishfry

The central point is the difference between the inductive conclusion, which states something general, and the modeling of a "thing", which is a particular instance. At this point, we take the generalization, and apply it to the more specific. It must be determined how well the generalization is suited, or applicable to the situation. This requires a judgement of the thing, according to some criteria.

Ok fine, then order is physical and the mathematical theory of order is an abstraction or model that necessarily misses many important real-world aspects of order yet still allows us to get some insight. That's the point of abstraction, which I already beat to death in my last post. — fishfry

I think your description of abstraction as missing things, is a bit off the mark. What abstraction must do is derive what is essential (what is true in all cases of the named type), dismissing what is accidental (what may or may not be true of the thing). Now, if order is essential to being a thing, then we cannot abstract the order out of the thing, to have a thing without order, because it would no longer be a thing.

I'm explaining to you that whatever your concept of physical order is, mathematical order is an abstraction of it, which is necessarily a lie by virtue of being an abstraction or model, yet has value just as a map is not the territory yet lets us figure out how to get from here to there. — fishfry

This is not true in a number of ways. First, good abstractions, inductive conclusions, or generalizations, do not lie because they stipulate what is essential to the named type. They speak the truth because every instance of that named type will have the determined property.

Second, your proposed "mathematical order" is not an abstraction, inductive conclusion, or generalization. You started with the principle that there is a unity of things with no inherent order. So you have separated yourself from all abstraction, induction, or generalization, to produce a purely imaginary, and fictitious starting point. You cannot claim that the imaginary, and purely fictitious starting point, of "no inherent order" is a generalization, or an inductive conclusion, or in any way an abstraction of the physical order. You are removing what is essential to "order", by claiming "no order", therefore you have no justification in claiming that this is an abstraction of physical order.

Do you recognize the difference between abstracted and imaginary? Imagination has no stipulation for laws of intelligibility, while abstraction does.

I've conceded your point, now that I understand what you mean by inherent order. — fishfry

OK, now lets proceed to look at your imaginary "mathematical order". Do you concede as well, that by removing the necessity of order from your "set", we can no longer look at the set as any type of real thing. Nor is it a generalization, an inductive conclusion, or an abstraction of physical order. It is purely a product of the imagination, "no order", and as such it has no relationship with any real physical order, no bearing, therefore no modeling purposefulness. It ought to be disposed, dismissed, so that we can start with a new premise, a proper inductive conclusion which describes the necessity of order.

It's an abstraction that necessarily includes SOME aspects of the thing being modeled and excluces OTHER aspects. Just as a street map includes the orientation of the roads but ignores the traffic lights. — fishfry

The idea of something with "no inherent order" is not an abstraction, as explained above. It is a product of fantasy, imaginary fiction.

That's right. A map is correct about some aspects of the world and incorrect about others. It's an abstraction. — fishfry

A map is not an abstraction, it is a representation. I see that we need to distinguish between abstraction, which involves the process of induction, producing generalizations, and as different, the art of applying these generalizations toward making representations, models, or maps. Do you see, and accept the difference between these two? We cannot conflate these because they are fundamentally different. The process of abstraction, induction, seeks what is similar in all sorts of different thing, for the sake of producing generalizations. The art of making models, or maps, involves naming the differences between particulars. These are very distinct activities, one looking at similarities, the other at differences, and for this reason abstraction cannot be described as map making.

Maps are imaginary principles and don't formalize anything? Do you see why I think you're trolling? — fishfry

I was referring to the principles of "no inherent order", and "infinity", with the claim that these do not formalize anything. I wasn't talking about maps.

If you would engage with my examples of maps and globes, I would find that helpful. — fishfry

The map analogy is not very useful, for the reason explained above, it doesn't properly account for the nature of inductive principles, abstraction. Generalizations may be employed in map making, but they are not necessarily created for the purpose of making maps. Now the map maker takes the generalizations for granted, and proceeds from there, but must choose one's principles. In making a map, what do you think is better, to start with a true inductive abstraction like "all things have order", or start with a fictitious imaginary principle like "there is something without order"? Wouldn't the latter be extremely counterproductive to the art of map making, because it assumes something which cannot be mapped?

And sets represent aspects of collections, which exist in the world. And they omit "inherent order," which for sake of argument I'll agree collections in the world have. — fishfry

So, for the sake of argument, we can make the inductive conclusion, all collections which exist in the world have an inherent order. This is a valid abstraction, based in empirical observation, and it states that what is essential to, or what is a necessary property of, a collection, is that it has an inherent order. Do you agree then, that if we posit something without inherent order, this cannot be a collection? It doesn't have the essential property of a collection, i.e. order; therefore it is not a collection.

Well that has nothing to do with anything. Maps don't show things that aren't there. The question is, how do you feel when a map omits things that ARE there, like wet lakes and rivers, cars, and the size and scale of the actual territory being modeled. — fishfry

Each map maker, based on the needs of that map maker's intentions, chooses what to include in the map. Abstraction, inductive reasoning, is very distinct from this, because we are forced by the necessities of the world to make generalizations which are consistent with everything. That's what makes them generalizations

Then you don't see it. — Luke

Perhaps, but I disagree. It's a matter of opinion I suppose. You desire to put a restriction on the use of "see", such that we cannot be sensing things which we do not apprehend with the mind. I seem to apprehend a wider usage of "see" than you do, allowing that we sense things which are not apprehended. So in my mind, when one scans the horizon with the eyes, one "sees" all sorts of things which are not "forgotten" when the person looks away, because the person never acknowledged them in the first place, so they didn't even register in the memory to be forgotten, yet the person did see them.

And you claimed earlier that we could not possibly see it, in principle — Luke

No, I think you misunderstood. Perhaps it was the use of "perceive" which is like "apprehend". I said we could not apprehend it with the mind, the mind being deficient. This does not mean that we cannot sense, or "see" it at all. But your limiting of "see", to only that which is apprehended by the mind, instead of allowing (what in my opinion is the reality of the situation) that we are sensing things which are not being apprehended by the mind, not "perceived", is making you think that just because we cannot apprehend it with the mind, therefore we are not sensing it at all.

I know it's a difficult issue and it appears as incoherency, as ontological issues often do, because they are difficult to understand, but I think we need to establish a separation between what is sensed, and the apprehension of it, to account for the differences between how different people apprehend very similar sensations.

Have you rejected your claim that we can see the inherent order? — Luke

No, I think we see it in exactly the way that I explained.

2. How do you reconcile this with your statements that order is not visible? — Luke

I explained that. We see the object. The object exists as an instance of ordered parts, inherent order. Therefore we must be seeing the inherent order even though strictly speaking the order is not visible to the person who is seeing it. The "not visible" property is due to a deficiency in the capacity of the person who is seeing the order.

I used the molecule example. Molecules are not visible to the naked eye. But we see the object, and the object is composed of molecules, therefore we must be seeing the molecules. That the molecules are not visible to the person seeing them is due to a deficiency in that person's capacities.

It's the same principle as when someone is pointing something out to you, and you're looking right at it, so you're definitely seeing it, because it's right there in your field of vision, yet you don't see the particular thing that the person is pointing out. Have you ever looked at stars, and had someone try to point out specific constellations to you? You can be looking right at the stars, and see them all, therefore you are seeing the mentioned constellation, yet you still might not be able see that specific constellation.

See the different senses of "see", and how "visible" might be determined based on the capacity of the observer, or the capacity of the thing to be observed? The inherent order is not visible to us, due to our deficient capacities, yet we do see it, because it exists as what we are seeing. Go figure.

It is the content that is valuable, — Sir2u

So, who's the author?

You didn't get the molecule analogy so I went back to the language one, I believe I used it earlier. Now you claim not to get the language one, but that appeared to me like an intentional misinterpretation. You pretended as if you didn't understand that apprehending language is understanding meaning.

Each is an example of sensing something without apprehending what is being shown by the thing being sensed.

You think it must be "hidden", if we sense something without understanding it, but I think that idea is what's misleading you. It's not at all hidden, the mind is just lacking in the capacity to understand what is being sensed. Thinking it is "hidden" is a feature of your accusative nature. When you can't understand a person you blame the other, instead of introspecting your own capacity. And if you cannot see what is right in front of you, you think it must be "hidden" from you, instead of considering the possibility that your eyes are actually sensing it, but your mind is just not apprehending it.,

You said that we sense a foreign language without apprehending it. — Luke

To apprehend the language being spoken, is to understand the meaning. You work very hard to make understanding difficult for yourself.

Metaphysics is much more valuable than that. It's priceless.

Now you say that we neither sense nor perceive the meaning of a foreign language: — Luke

I don't see the problem. Do you not grasp a difference between hearing people talking, and apprehending the meaning? Meaning as analogous with order, was the example.

Do you have an attention deficit or memory disorder? You seem incapable of maintaining your own position. A moment ago you were talking about "the reality of the situation" that we see the inherent order without apprehending it, and now you've switched back to saying that we can neither see nor apprehend the inherent order. If you think there are two different senses of the word "see" involved here, then define them both. Because one of them seems to refer to what we cannot see, which is not a familiar definition of the word "see". — Luke

You seem to be going through great effort to create problems where there are none. Oh well, it's what I've come to expect from you.

The truth of the assumption that a photon is massless is questionable:
https://www.sciencedirect.com/science/article/pii/S2211379719330943

Can you not hear foreign languages? This is a terrible analogy. This is something which we can perceive but cannot apprehend. Your analogy with molecules is equally bad, since it is something we can apprehend but cannot perceive. It is (or very recently was) your position that we can neither perceive nor apprehend the inherent order. Remember? You said that order is "not visible". — Luke

I don't think the analogies are bad. That there is order inherent within the thing seen is something inferred, just like that there is meaning in the foreign language which is heard, is something inferred, and that there are molecules in the object seen is something inferred. We neither perceive nor apprehend the inherent order but we infer that it is there, just like we infer that there is meaning in the foreign language, and that there are molecules within the thing seen. But we neither perceive nor apprehend the meaning in the foreign language, nor do we perceive or apprehend the actual molecules in the object seen. We apprehend a representation of the molecules, just like we apprehend a representation of the inherent order. And, when we come to understand the language we apprehend a representation of the meaning intended (what is meant) by the author.

There's no contradiction here, I take it? — Luke

I assume there are many different senses to the word "see". The word is used sometimes to refer strictly to what is sensed, and other times to what is apprehended by the mind.

So how can it be seen? — Luke

I really don't know how, it's just the reality of the situation. We sense things without apprehending what it is that is being sensed, as in my example of hearing a foreign language. There is a matter of distinguishing the individual elements, one from another, which the sense organ does not necessarily do, despite sensing the elements together as a composite.

From your side it must seem like you're being tag-teamed by Luke and myself, but I'm not reading his posts. I'm not aware of that half of the conversation. — fishfry

Don't worry about that, the conversations are completely different. Luke is on a completely different plane.

It's an abstraction intended to formalize an aspect of nature. If you think it's a generalization of something, you might be missing the point. Hard to say. — fishfry

I don't see the distinction you're trying to make here, between an inductive conclusion, and "an abstraction intended to formalize an aspect of nature". What do you mean by "formalize" other than to state an inductive conclusion.

I see the majority of definitions as inductive conclusions. Either they are like the dictionary, giving us a formalization (inductive conclusion) of how the word is commonly used, or they are intended to say something inductive (state a formalization) about some aspect of nature.

I think you are missing the point. If I drop a hundred bowling balls and I say, "Bowling balls fall down. That's a law of nature," then THAT is an inductive conclusion.

But if you see 100 bowling balls fall down and you go, F = ma, that is an abstraction and a mathematical formalization. You don't seem to have a firm grasp on this. Do you follow my point here? — fishfry

I think it's you who is missing the point. I do not have a firm grasp on the distinction you are trying to make, because there are no principles, or evidence to back up your claim of a difference between these two.

F=ma says something about a much broader array of things than just bowling balls. So one could not produce that generalization just from watching bowling balls, you'd have to have some information telling you that other things behave in a similar way to bowling balls. Mass is a property assigned to all things, and the statement "f=ma" indicates that a force is required to move mass. How can you not see this as an inductive conclusion? It's not just a principle dreamed up with no empirical evidence. In all cases where an object starts to move, a force is required to cause that motion. It might have been the case that "force" was a word created, thought up, or taken from some other context and handed that position, as being what is required to produce motion (acceleration), but this does not change the inductive nature of the statement.

Your notion of induction is wrong. "All bowling balls fall down," is an inductive conclusion. F = ma is a formalization. — fishfry

As I said, I really do not understand how a "formalization" as used here, is anything other than an inductive conclusion. So I do not understand how you think my notion of induction is wrong. Perhaps you should look into what inductive reasoning is, and explain to me how you think a "formalization" is something different. I think induction is usually defined as the reasoning process whereby general principles are derived from our experiences of circumstances which are particular.

But there are non-physical parts of the world that we are interested in, such as quantity, order, shape, symmetry, and so forth. Those are the non-physical parts of the world that are formalized by math. — fishfry

That such things are non-physical is what I dispute. How could there be a quantity which is not physical? "Quantity" implies an amount of something, and if that something were not physical it would be nothing. "Order" implies something which is ordered, and if there was no physical things which are ordered, there would be no order. And so on, for your other terms. It makes no sense to say that properties which only exist as properties of physical things are themselves non-physical.

Things in the world have order, and we have a mathematical theory of order that seeks to formalize the idea. — fishfry

When you say "formalize" here, do you mean to express in a formal manner, to state in formal terms? If it is physical things in the world which have order, and mathematics seeks to express this order in a formal way, then how is this not making a generalization about the order which exists in the phyiscal world, i.e. making an inductive conclusion?

On the other hand, of course there are non-physical, non-part-of-the-world abstractions too. Chess, for instance. Chess is a formal game, it's its own little world, it has a self-consistent set of rules that correspond to nothing at all in the real world. Knights don't "really" move that way. Right? Say you agree. How can anyone possibly disagree? — fishfry

How can I agree with this? Chess is a game of physical pieces, and a physical board, with rules as to how one may move those physical pieces, and the results of the movements. The physical board and pieces are not "nothing at all in the real world", they are all part of the world.

What's with your motive here? Why do you insist on taking rules like those of mathematics, which clearly refer to parts of the real world, and remove them from that context, insisting that they do not refer to any part of the real world? Your analogy clearly does not work for you. The chess game is obviously a part of the world and so its rules refer to a part of the real world, just like quantity, order, shape, and symmetry are all parts of the real world, and so the rules (or formalities) of these also refer to parts of the real world.

But you are the one that insists that physical collections of things have an inherent order. And that's what the mathematical concept of order is intended to formalize. Things in the world have order, and we have a mathematical theory of order that seeks to formalize the idea.

Right? When mathematicians formalize numbers, they're abstracting and formalizing familiar counting and ordering. When they create abstract sets, they are formalizing the commonplace idea of collections. A bag of groceries becomes, in the formalization, a set of groceries. Surely you can see that. Why would you claim math is not based on everyday, common-sense notions of the world? — fishfry

Yes, I agree with this here. Now the issue is how can you say that there is a collection of things which has no inherent order. If things in the world have order, and mathematicians seek to formalize that order, then where does the idea of "no inherent order" come from? That notion of "no inherent order" is obviously not derived from any instance of order, and if mathematicians are seeking to formalize the idea of order, the idea of "no order" has no place here. It is in no way a part of the order which things have, and therefore ought not enter into the formalized idea of "order".

Like what? Can you name some of these? Sets correspond to collections. — fishfry

Have you lost track of our conversation? The idea of "no inherent order" is what we are talking about, and this is what I say does not correspond with our observations of the world. We observe order everywhere in the world. Sets do not correspond to collections, because any collection has an inherent order, existing as the group of particular things which it is, in that particular way, therefore having that order, yet as a "set" you claim to remove that order.

But again I ask you, exactly WHICH mathematical ideas are not based on or inspired by the natural world? You must have something in mind, but I am not sure what. — fishfry

I'll repeat. It's what we've been discussing, your idea of "a set", as a collection of things with no inherent order. Something having no inherent order is not based in, nor inspired by the real world, we don't see this anywhere in the world. We can also look at the idea of the infinite. It is not inspired by anything in the natural world. It is derived completely from the imagination.

That's a useful mindset to have, so that we don't allow our everyday intuitions interfere with our understanding of the formalism. But of course historically, math is inspired by the real world. Even though the formalisms can indeed get way out there. — fishfry

Let's try this. We'll say that a "formalism" relates to the real world in one way or another, and then we can avoid the issue of whether it is an inductive conclusion. We'll just say that it relates to the world. Now, can we make a category of ideas which do not relate to the real world? Then can we place things like "infinity", and "no order" into this category of ideas? But rules about quantifying things, and rules about chess games do relate to the real world, as formalisms.

Can you see that these ideas are not formalisms, nor formalizations in any way? Because they are purely imaginary, and not grounded in any real aspects of the natural world, there is no real principles whereby we can say that they are true or false, correct or incorrect. They cannot be classed as formalizations because they do not formalize anything, they are just whimsical imaginary principles. To use your game analogy, they are rules for a game which does not exist. People can just make up rules, and claim these are the rules to X game, but there is no such thing as X game, just a hodgepodge of rules which some people might choose to follow sometimes, and not follow other times, because they are not ever really playing game X, just choosing from a vast array of rules which people have put out there. Therefore there is nothing formal, so we cannot call these ideas formalisms or formalizations.

The truth is in the thing. — fishfry

I disagree with your notion of truth. I think truth is correspondence, therefore not in the thing itself, but attributable to the accuracy of the representation of the thing. Identity is in the thing, as per the law of identity, but "true" and "false" refer to what we say about the thing.

If I want to study the planets I put little circles on paper and draw arrows representing their motion. The truth is in the planets, not the circles and arrows. I hope you can see this and I don't know why you act like you can't. — fishfry

I think this is a completely unreasonable representation of "truth", one which in no way represents how the term is commonly used. We say that a proposition is true or false, and that is a judgement we pass on the interpreted meaning of the proposition. We never say that truth is within the thing we are talking about, we say that it is a property of the talk. or a relation between the talk and the thing.

First, sets are intended to model our everyday notion of a collection. And in order to do a nice formalization, we like to separate ideas. So we have orderless sets, then we add in order, then we add in other stuff. If I want to put up a building, you can't complain that a brick doesn't include a staircase. First we use the bricks to build the house, then we put in the staircase. It's a process of layering. — fishfry

Take a look at your example. The bricks are never "orderless". They come from the factory on skids, very well ordered. Your idea of "orderless sets" in no way models our everyday notion of a collection.

Our formalization begins with pure sets. It's just how this particular formalization works. — fishfry

The point is that orderlessness is in no way a formalization. A formalization is fundamentally, and essentially, a structure of order. Therefore you cannot start with a formalization of "no order". This is self-contradictory. As I proposed above, the idea of orderlessness, just like the idea of infinite, must be removed from the category of formalizations because it can in no way be something formal. To make it something formal is to introduce contradiction into your formalism.

If I represent a planet as a circle, you don't complain that my circle doesn't have rocks and and atmosphere and little green men. I'll add those in later. — fishfry

What I'm complaining about is your attempt to represent nothing, and say that it is something. You have an idea, "no inherent order", which represents nothing real, It's not a planet, a star, or any part of the universe, it's fundamentally not real. Then you say that this nothing exists as something, a set. So this nothing idea "no inherent order" as a set. Now you have represented nothing (no inherent order), as if it is the property of something, a set.

You act like all this is new to you. Why? — fishfry

The idea of contradictory formalisms is not at all new to me. I am very well acquainted with an abundance of them. That's why I work hard to point them out, and argue against them.

I refer you to Galileo's sketch of Jupiter's moons. With this picture he started a scientific and philosophical revolution. Yet anyone can see that these little circles are not planets! There are no rocks, no craters, no gaseous Jovian atmosphere. Why do you pretend to be mystified by this obvious point? — fishfry

I don't see how this is analogous. Galileo represented something real, existing in the world, the motions of Jupiter's moons. What I object to is representing something which is not real, i.e. having no existence in the world, things like "no inherent order". This is not a representation, it is a fundamental assumption which does not represent anything. If a formalism is a representation, then the fundamental assumption, "no inherent order" cannot be a part of the formalism.

Do you feel the same way about maps? — fishfry

Consider this analogy. The idea of "no inherent order" describes nothing real, anywhere. So why is it part of the map? Obviously it's a misleading part of the map because there is nowhere out there where there is no inherent order, therefore I would not want it as part of my map.

Tell me this, Meta. When you see a map, do you raise all these issues? — fishfry

Yes, I get very frustrated when the map shows something which is not there. I look for that thing as a marker or indicator of where I am, and when i can't find it I start to feel lost. Then I realize that it was really the maker of the map who was lost.

An order that is shown can be seen: — Luke

But we cannot see the inherent order: — Luke

I already explained in what sense we see the inherent order, and do not see it, just like when we look at an object and we see the molecules of that object. The order is there, just like the molecules are there, and what our eyes are seeing, yet we do not distinguish nor apprehend the molecules nor the order, so we cannot say that we see it. We are always seeing things without actually seeing them, because it is a different sense of the word "see".

There was no change to my position, just a need to go deeper in explanation, to clarify the use of common terms, to assist you in understanding.

The idea, as with anything else mathematical, is that we have some aspect of the real world, in this case "order"; and we create a mathematical formalism that can be used to study it. And like many mathematical formalisms, it often seems funny or strange compared to our everyday understanding of the aspect of the world we're trying to formally model. — fishfry

I follow this, it seems to be exactly what I've been trying to explain to Luke, so we're on the same page here.

After all bowling balls fall down, and the moon orbits the earth. To help us understand why, Newton said things like F=maF=ma, and F=m1m2r2F=m1m2r2. And E=12mv2E=12mv2, and things like that. And you could just as easily say, "Well this doesn't seem to be about bowling balls. These are highly artificial definitions that Newton just made up." And you'd essentially be right, while at the same time totally missing the point of how we use formalized mathematical models in order to clarify our understanding of various aspects of the real world. — fishfry

These are what I would call universals, generalities produced from inductive reasoning, sometimes people call them laws, because they are meant to have a very wide application. As inductive conclusions they are derived from empirical observations of the physical world

So if you can see the difference between a real world thing like order, on the one hand; and how mathematicians formalize it, on the other; and if you are interested in the latter, if for no other reason than to be better able to throw rocks at it, I'm at your service. — fishfry

The issue is with what you call the purely abstract. It appears to me, that you believe there are some sort of "abstractions" which are completely unrelated to the physical world. They are not generalizations, not produced from inductive reasoning, therefore not laws, or "artificial definitions", in the sense described above. You seem to think axioms of "pure mathematics" are like this, completely unrelated to, and not derived from, the physical world.

That's the mindset for understanding how math works. You seem to object to math because it's a formalized model and not the thing itself, but that's how formal models and formal systems like chess work. They are not supposed to be reality and it's no knock agains them that they are not reality. They're formal systems. If you can see your way to taking math on its own terms, you'd be in a better position to understand it. And like I say, for no other reason than to have better arguments when you want to throw rocks at it. — fishfry

I object to the parts of these formalizations which do not correspond with our observations of the world. These would be faulty inductive conclusions, falsities. You claim that they do not need to correspond, that they a completely unrelated to the physical world. Yet when you go to describe what they are, you describe them as inductive conclusions, above, which are meant to correspond, in order that they might accurately "clarify our understanding of various aspects of the real world.".

So I see a disconnect here, an inconsistency. You describe "pure abstractions" as being related to the world in the sense of being tools, or formalizations intended to help us understand the world. Yet you insist that those who create these formalizations need not pay any attention to truth or falsity, how they correspond with the physical world, in the process of creating them. And you claim that when mathematicians dream up axioms, they do not pay any attention to how these axioms correspond with the world, because they are working within some sort of realm of pure abstraction.

As an example consider what we've discussed in this thread concerning " a set". It appears to me, that mathematicians have dreamed up some sort of imaginary object, a set, which has no inherent order. This supposed object is inconsistent with inductive conclusions which show all existing objects as having an inherent order. You seem to think, that's fine so long as this formalized mathematical system helps us to understand the world. I would agree that falsities, such as the use of counterfactuals, may help us to understand the world in some instances. But if we do not keep a clear demarcation between premises which are factual, and premises which are counterfactual, then the use of such falsities will produce a blurred or vague boundary between understanding and misunderstanding, where we have no principles to distinguish one from the other. If axioms, as the premises for logical formalizations are allowed to be false, then how do we maintain sound conclusions?

I don't care about your latest position. In case you missed it, my entire point for the last three or four pages is that you changed your position three or four pages ago. This is obvious from the quote that you somehow managed to overlook: — Luke

As I explained, I haven't changed my position. You have not yet understood it.

Here you say that "the exact spatial positioning" is not what is being demonstrated (i.e. shown) in the diagram. — Luke

No that's not a good interpretation. You need to respect the fact that what is being shown to the observer, as inhering within the physical thing being used in the demonstration, is not the same order as that which exists in the mind of the person performing the demonstration. I said there is a demonstration of "an order". I also said "the order which the mind apprehends, based on the demonstration is not the same order as that which inheres within the things shown." Then I said "the order apprehended in the mind is not the same as the order in the object. Therefore 'the exact spatial positioning' is not what is being demonstrated." The exact spatial positioning is what inheres within the object, and though it is what is being shown by the one doing the demonstration, it is not the same order as what the person is trying to demonstrate. This is why I said fishfry's claim that the order was random is false. That's what the person doing the demonstration was trying to demonstrate, but it was not what the demonstration actually showed.

What is "being demonstrated" is an order which exists in the mind of the person making the demonstration. This is the first line, the "demonstration of an order". What appears to the person making the interpretation, as what is "shown", is the physical object with an inherent order. This is a representation of the order which exists in the mind of the person making the demonstration. It is not the same order, but a representation of it. So the order being demonstrated is not the same as the order which inheres within the representation, (as a representation is different from the thing it represents), and the order in the mind of the person interpreting what is shown, is not the same as the order which inheres in the object. And, because of this medium, which exists between the one demonstrating and the one interpreting, the physical object as symbols, the order on the minds of the two individuals is not the same. That as I said is why we misunderstand each other.

Which is it? — Luke

As I said, numerous times, the mind creates an order to account for the order assumed to be in the thing Therefore the order in the mind it is not the order shown by the thing. No change of position, just a difficult ontological principle to describe to someone with a different worldview.

But you didn't say any of those things. Instead you just accepted the mathematical definition I repeatedly gave you, and then kept arguing from your own private definition. When I finally figured out what you were doing, I was literally shocked by your bad faith and disingenuousness. I'm willing to have you explain yourself, or put your deliberate confusion-inducing equivocation into context, but failing that I no longer believe you are arguing in good faith at all. You have no interest in communication, but rather prefer to waste people's time by deliberately inducing confusion. — fishfry

Let me remind you. You started in the discussion with the repeated assertion "sets have no inherent order". Check this post, I think you'll see that claim stated a number of times.

My God, you wield your ignorance like a cudgel. I could have just as easily notated the two ordered sets as:

* ({1,2,3,4,…},<)({1,2,3,4,…},<) and

* ({1,2,3,4,…},≺)({1,2,3,4,…},≺)

which shows that these two ordered sets consist of the exact same underlying set of elements but different linear orders. Remember that sets have no inherent order. So {1,2,3,4,...} has no inherent order. The order is given by << or ≺≺. — fishfry

When I said order is spatial and temporal, you claimed a completely "abstract order", which I didn't understand, and still don't understand because you haven't yet explained this in a coherent way. So I continued to insist order was spatial or temporal until you gave me examples of first and second place in competition, what I called order relative to best. I accepted this as non-spatial or temporal ordering, but I still don't see it as completely abstract because it still is based in concrete criteria for judgement.

You proceeded to define order in terms of "less than", as if you thought that this is purely abstract. However, I had already explained how "less that" is dependent on, defined in relation to, quantity. So you only contradicted your earlier claim that order is logically prior to quantity, by defining order in relation to quantity. And, since quantity is dependent on spatial separation between individuals you have not really escaped the spatial aspect of order, to get to a purely abstract order.

So this is where we stand. You have claimed a purely abstract order, but given me an order based in "less than" which is based in quantity. And quantity relies on spatial conception, so you have really given me a concept of order based in spatial conceptions..

By "shown" you do not mean "displayed". After all, "it is not visible". Therefore, you must not be making the argument - as you did earlier - that we see the order but do not apprehend it. — Luke

Luke. I very consistently said, over and over again, that we do not see the order.

You are saying that the "exact spatial positioning" is logically demonstrated by
("shown" in) the diagram, but it is not apprehended? If the exact spatial positioning is not (or cannot be) apprehended, then how has it been logically demonstrated by the diagram? — Luke

I went through that already, more than once. There is a logical demonstration of an order. The order which the mind apprehends, based on the demonstration is not the same order as that which inheres within the things shown. You keep neglected the principal point of the argument, that the order apprehended in the mind is not the same as the order in the object. Therefore "the exact spatial positioning" is not what is being demonstrated. So, do not ask again, this same strawman question. Check out these quotes:

Of course, location is intelligible, conceptual, so it's not actually sensed it's something determined by the mind, just like meaning. When you tell someone something, they do not sense the meaning. This is "showing" in the sense of a logical demonstration. And the point is that upon seeing, or hearing what is shown, the mind may or may not produce the required conceptualization, which would qualify for what we could call apprehending the principle. More specifically, the conceptualization produced in the mind being shown the demonstration is distinct and uniquely different from the conceptualization in the mind which is showing the demonstration, therefore they are not the same. That is why people misunderstand each other.. — Metaphysician Undercover

I answered the question, it's just like a logical demonstration. Like when one person shows another something, and the other makes a logical inference. All instances of being shown something intelligible, i.e. conceptual, bear this same principle. We perceive something with the senses and conclude something with the mind. The things that I sense with my senses are showing me something intelligible, so I produce what serves me as an adequate representation of that intelligible thing, with my mind. — Metaphysician Undercover

Inherent order is a wider concept, applying in particular to biological systems and natural phenomena. Ordering is more specific having to do with listing. I think you are discussing the latter. — jgill

Fishfry claimed that a set has no inherent order, and I questioned whether it is possible that there could be a thing with no inherent order.

i really do not think that "listing" is the subject here, because listing Is an ordering of symbols, not the things represented by the symbols. The list may represent an order, but the reason for the order is something other than the spatial order of the symbols. And fishfry insisted on the reality of a purely abstract order, which could not be a spatial relation of symbols, as listing is. We would need to find a principle of order which is purely abstract.

Sorry, I haven't kept up. Are you speaking of inherent order or inherent ordering? — jgill

I think I said "inherent order", but I don't quite understand the point to making the difference.

But you now concede that sense perception is involved in showing. — Luke

Of course sense perception is involved! Where have you been? We've been talking about seeing things and inferring an order. My point was that we do not sense the order which inheres within the thing, we produce an order in the mind. I never said anything ridiculous like we do not use the senses to see the thing, when we produce a representation of order for the thing.

I would say that the word "shown" here means what is visible in, or displayed by, the diagram; not what is demonstrated or proved by the diagram. — Luke

But we went through this already. I explained that this is not what I meant by "shown"., and the reason why, being that order is inferred by the mind, it is not visible. I went through a large number of posts explaining this to you. It seemed to be a very difficult thing for you to grasp. And now, when you finally seemed to grasp the meaning associated with the way I used the term, you've gone right back to assuming that this is not the way I used it, despite all those explanations. Why? We just go around in circles, it's stupid. You pretend to have understood my explanation as to what I meant by "shown", then all of a sudden you say but obviously that's not what you meant. It's ridiculous. It' like you're saying 'I would not have used "shown" that way, therefore you did not'. And when i go through extreme lengths to explain that this is actually how I used the term, to the point where you seem to understand, you turn right back to the starting point, claiming but I would not have used it that way, therefore obviously you didn't. What's the point?

All that remains for you to explain is your contradictory pair of claims that (i) the inherent order is the exact spatial positioning that we do apprehend in the diagram; and that (ii) we are unable to apprehend the inherent order. — Luke

I stated repeatedly that we do not apprehend the exact spatial positioning, so you have a strawman here.. You don't seem to be capable of understanding any of what I am saying, we're just going around in circles of misunderstanding. it's pointless.

You avoid the question instead of answering it. How can location be shown to someone without it being sensed? — Luke

I answered the question, it's just like a logical demonstration. Like when one person shows another something, and the other makes a logical inference. All instances of being shown something intelligible, i.e. conceptual, bear this same principle. We perceive something with the senses and conclude something with the mind. The things that I sense with my senses are showing me something intelligible, so I produce what serves me as an adequate representation of that intelligible thing, with my mind.

"Shown" in the sense of a logical demonstration is different to "shown" in the sense of your statement: "the exact spatial positioning shown in the diagram". That's obvious. — Luke

Sorry, you've lost me. You appear to be making up a difference in the meaning of "shown", for the sake of saying that I contradict myself. I take back my apology, I'm going back to thinking that you do it intentionally.

There's an odd sort of reality of life which is almost a sort of paradox. The individual living being in the extreme complexity of its existence, as a delicately balanced organism, is very susceptible to death. We all run the risk of dying on a daily basis. Death may be waiting for you around any corner, or curve. But life in general, as a beautiful vast array of all sorts of different organisms, is extremely robust, and resilient in consequence to the occurrence of any possible extermination events.

The beauty of life is found in its diversity, and this provides its strength. Take a look at all the different colours of flowers there are, and think about how difficult it would be to produce such an extensive array. And that's just one simple property, colour.

The fragility of the individual, although it results in the death of each and every one of us, is not a weakness however, because this is the means by which life tests all the different boundaries of the the environment which it inhabits, thereby producing all the diverse individuals which provide its overall strength. We ought not seek to limit diversity, because that would be a self-imposed weakness, making the vulnerability of the individual, universal.

Do you think that location can be shown to someone without it being sensed? — Luke

Of course, location is intelligible, conceptual, so it's not actually sensed it's something determined by the mind, just like meaning. When you tell someone something, they do not sense the meaning. This is "showing" in the sense of a logical demonstration. And the point is that upon seeing, or hearing what is shown, the mind may or may not produce the required conceptualization, which would qualify for what we could call apprehending the principle. More specifically, the conceptualization produced in the mind being shown the demonstration is distinct and uniquely different from the conceptualization in the mind which is showing the demonstration, therefore they are not the same. That is why people misunderstand each other..

I now see why we have such a hard time understanding each other, we seem to be very far apart on some fundamental ideas, which form the basis for our conceptualizing what is shown by the other. I thought you were intentionally misreading me, in order to say that I contradict myself. But now I see that this is the way you actually understand those words. My apologies for the accusation.

As a result you can find yourself living with people who are simple in thought who don't give the extra effort to think from a philosophers perspective. — Tiberiusmoon

Each person has one's own place within a society, and many of these places do not require complex philosophical thought, so there is not need to compel these people toward it. What is a problem though, I believe, is bad habits of thought. Bad habits may enter into any field or discipline involved in complex thought, and may in some cases be associated with a form of laziness. For instance, in some cases we are encouraged to accept the principles presented by others whom we apprehend as authorities, without asking for justification. This form of laziness seems to pervade modern academia.

Sorry Luke, now it's me who can't understand what you're saying. Do you think that we sense location?

Given that (1) we do not perceive order via the senses and that (2) we cannot apprehend inherent order, then how can the inherent order be the exact spatial positioning shown in the diagram? — Luke

I think I've answered this about three times, so either I don't understand your question, or you don't understand my answer, or both.

Even if I grant you that there is an inherent order to the universe, how can you say that the inherent order of the diagram is the same as the order that we perceive via the senses, or "the exact spatial positioning shown"? — Luke

I told you, we don't perceive order with the senses, we create orders with the mind. Judging by this statement, I'm thinking it's you who is the one not understanding.

I note your change in position. You are no longer arguing that the inherent order cannot be apprehended. You have now adopted the weaker claim that the inherent order cannot be completely apprehended. — Luke

Again, you're looking for hidden meaning to make unjustified inferences. The inherent order cannot be apprehended by us. I can't even imagine what it would mean to partially understand an order. If my use of "completely" misled you, I retract it as a mistake, and apologize.

More importantly, as far as I can tell, inherent order is not the kind of order that mathematicians are concerned with. — Luke

Maybe, but fishfry claimed that a set has no inherent order. So if mathematicians are making such assumptions in their axioms, then they are concerned with it; concerned enough to exclude it from the conceptions of set theory. The issue I'm concerned with is the question of whether a thing without inherent order is a logically valid conception.

You're factually wrong.

Is the set {0,1,2,3,4} identical to the set {0,1,2,3,4}? I have to assume you'd say yes.

But 2 + 3 and 5 are both representations of the set {0,1,2,3,4}. So they're identical. — fishfry

The way you described sets in this thread, a set is something which cannot have an identity because it has no inherent order. Therefore I cannot agree that the set {0,1,2,3,4} is identical to the set {0,1,2,3,4}. It seems like a set is an abstraction, a universal, rather than a particular, and therefore does not have an identity as a "thing". It is particulars, individual things, which have identity according to the law of identity. Notice that the law of identity says something about things, a thing is the same as itself.

The law of identity is intended to make that category separation between particular things, and abstractions which are universals, so that we can avoid the category mistake of thinking that abstractions are things. "The set {0,1,2,3,4}" refers to something with no inherent order, so it does not have an identity and is therefore not a thing, by the law of identity, To say that it is a thing with an identity is to violate the law of identity.

Well, math does not violate this principle. 2 + 3 and 5 are identical. They are both representations of the set represented by {0,1,2,3,4}, which of course is not actually "the" set, but is rather yet another representation of that abstract concept of 5. — fishfry

This is the whole point of the law of identity, to distinguish an abstract concept from a thing, so that we have a solid principle whereby we can avoid the category mistake of thinking of concepts as if they are things. A thing has an identity which means that it has a form proper to itself as a particular. To have a form is to have an order, because every part of the thing must be in the required order for the thing to have the form that it has. So to talk about something with no inherent order, is to talk about something without a form, and this is to talk about something without an identity, and this is therefore not a thing.

Only to the extent that you don't seem to think a thing is identical to itself. Because when mathematicians use equality, they mean identity, and this is provable from first principles. They either mean identity as sets; which is easy to show; or, they often mean identical structurally. This is a more subtle philosophical point. — fishfry

The problem is not that I don't think a thing is the same as itself. That is the law of identity, which I adhere to. The problem is that you make the category mistake of believing that abstract conceptions are things. Because you will not admit that a concept is not a thing, you make great effort to show that two distinct concepts, like what "2+3" means, and what "5" means, which have equal quantitative value, refer to the same "thing". Obviously though, "2+3" refers to a completely different concept from "5".

If you would just recognize the very simple, easy to understand, fact, that "2+3" does not mean the same thing as "5" does, you would understand that the two expressions do not refer to the same concept. So even if concepts were things, we could not say that "2+3" refers to the same thing as "5", because they each have different associated concepts. And it's futile to argue as you do, that the law of identity is upheld in your practice of saying that they refer to the same "mathematical object", because all you are doing is assuming something else, something beyond the concepts of "2+3", and "5", as your "mathematical object". This supposed "object" is not a particular, nor a universal concept, but something conjured up for the sake of saying that there is a thing referred to. But there is no basis for this object. It is not the concept of "2+3" nor is it the concept of "5", it is just a fiction, a false premise you produce for the sake of begging the question in your claim that the law of identity is not violated.

You said that "1) We do not perceive order with the senses" and that "2) We cannot apprehend the inherent order". Therefore, how do you know that what's shown in the diagram is the exact positioning of the parts (i.e. the inherent order)? — Luke

It is a fundamental ontological assumption based in the law of identity, that a thing has an identity. In Kant we see it as the assumption that there is noumena, which is intelligible, just not intelligible to us. In Descartes we see skepticism as to whether there even is external objects.

So we assume that there is something, the sensible world, and we assume it to be intelligible, it has an inherent order. To answer your question of how do we "know" this, it is inductive. We sense things, and we conclude that there is reality there. Also, we have some capacity to understand and manipulate what is there, so we conclude that there is intelligibility there, intelligibility being dependent on ordering. We have some degree of reliability in our understanding of the ordering therefore there must be some ordering.

Isn't the positioning of the dots that I perceive the "perspective dependent order" which you earlier stated was not the inherent order? So how can the diagram show the inherent order to anybody?

The inherent order cannot be perceived by the senses and we can't apprehend it, anyway. — Luke

Yes, you perception provides for you, the basis for a perspective dependent order, which your mind produces. What the object is showing you, its inherent order, and the order which you are producing towards understanding the inherent order, are two distinct things. As I described, there is some degree of inconsistency, constituting a difference, between what is shown to you, and what you apprehend from that showing. The claim of difference is justified by our failures. The inherent order is shown. It is not perceived by the senses. If you try to understand the inherent order, your mind will produce an order which you think best represents that which inheres in the object.

Consider, that in seeing objects we do not see the molecules, atoms or other fundamental particles, we have to figure those things out as a representation of the order which inheres within. But we cannot completely apprehend that order because our minds are deficient. This doesn't mean that sentient beings will never be able to apprehend it, or that there isn't an omniscient being which already can apprehend it. And even if it is impossible that human beings or any sentient beings will ever be able to understand it in perfection, like an omniscient being is supposed to be able to, we can still improve our understanding, i.e. get a better understanding, and decrease our failures.

If "We cannot apprehend the inherent order", then how do you know that our representations are inaccurate? — Luke

I think we judge the accuracy of our understanding mostly by the reliability of our predictions. But reliability is perspective dependent and subjective. So where some people see reliability, I see unreliability. It all depends on what type of predictions you are looking for the fulfillment of.

If the inherent order is unintelligible to the human mind by definition, then what makes inherent order preferable to (or distinguishable from) randomness? — Luke

Order is fundamentally intelligible. So assuming order is to assume the possibility of being understood, which is to inspire the philosophical mind which has the desire to understand. To assume randomness is to assume unintelligibility which is repugnant to philosophical mind which has the desire to understand.

So, as I explained. If the object appears (seems) to be unintelligible (without inherent order), we need to determine why. Is it our approach (are we applying the wrong principles in our attempt to understand), or is it the reality, that the object truly has no inherent order? The latter is repugnant to the philosophical mind, and even if it were true, it cannot be confirmed until the possibility of the former is excluded. Therefore, when the object appears to be unintelligible (without inherent order), we must assume that our approach is faulty (we are applying the wrong principles in our attempt to understand), and we must subject all principles to extreme skepticism, before we can conclude that this object is truly unintelligible (without inherent order). The rational approach is to assume that we are applying the wrong principles, and to assume that the object has no inherent order is irrational.

On the contrary. 2 + 3 and 5 are mathematically identical. There is not the slightest question, controversy, or doubt about that. — fishfry

As per the quotes above, from Wikipedia, the mathematical notion of identical , as equal, is not consistent with the philosophical notion of identity, described by the law of identity. In other words, mathematicians violate the law of identity to apply a different concept of identity, making two things of equal value mathematically identical. You might accept this, and we could move on to visit the possible consequences of what I believe is an ontological failure of mathematics, or you could continue to deny that mathematicians violate this principle. The latter is rather pointless.

You spoke of an "external perspective", which implies an internal perspective. You might recall I asked you about it and you responded: — Luke

If all perspectives are external to the object, then "perspective" is necessarily external, and saying "external perspective" just emphasizes the fact that perspective is external. Internal perspective is not implied, just like saying "cold ice" doesn't imply that there is warm ice. That's why I referred to Kant, to show how our perspective of the thing in itself is external to the thing.

Your current argument is that we do not perceive order with the senses, and that we cannot apprehend inherent order at all. Therefore, how is it possible that the inherent order is the exact spatial positioning shown in the diagram? — Luke

Why not? I don't understand your inability to understand. Let me go through each part of your question. 1) We do not perceive order with the senses. No problem so far, as we understand order with the mind, not the senses. 2) We cannot apprehend the inherent order. Correct, because the order which we understand is created by human minds, as principles of mathematics and physics, and we assign this artificially created order to the object, as a representation of the order which inheres within the object, in an attempt to understand the inherent order. But that representation, the created order is inaccurate due to the deficiencies of the human mind. 3)The inherent order is the exact positioning of the parts, which is what we do not understand due to the deficiencies of the human mind.

Does that help? You have emboldened the word "shown". Why? Do you understand that something can be shown to you which you do not have the capacity to understand? The physical world shows us many things which we do not have the capacity to understand. For example, the theologians used to argue that the physical world shows us the existence of God. Most people would claim that the physical world is not evidence of God, and in no way does the physical world show us God. The theologian would say that you just do not understand what is being shown to you. the exact order is being shown to us but we do not understand it.

Fishfry will argue fervently that "pure mathematics" is not influenced by physics. Perhaps some mathematicians actually have no respect for physical principles, and that's why infinities have become the norm, rather than the abnormal.