What the moon and earth actually do in terms of these descriptions is that both revolve around a common moving center as they cork-screw their way along curved geodesics in space-time - or at least I think that's the most recent and accurate description. — tim wood

What are you saying now, that both things and their relations exist independently of the ideas which represent them? If you agree that both the moon and the earth exist independently of ideas, how can you deny that their intertwined activities also exist independently. And therefore their relationsare independent

I divide in two, then, things and ideas. Material and products of mind. You either divide into more than two, or one of your two is quite different from mine. and this the extra- or non-mind existence of ideas. Or, if I get it right, a) ideas have independent non-material existence, and b) you don't need a mind to have ideas. — tim wood

How can you continue to refuse to acknowledge the third category, the relations between things? This is what we observe as the interactions between things. So, we need three categories, things, the relations between things, and ideas. If we deny the validity of this category, "the relations between things", then how could there be any truth to what the moon and earth are doing with each other in their interactions? If this is only ideas, then one description is just as true as the other. The description of the sun going around the earth every day is just as true as the description of the earth spinning on its axis, because it's all just ideas, and there's no real relationship which we are trying to truthfully describe.

In passing: you note what appears to be the existence of non-material, non-idea things like relations, forces(?), intentions, purposes, and the like. I think if you look closely enough at them, you will see that they're all ideas, all usefulness granted, but, I think you will agree, utility not itself constitutive of separate and independent existence. — tim wood

No, as explained above, they cannot be "all ideas", or else there would be no truth or falsity about what the earth and moon are doing with each other, and what the earth and sun are doing with each other. Your perspective is known as Protagorean relativity. Your ideas about what these things are doing are no more true than mine, even though they are completely different, because there is no truth, it's just ideas, yours mine, or whoever.

No it's perfectly sensible. You have a class of screaming school kids, eight year olds say, on the playground. They're totally disordered. The only organizing principle is that you have a set of kids. — fishfry

They're not totally disordered though. At any time you can state the position of each one relative to the others, and that's an order. When you say "they're totally disordered", that's just metaphoric, meaning that you haven't taken the time, or haven't the capacity, to determine the order which they are in.

Then you tell them to line up by height. Now you have an ordered set of kids. Or you tell them to line up in alphabetical order of their last name. Now you have the same set with a different order. — fishfry

Those are just 'identified orders'. When the kids are running free, in what we might call a 'random order', what you called "totally disordered", there is still an order to them, it has just not been identified. So, for the principle "height", we could make a map and show at any specific time, the relations of the tallest, second tallest, etc., and that would be their order by height. And we could do the same for alphabetic order. So we number them in the same way that you would number them in a line, first second third etc., then show with the map, the positions of first second third etc., and that is their order. The supposed "random order", or "totally disordered" condition, is simply an order which has not been identified.

Now maybe you are making the point that everything is in SOME order. The kids in the playground could still be ordered by their geographical locations or whatever.

But sets don't have inherent order. — fishfry

Yes, that's very apprehensive of you fishfry, and I commend you on this. Most TPF posters would persist in their opinion (in this case your claim of "totally disordered", which implies absolute lack of order), not willing to accept the possibility that perhaps they misspoke.

So that is the point, everything is in "SOME" order. Now, consider what it means to say "sets don't have inherent order". Would you agree that this sets them apart from real collections of things? A real collection of things, like the children, must have SOME order. And, this order which they do have, is very significant because it places limitations on their capacity to be ordered.

So when you said "first you have things, then you place them in order", we need to allow that the "things" being talked about, come to us in the first place, with an inherent order, and this inherent order restricts their capacity to be ordered. For example, let's say that the things being talked about are numbers. We might say that 1 is first, 2 is second, 3 is third, etc., and this is their "inherent order". This is the way we find these "things", how they come to us, 1 is synonymous with first, 2 is synonymous with second, etc., and that is their inherent order. The proposition of set theory, that there is no inherent order to a set, removes this inherent order, so we can no longer say that one means first, etc.. Now there cannot be any first, second, or anything like that, inherent within the meaning of the numbers themselves. This effectively removes meaning from the symbols, as you've been saying.

Another way to look at it is that, as you say, perhaps every set has some inherent order, but we are just ignoring the order properties to call it a set. Then we bring in the order properties. It's just a way of abstracting things into layers.

But mathematical sets by themselves have no inherent order till we give them one. It's just part of the abstraction process. — fishfry

Yes, I think I see this. I would say it's a type of formalism, the attempt to totally remove meaning from the symbols. The problem though, is that such attempts are impossible, and some meaning still remains, as hidden, and the fact that it is hidden allows it to be deceptive and misleading. So, by the abstraction process you refer to, we remove all meaning from the symbols, to have "no inherent order". Now, what differentiates "2" from "3"? They are different symbols, with different applicable rules. If what is symbolized by these two, can have "no inherent order", then the rules for what we can do with them cannot have anything to do with order. This allows absolute freedom as to how they may be ordered.

However, we can ask, can the two numbers,2 and 3, be equal? I don't think so. Therefore we can conclude that there actually is a rule concerning their order, and there actually is not absolute freedom as to how they can be ordered. The two symbols cannot have the same place in an order. Therefore, there actually is "SOME" inherent order to the set, a rule concerning an order which is impossible. And this is why I say that these attempts at formalism, to completely remove meaning which inheres within what is symbolized by the symbol itself, are misleading and deceptive. We simply assume that the formalism has been successful, and inherent meaning has been removed (we take what is claimed for granted without justification), and we continue under this assumption, with complete disregard for the possibility of problems which might pop up later, due to the incompleteness of the abstraction process which is assumed to be complete. Then when a problem does pop up, we are inclined to analyze the application as what is causing the problem, and the last thing we would do is look back for faults in the fundamental assumptions, as cause of the problem.

Yes, I am starting to come around to your point of view. But tell me this. Since, given a set, there are many different ways to order it, how do you know which one is inherently part of it? — fishfry

As described above, you need to look for what is inherent within the meaning of the symbol. Formalism attempts the perfect, "ideal" abstraction, as you say, which is to give the imagination complete freedom to make the symbol mean absolutely anything. However, there is always vestiges of meaning which remain, such as the one I showed, it is impossible that 2=3. The vestiges of meaning usually manifest as impossibilities. Any impossibility limits possibility, which denies the "ideal abstraction", by limiting freedom.

So to answer your question, the order which is inherent is not one of the orders you can give the set, it is a preexisting limitation to the orders which you can give. When we receive the items, what you express as "first we have the items", there is always something within the nature of the items themselves (what you call "SOME order"), as received, which restricts your freedom to order them in anyway whatsoever.

But if you ask me whether I think that two sets that are equal are identical, I'd have to say yes. Because if they're equal, they're the same set. Not because of metaphysics, but because of set theory. Set theory only talks about sets, and doesn't even say what they are. Nobody knows what sets are. They're fictional entities. They obey the axioms and that's all we can know about them. — fishfry

There are many different ways that "same" is used. You and I might both have "the same book". The word "set" used here is "the same word" as someone using "set" somewhere else. So it's like any other word of convenience, it derives a different meaning in a different sort of context. In common parlance, mathematicians might say "they are the same set", but I think that what it really means is that they have the same members. So that's really a qualified "same".

I can see that you've developed a bit of a, what is the word, obsession? attitude? annoyance? with him. — fishfry

Actually I got annoyed with Tones rapidly, when we first met, but now he just amuses me.

Great, let these, then, be the examples of your insisting on the reality of a fiction and of reifying ideas in some kind of form which they don't have. The moon does not orbit the earth. But to you that's a fact and a relation that exists. How and where? Made of what? I keep inviting you to make your argument, to make your case, and you cannot or will not do it. And you can shift gears all you want, but until you engage your clutch, you're going nowhere, even if your engine is racing. You have your beliefs: some are imo nonsense. But they're your beliefs. If you want them to be more than merely your beliefs, you'll need more than just your insistence.

I would appreciate it if in your reply, if you reply, you acknowledge that the moon does not orbit the earth, and follow that with an explanation of how a false belief - the relation - can exist other than as an idea. If you get that far, please include how any belief can be other than an idea, and how any idea can be real and exist in whatever your sense of "exist" is. Ideas being the stuff of minds, it's hard to see how there can be such absent mind. — tim wood

To be clear, I said there is activity which is described as "the moon orbits the earth", and that this activity exists.

Anyway, I think I'm starting to understand your perspective. Would you agree that the moon does not exist, and the earth does not exist? These words signify ideas, just like "the moon orbits the earth" signifies an idea. If you can agree with this, then we might have a starting point.

I approached this point when I made the statement about judging the truth or falsity of the description of the screw and the engine. The first step was to agree that there is a thing called "the screw", and a thing called "the engine". But if you want to insist that words refer to ideas, not the things or activities associated with those ideas, as you are doing, then we must start right from the bottom.

when we write:

x = y

we mean:

x is identical with y

x is equal to y

x equals y

x is y

x is the same as y

However, the poster, in all his crank glory, continues to not understand:

x = y

does NOT mean:

'x' is identical with 'y'

'x' is equal to 'y'

'x' equals 'y'

'x' is 'y'

'x' is the same as 'y'

but it DOES mean:

what 'x' stands for is identical with what 'y' stands for

what 'x' stands for is equal to what 'y' stands for

what 'x' stands for equals what 'y' stands for

what 'x' stands for is what 'y' stands for

what 'x' stands for is the same as what 'y' stands for — TonesInDeepFreeze

Just to humour you Tones, I read this post. So here's a question for you. When you state the law of identity as "a thing is identical with itself", would this identity include not only all of the thing's constituent elements, but also the ordering of those elements? For example, if I say that this rock is identical with itself, not only would this indicate that all the elements which compose the rock are identical with the rock, but also the ordering of those elements. If the ordering of the elements was not the same, then it would not be identical with the rock.

Meta, once I understood that Tones was arguing that set equality is the law of identity, I realized why you're arguing this point. I entirely agree with you. I apologize to you for jumping to multiple wrong conclusions. — fishfry

Apology accepted. I wrote most of the following before reading this, so ignore, or read, whatever suits you. The deleted post must have occurred in the transfer from the other thread. Michael was concerned about derailing the thread, and took out certain posts and transferred them.

I haven't yet worked through Tones's reply to me outlining his argument, so I should reserve judgment. But at this moment it seems to me that set equality is a defined symbol in a particular axiomatic system. As such has no referent at all, any more than the chess bishop refers to Bishop Berkeley. It doesn't refer to anything concrete, nor anything abstract. It simply stands for a certain predicate in ZF. It can't possibly "know" about logic or metaphysics. It can't refer to "sets" since nobody knows what a set is. A set is whatever satisfies the axioms. And set equality is a relation between sets, which have no existence outside the axioms; and have no meaning even within the axioms. — fishfry

As I indicate in my latest post in the supertask thread, Tones has a knack for taking highly specialized definitions designed for a particular axiomatic system, and applying them completely out of context. Be aware of that.

But nobody claims mathematical equality is identity. — fishfry

Tones does, obviously.

You would be fun in set theory class. You're entirely hung up on the very first axiom. "Class, Axiom 1 is the axiom of extensionality. It tells us when two sets are equal." You, three years later: "But that's not metaphysical identity! You mathematicians are bad people. And you don't understand anything!" And your professor goes, Meta, We still have a countable infinitely of axioms to get through! Can we please move on? — fishfry

I dropped out of abstract mathematics somewhere around trigonometry, for that very reason. I got hung up in my need to understand everything clearly, and could not get past what was supposed to be simple axioms. I had a similar but slightly different problem in physics. We learned how a wave was a disturbance in a substance, and got to play in wave tanks, using all different sorts of vibrations, to make various waves and interference patterns. Then we moved along to learn about light as a wave without a substance. Wait, what was the point about teaching us how waves are a feature of a substance?

But Tones is a bit different. Tones forges ahead with misunderstanding of fundamental axioms. Tones insists that the axiom of extensionality tells us when two sets are identical. He refers to something he calls "identity theory", which I haven't yet been able to decipher.

But axioms don'g mean anything. They're just rules in a formal game, like chess. As I say, if you asked a mathematician if mathematical equality is metaphysical identity, a few of them would have an educated opinion about the matter and they'd immediately agree with you. The rest, the vast majority, wouldn't understand the question and would be annoyed that you interrupted them. — fishfry

If axioms are rules, then they mean something. They dictate how the "formal game" is to be played. If the rules are misunderstood, as is the case with Tones, then the rules will not be properly applied.

You're fighting a straw man of your own creation. — fishfry

Tones is a monster, not of my own creation.

I remember fondly when I spent weeks trying to explain order theory to you, back when I thought you were trying to understand anything. You are still at this. If two sets have the same elements and the same order, they are equal as ordered sets. It's just about layers of abstraction, separating out concepts. First you have things, then you place them in order.

Somehow this offends you. Why? — fishfry

It is self-contradicting, what you say. " First you have things, then you place them in order."

If you have things, there is necessarily an order to those things which you have. To say "I have some things and there is no order to these things which I have, is contradictory, because to exist as "some things" is to have an order. Here we get to the bottom of things, the difference between having things, and imaginary things.

Yes I did actually understand that! I was just startled that Meta was still going on about order being an inseparable and inherent aspect of a set, when I had already had such a detailed conversation with him on this subject several years ago. I did actually realize you were quoting him -- I was just surprised to see him still hung up on that topic. — fishfry

You are taking Tones' misrepresentation. I fully respect, and have repeatedly told Tones, that sets have no inherent order, exactly as you explained to me, years ago. What I argue is that things, have an order to their constituent elements, and this is an essential aspect of a thing's identity. So I've been trying to explain to Tones, that the "identity" of a set (as derived from the axiom of extensionality) is not consistent with the identity of a thing (as stated in the law of identity). But Tones is in denial, and incessantly insists that set theory is based in the law of identity.

Plato is right. By definition #2, there are no physical limitations. A dog that eats the most, and a dog that eats the least implies two physical limits, which violates #2

Density is a property of orderings. An ordering is dense if and only if between any two points there is another point. If time is divisible ad infinitum, then the ordering of points of time is dense. — TonesInDeepFreeze

As usual, you're making things up to suit your purpose. "Dense order" is a property of the elements of sets, commonly numbers, and never "points". Points do not make up the elements of a set, neither does time make up the elements of a set. You continue in your sophistry, taking a definition from set theory which is specifically applicable only to the elements of a set, and applying this definition to points and time. TIDF, the epitome of a sophist, taking a term with a specific articulated definition, designed for a very specific application, and applying it somewhere else, where it is not suited. How do you propose that a multitude of "points" could be the distinct elements of a set?

And this is where to my ear your answer equivocates. Where is the relation? What is it made of? Thing or idea? — tim wood

Oh yes, I forgot to answer your question, I know you dislike that. Your act of limiting possible answers to two choices, "thing or idea", imposes a restriction which leaves the world unintelligible, as I explained here:

This problem is the result of the restrictions on language which you are trying to enforce. You are insisting that "a relation" must be either an idea or an expression of an idea. You are refusing to acknowledge that in order to develop an adequate understanding of reality, we must allow that relations have independent existence. Do you understand, and respect this conclusion? In order to have an accurate and adequate understanding of reality, and truth about the world, we need to allow that relations exist independently from the human ideas which attempt to understand them, just like we do with objects. Objects have independent existence, and so do their relations. Therefore we must allow that relations are not just human ideas, or expressions of human ideas, that is a linguistic restriction which would render the world as unintelligible. — Metaphysician Undercover

The majority of your thread I apprehend as an irrelevant rant, so I'll skip it and get right to the point.

And just this an example of the kind of place where we have to be "damned careful" with what we say and mean. The proposition here is whether, not the map as you put it exists, but if the territory, the relation itself independent of mind, exists. I invite you here to think carefully about just what exactly it is that you believe - affirm - exists. My quick answer is the moon, the earth, and ideas about them. And people who have those ideas. The notion of accuracy of idea being here a test. If the idea is wrong, does it exist in your sense? That is, can existing things that cannot exist, exist? They can as ideas. If pressed I can affirm six impossible things before morning tea - as ideas. — tim wood

The moon exists, and the earth exists, so says you. Do you agree that the activities of these things also exist, and that these activities are not just ideas about the things, they are what the things are actually doing? So for instance, we describe an activity as "the moon orbits the earth", and another as "the earth has tides which are the effects of the orbiting moon". These sorts of activities and relations exist independently of our thought and ideas about them, and our representations of them. Can you agree?

Gravity a great example: of course it exists, except that it doesn't. — tim wood

What could this possibly mean?

The division of time mentioned in the thought experiment doesn't require continuousness of time; it only requires density time (via the density of the rationals). — TonesInDeepFreeze

Infinite density of time. What could that possibly mean? "Density" implies two distinct substances, as a ratio (weight per volume for example). Are you suggesting that time consists of two distinct substances, in a relation which is infinitely dense? That seems absurd.

I know your sophistry TIDF. When cornered in an argument, instead of retreating, you create an absurd concept, by combining words in an incoherent, irrational way, hoping that the incoherency will go unnoticed. This would allow you to slither away through the crack between the infinitely dense particles of time. This is better represented as the irrational space between the rational numbers, and the slippery sophist slides out of that possible world, through the irrational exit.

Why do you want to turn this into a discussion about the shortcomings of language, rather than sticking to the subject? Everyone knows that language has problems, ambiguity, redundancy, and simple lack of scope. We can either take a defeatist attitude, and assume that our goals will never be obtained due to these problems, or we can accept the problems of language and continue on, recognizing the shortcomings and working around them. You seem to be in the defeatist camp. I learned from Plato, and his artful demonstration of "dialectics" that these problems, which many take as impassable roadblocks, are really just minor obstacles, requiring slight detours.

We can talk all the day long about engines and screws and their purposes and intentions and relation to each other, but I and I suspect you too know perfectly well that these descriptive terms, while about the objects, are in no sense part of the objects themselves. — tim wood

Tim, why do you keep coming back to this point? I've explicitly said, numerous times, that purpose is not "in the object". It is in the object's relations to other objects. We've passed that little obstacle long ago. The disagreement we have is that you claim that relations only exist as ideas in human minds. I think that relations exist independently of human minds, just like the objects which are related to each other exist independently of human minds.

Here's a compromise proposal. You say relations exist as "ideas", or "expressions of ideas". I say relations exist outside of human minds. Can we agree that "ideas", or "expression of ideas" may exist outside of human minds? So, let's say that the screw has a relation to the engine, and this relation is an idea, or an expression of an idea, which is outside of all human minds.

Newton's gravity can stand here is an example: a mighty piece of description - which as a shortcoming apparently Newton himself understood better than most - but now replaced with the curvature of space-time, and some even newer, tentative theories. The-force-of-gravity is still a useful piece of description, but it would seem that there actually is no such thing. — tim wood

Let's look at gravity as an example then, then, under the principles of my proposal. Let's use the word "gravity" to refer directly to a specific type of relation between two objects. We can easily avoid the descriptive shortcomings you talk about, by saying that the way we describe the observed effects of "gravity" is completely irrelevant. For example, we say that there is a specific type of relation between the earth and the moon, which we know as "gravity", and whether we describe the effects of gravity in a Newtonian way, or an Einsteinian way, is completely irrelevant to us, because we are interested in the relation itself, not the description of the relation. This is commonly known as the difference between the map and the territory. We are not interested in the map, (whether the map is Einsteinian or Newtonian), we are interested in the territory, that specific type of relation between the earth and moon, known as "gravity".

Now, to adhere to my compromise proposal, we'd have to say that this relation is either an idea, or an expression of an idea. But how could that be the case? The earth and moon, each with one's own gravity having an effect on the other, through that relation we are calling "gravity", existed long before human beings and their ideas and expressions of ideas? Such an "idea" or "expression of idea" could not be human.

This problem is the result of the restrictions on language which you are trying to enforce. You are insisting that "a relation" must be either an idea or an expression of an idea. You are refusing to acknowledge that in order to develop an adequate understanding of reality, we must allow that relations have independent existence. Do you understand, and respect this conclusion? In order to have an accurate and adequate understanding of reality, and truth about the world, we need to allow that relations exist independently from the human ideas which attempt to understand them, just like we do with objects. Objects have independent existence, and so do their relations. Therefore we must allow that relations are not just human ideas, or expressions of human ideas, that is a linguistic restriction which would render the world as unintelligible.

Thank you sir.

Yeah? How? Does the screw discuss with the engine? Or do they talk to you? What language does a screw speak? The screw and the engine - or any inanimate things - cannot partake of relationship - that can only be assigned by a being, and no guarantee the being gets it right. — tim wood

Do you think that "relation" requires communication? if one thing affects another, for example, there is a relation between them. Communication is not a requirement for a relation. The sun has an effect on the earth, the moon has an effect on the earth, and the screw has an effect on the engine. There are relations between these things.

Until you pay more attention to your own use of language, we're going to have a difficult time. — tim wood

Sorry, I have no inclination to restrict my language to suit your desires. You demonstrate severe obstinance, most likely the feature of a closed mind, which greatly limits your capacity to understand. Restricting my language in the way required for you to understand would disable me from being able to say what I want to say. This would simply leave me saying what you want me to say, so that your limited capacity for understanding could understand the things I say, within your own little world of 'how the world must be described' according to your dictates of 'the world is like this'. If you have no inclination to expand your little world to include the way that other people see the world, within your world, this type of discussion is pointless.

You are confusing yourself with language. A relation is either an idea - or the expression of one - or a thing. I don't see how a screw can in any sense have an idea, nor how it can be one, and at the same time a screw. Nor do I see how an idea can be a thing. And the screw is a part of the engine not in virtue of any idea or relation, but on the simple fact that it is. — tim wood

I don't understand this. My OED defines "relation" as what a thing has to do with another. If you believe that a thing is not just an idea (don't you?), then why wouldn't you think that a relation is not just an idea? Do you believe that the earth and the sun are things, and not just ideas? How could you believe that these two things are not ideas, yet the relation between them is just an idea? That seems so inconsistent, so as to be incoherent.

And the screw is a part of the engine not in virtue of any idea or relation, but on the simple fact that it is. — tim wood

So here, you are saying that the relation which you call "a part of", is not an idea, but a fact. So you really do believe that relations are more than just ideas. Can I have some consistency please?

I agree on this section, but did you mean artifact instead of "artifice"? — tim wood

No, I meant artifice. An artifice is a clever device. Do you not think that an engine fits this description? Maybe you are thinking of a different meaning.

Great, what do they explain? — tim wood

I gave you the example. Why don't you address it? Here, have another look:

So, let's look at the above example. There's a thing called "the engine", and a thing called "the screw". Assume we know nothing about these things just their names. Now you say that the screw is a part of the engine. I say "the engine" is an artifice, a device intentionally built, and the screw has a purpose dictated by the creator's design. Do you honestly believe that my description provides no extra "explanatory value" over yours? — Metaphysician Undercover

Look, we can describe the engine as "a piece of metal" like you did, or we can describe the engine as a piece of metal designed and built with intention. Do you honestly believe that the latter explains no more about what an engine is, than the former?

I think you make an error in logic. You have purpose implying intentional creation. P => IC. And if in fact you have the P, then you have the IC - simple modus ponens. But you infer P; you don't have it; and thus you do not have IC. — tim wood

This is not an issue of the validity of the logic, it is an issue of the truth or falsity of the premise. The premise year is a description, and any empirically supported premise suffers the same problem. There is a description, and the truth or falsity of the description must be judged. The judgement is always to some extent subjective, as is the description, the extent of which varies greatly depending on the type description.

We have a screw and the engine it's a part of. — tim wood

So, this premise needs to be judged for truth or falsity. First, we must judge, 'is that thing a screw?', 'is that thing an engine?'. Assuming we agree that the items indicated fulfil the criteria of those terms, we need to ask by what principle is one said to be " a part of" the other. I would say that "part" here implies a specific relation, meaning that one is a component of the other, such that the other is a larger item, having a number of such "parts". If we agree on something like this, we can also agree on the truth of that description.

These things themselves entirely innocent of any intention, purpose, or creation, being just (presumably) pieces of metal. So also any relation, relation itself being just an idea. Are we in complete agreement on this? — tim wood

No, we are not in agreement on this. By saying that one is a part of the other, you already include a relation. You want to deny my description, that the screw has purpose in relation to the engine, and replace it with your description, that the screw is a part in relation to the engine. Each description involves a relation between the screw and the engine, and neither description is more true than the other.

My description is just a little more detailed than yours. While you use the more general part/whole relation in your description, I proceed further in accuracy and precision in my description to say that the part has purpose. This is simple recognition that the thing you call "the engine" is also an artifice, therefore built with intention. This does not at all reduce the truth of the description. It is a simple fact that the thing you call "the engine", could also be truthfully called "the artifice". So, we simply have two different, yet both truthful descriptions of the very same thing. You say there is an engine and a screw is a part of the engine, I say there is an artifice which we call an engine, and the screw as part of that artifice has a purpose. You ought to be able to see that my description is just a more precise and accurate description of the items indicated, and the relations which constitute a part of the description.

As to freedom of choice, I merely say that, it seems to me, creation involves discontinuity, from not-being to being. And freedom necessary because no freedom, no discontinuity, no becoming. Rather instead it - whatever it is - in some sense inevitable. Which I call operation according to law. As to human freedom, you seem to hold that there is no freedom to not choose - not choosing itself being a choice. And this in this context both trivial and vapid - and counter-productive. Unless at the ice-cream parlor, you being offered a choice between vanilla and strawberry and choosing neither, are pleased to pay your four dollars for an empty dish full of neither. — tim wood

I'm going to drop this subject of freedom and choice. It's only relevant in a tangential way, and we do not need the long posts.

That's right. I hold the words "learn, intention, and will-power" in themselves have no explanatory value. — tim wood

Really? I find that highly unusual, even absurd. So, let's look at the above example. There's a thing called "the engine", and a thing called "the screw". Assume we know nothing about these things just their names. Now you say that the screw is a part of the engine. I say "the engine" is an artifice, a device intentionally built, and the screw has a purpose dictated by the creator's design. Do you honestly believe that my description provides no extra "explanatory value" over yours?

Come on now tim, does the difference between something produced intentionally, and something produced without intention have absolutely no significance to you? Have you never spent time in a court of law where intention provides great leverage with its explanatory value?

Yes, we are language-using agents, but what are we reading? Yes, we can read letters, but we can also read landscapes, speed, color as well as faces (Many of us, and to varying degrees and to certain points). Moreover, we can also 'read' our own bodies.

The problem I see with saying that things convey "no meaning" is that you are adding 'organization' post-hoc. If you have a book, but you can't read, the letters there also don't convey any meaning to you, despite the book being both intentionally and purposefully written and bound. So, if you learned how to read, you would say "oh, this is meaningful". But the meaning was already inherent in the book, you only learned how to read.

Which I don't see clash with your argument at all. I'm not arguing that atoms and matter account for the nature of experience, but that treating atoms and matter as inconsequential to our understanding of purpose and meaning, seems arbitrary at best. — Caerulea-Lawrence

I think that the is a very good approach, the differences, and similarities, of "purpose" and "meaning". Both are closely related to intention, but in different ways. And both, purpose and meaning, exist as relations, in the way I described earlier.

Suppose an author writes some material, a book or something. Communication such as this is done with purpose, as intentional, the author has goals in this act. So, from the perspective of the author, there is purpose to that communicative material, that writing. The reader however, does not access the author's intentions directly, and so does not put the material in a relationship with the author's intentions, to apprehend the author's purpose. That is why deception is possible. Instead, the reader puts the material into relations, or associations within one's own mind, to apprehend the meaning.

I suggest that this constitutes a significant difference between purpose and meaning. "Purpose" relates the observable actions, or things, which the artist is working with directly to a goal or end which the artist has in mind. This is best described as the first-person perspective, because only the author could ever know the true intentions, and therefore the purpose of the writing. "Meaning" on the other hand relates the observable actions, or things, which the artist has worked with (notice the necessity of the past tense here) to memories, habits, acquired rules and conventions, within the mind of the observer. "Meaning" is what the observer derives from the work.

So in the latter, despite the fact that we define "meaning" as "what is meant", "what is intended" by the author or artist, there is really no direct involvement with intention here at all. In this way "intention" is completely removed from "meaning", and the common understanding of "the meaning of that writing", is that there is some sort of objective way that the writing is supposed to be understood, based in some kind of rules, and "the meaning" therefore is totally independent from what the author intended, i.e. the author's purpose.

Moreover, the context is the law of identity vis-a-vis mathematics. — TonesInDeepFreeze

The law of identity in its historical form is ontological, not mathematical. Mathematics might have its own "law of identity", based in what you call "identity theory", but it's clearly inconsistent with the historical law of identity derived from Aristotle. He proposed this principle as a means of refuting the arguments of sophists such as those from of Elea, (of which Zeno was one), who could use logic to produce absurd conclusions.

Discussion with you about this is pointless because you make statements like the one above, where you acknowledge the difference between the mathematical concept of "identity" and the ontological concept of "identity", but you claim that the only relevant concept of "identity" is the mathematical one.

Of course, relevance depends on one's goals, and truth is clearly not one of yours.

What specific philosophers is the poster referring to? — TonesInDeepFreeze

Hegel for example:
https://thephilosophyforum.com/discussion/9078/hegel-versus-aristotle-and-the-law-of-identity/p1

But in the past the poster argued that therefore the axiom of extensionality is wrong, because there IS the ordering of a set. — TonesInDeepFreeze

Blah, blah, blah., so much hot air. Show us your evidence. Fishfry showed me years that there is no necessary order to the elements of a set. That's definitional, why would I argue against it?

What I argue, as I've argued for years, is that the so-called "identity" of set theory, is inconsistent with, therefore in violation of, the law of identity. And, the fact that there is no order to the elements of a set is very good evidence for what I argue. However, I do not argue that set theory is "wrong" on account of this violation, because some philosophers suppose the law of identity to be unacceptable. I argue that people like you, who insist that identity in set theory (or what you call identity theory), is consistent with the law of identity, are wrong.

So fly away now, Mr. Balloon, because you expulsions of hot air are threatening to blow the thread off track. .

We’re loosing sight of the OP. The question was ‘what is purpose, how does it arise’. My argument is that in ‘modern’ vision of the Cosmos, described by classical physics and Galilean science, purpose can only be understood in terms of intentional agents or agencies. The laws that ‘govern’ the cosmos, and also evolution, are devoid of intentionality and purpose. So it was presumed that the Cosmos and everything in it arises as a consequence of the ‘accidental collocation of atoms’ (Bertrand Russell’s term.) — Wayfarer

Newton described his first law of motion as dependent on the Will of God. What this law describes is the continuity of existence, as time passes, inertia. Things will continue to be, into the future, exactly as they have been in the past, unless a force causes something to change. What this law does is remove the necessity for a cause of the continuity of existence as time passes (the cause which Newton called God's Will), by making it something that we take for granted.

Now, when we take this thing for granted (what is expressed by the first law), the continuity of existence as time passes, then a "cause" is required to change it. This effectively removes the need for a cause of the continuity of existence as time passes (God's Will), by taking it as granted, and replacing it with the need for a cause of any change to this continuity of existence.

And now he's denying he said that sets do have a certain ordering that is the ordering of the set. — TonesInDeepFreeze

Over and over, the poster argued against the axiom of extensionality on the grounds that there is THE ordering of a set. Yes, I do remember.

And now he's denying he said that sets do have a certain ordering that is the ordering of the set. — TonesInDeepFreeze

Tones, I argued that the axiom of extensionality does not indicate identity in a way which is consistent with the law of identity, because the identity of a thing (by the law of identity) includes the order of the constituent elements, while the identity of a set (by the axiom of extensionality) does not include the order of the elements. Therefore, i conclude that "identity" in set theory, as indicated by the axiom of extensionality is inconsistent with the law of identity. That sort of "identity", found in set theory, is a violation of the law of identity. If you really think that I was arguing the opposite to this, then I'm sure you can provide a reference.

If anyone is lying, it is you in your misrepresentation of what I argued in the past. However, I do not think you are lying, I think you have difficulty understanding English. Perhaps you have been overworking yourself, being immersed in mathematical symbols for so long that you no longer understand common language.

Or are you suggesting purpose resides somehow in the engine and screw combined, you having already made clear it cannot be in either separately. — tim wood

Yes I've said this for a number of posts now, purpose is in the relation. In this example, the purpose of the part (the screw) is in its relation to the thing which it is a part of (the machine), which can be called "the whole". And I explained that this relationship is not invertible. Purpose is in the relationship of the part (screw) to the whole (machine), not in the relationship of the whole to the part. That is why we say "the screw has purpose", referencing the relation of the screw to the machine, not "the machine has purpose" in relation to the screw. The latter expression, "the machine has purpose" requires putting the machine into the context of a further relation.

My own view is that the purposes of both are inventions of a being capable of such... all being the sole property of the being and nothing at all to either the screw or the engine — tim wood

As I explained, purpose implies intention, therefore intentional creation is implied by any display of purpose. But it is clearly not the case that purpose is "the sole property of the being". If you look at the use of "purpose", in all cases it involves a relationship between things, and therefore cannot be the sole property of any being.

And here we're back in tune - I agree. — tim wood

How can you agree with this? I said the agent is independent from the purpose. But above, you say purpose is the sole property of the being. Don't these two contradict in your mind? If purpose can only be the property of the being, how can the being be independent from it? In other words, how could this property come to be in the being, if the being is independent from it and also it cannot exist independent from the being?

An engine builder (presumably) has intentions; his tools and his materials, not. And if no element of freedom in his intentions, e.g., the freedom to not intend, then it's not intentions that he has. — tim wood

This is contradictory as well. You are saying that an intentional being has the capacity to not-intend. However, to not-intend would contradict the premise of "intentional being". This is like saying that the intentional being could negate its own nature of being intentional, by intentionally not intending. But intentionally not intending would still be a case of intending. Therefore the capacity to not-intend contradicts "intentional being". This is like what they say about choosing not to choose. That's still a choice. And "choosing not to choose" is contradictory unless we separate the more specific from the more general, to give "choose" distinct references, or meanings. Therefore it's contradictory to say that the intentional being has the freedom not to intend.

Likely there are some adult English classes, maybe at night, you could take advantage of. Actually, I think you follow perfectly well, but don't want to admit it. — tim wood

To tell you the truth, I was being polite. I could only interpret what you said as contradictory. So instead of accusing you of contradiction, I was forgiving, and gave you the chance to reconsider, to express what you meant in a different, clearer way, in case the contradiction was unintentional. Since you simply reassert your contradictions I have no choice now but to tell you why I cannot understand. What you say is contradictory, and your contradiction appears intentional. That makes understanding impossible.

Nope, and neither should you. Yours a categorical statement, when at best it is contingent and speculative. — tim wood

You agreed that intention is the cause of purpose. Why is it that you cannot agree that when we see purpose, there is intention behind it? If you think that something else, other than intention might cause the purpose one observes, then you ought to disagree when I say that intention is the cause of purpose.

No. Intention, if intention is anywhere, is in the mind of the intender, and any purpose therefrom his purpose. The trouble is that we can suppose intention where there is none, and infer purpose wrongly. — tim wood

Wait, slow down, you're going off track and inverting things unnecessarily. You agreed that Intention is the cause of purpose. Then you said intention is in the mind of the intender, and I would agree to this. And because intention is located there, in the mind, it is only evident to oneself. My intention is only evident to me, and your intention is only evident to you Do we agree so far?

However, what you don't seem to accept, is that we find purpose in the world around us, like the screw has purpose in the machine. Further, since you accept that intention is the cause of purpose, you should see that whenever we find purpose in the world, we can infer intention as the cause of that purpose.

So, we do not "suppose intention" and then "infer purpose". We observe empirical evidence of purpose, as in the case of the screw in the machine, and from this empirical evidence we infer intention. We conclude that the machine was constructed intentional from the evidence of the purposeful relations of the parts to the whole, like the screw, as one such part The other way around, to suppose intention and then infer purpose would be pointlessly misleading, because we would not know when to assume intention, because it is hidden from us.

Since you agree with me, that this way is misleading, you ought to also agree that the other way is far more reliable. we observe purpose and infer intention. And this is because we can observe purpose, in the relations of things. We see it in the relation between the screw and the machine, for example.

I don't think dogs or whales have human intent, nor humans doggy or whale intent. But human intent can only come from humans. — tim wood

Of course, only human beings have human intent, that's tautological. To call it human intent is to say that a human being has it. However we find that other animals have intent. We can observe purpose in their actions and conclude that they have intent, in the way described above. But what would be the point of trying to distinguish human intent from the intent of other animals? Intent is very particular, specific to the individual. Your intentions are completely different from my intentions, as intentions vary substantially between one individual and another. So distinguishing "human intent" from "whale intent", would be at best completely insignificant, but most likely just arbitrary.

If not a being, and necessarily a particular being by type, human for human, eagle for eagle, etc., then what? — tim wood

I don't know what. That's the very problem I exposed at the end of the post. We really know so little about the nature of intention, that we cannot make any conclusions about what sort of subject is required for the predication of "having intention". We know from personal experience, that humans have intention, and we know from observation of purpose, that other creatures have intention, but we do not have anything to demonstrate to us the limits of intention, i.e. where it may and may not be.

Intention? Will power? Learn? For babies I do not think any of these terms are either well or meaningfully defined. Certainly they have no explanatory value, except perhaps as a naming of convenience for a result for which there is no good account. — tim wood

What!!? I am shocked and amazed at your naivety. You think "learn" has no explanatory value in the behaviour of babies? You think "intention" has no explanatory value in the behaviour of babies? You think "will power" has no explanatory value in the behaviour of babies? I conclude, that in your mind the behaviour of babies is simply unexplainable.

Maybe you could provide a clearer view of your perplexity? My own view is that an individual "gets purpose from a higher organization" through a process akin to consumption and digestion. — tim wood

Do you see, that you agreed with me, that intention is the cause of purpose? You ought also agree therefore, that where there is purpose, there is intention as the cause of that purpose. Therefore purpose is not acquired through a process like consumption, it is given, caused, by the actions of an intentional agent. Think of the screw and its purpose in the machine. The intentional agent who manufactured the machine, gave the screw its purpose. So, if the individual human being has purpose in relation to a higher organization, such as a family, business, community, society, or humanity in general, where is the intentional agent which gives this purpose to the individual?

These posts becoming long and exhausting. We should try to keep it simple and short. Given how we have proceeded with purpose and intention, I wonder if you care to reconsider your definition of teleology, here: — tim wood

Why? That definition appears consistent with what i am saying, What would be the purpose of redefining at this point? We haven't agreed on anything very conclusive.

Still interested in what is supposed to be the inherent ordering of a set such as the set of bandmates in the Beatles. — TonesInDeepFreeze

If this is addressed to me, please clarify what you are asking..

By the way, I never said that a set has an inherent order. I acknowledge that a set does not have an inherent order, and that is a problem for the "identity" of a set. A thing has an ordering of its parts as a feature of its identity, covered by the law of identity.. And that's why the "identity" of a set is inconsistent with "identity" by the law of identity. Do you remember now?

But that has no bearing on the principle of division. — TonesInDeepFreeze

Yes it surely does have bearing on "the principle of division". If, the principle of division indicates that when we divide a 6 kg item into two equal parts, we will have two pieces of 3 kg, yet when we repeatedly carry out the procedure, the closest we can get is two parts of 2.99999 kg, then the principle of division is proven to be false. It would be a theory which has been falsified by empirical evidence.

This intention, and indeed "the whole," will you assay quick definitions? — tim wood

As Plato demonstrated in the Theaetetus, some words are best left undefined until after the appropriate meaning is worked out through the dialectical process. So I'll leave these definitions for now, and hope that we can work out the meaning of these through discourse.

Thus given a machine - a whole - the purpose of the screw can be worked out, its relation as part to whole. But given just a random screw, its purpose is indiscernible. And further, in its purpose being fulfilled, the screw has zero choice; that is, in terms of the purpose articulated, if the something itself is without choice, then the something in itself has no purpose. - And this pretty much what you have already defined. — tim wood

I agree that the random screw, in that description, has no purpose, that's what the predication "random" implies. As I said, purpose is a feature of a things relation to something else, and "random" implies without any order in those relations. In the example of the screw and the machine, it is the relation of part to whole which gives the screw purpose. In many cases it is in the relation of the means to the end which gives purpose. The end gives purpose to the means, but the end is not necessarily a "whole". We call the end an "object" as a goal, that is not exactly the same as a whole.

I do not understand the relation between choice and purpose which you are outlining. "A thing", whether it is an act which is the means to an end, or a physical object like the screw, is given purpose by an intentional agent, but this does not mean that the act itself (the means), or the thing itself (the screw) has choice. Choice, and the agent who chooses are independent from the purpose. That is why choice is "free" in the sense of freely willed. Purpose follows from the freely willed choice, it is not prior to it.

As to intention, if there be such, then there must be (another) such that has it - presumably a being of some kind. And again I invoke freedom. If there be such a being, it must be free to not intend, its choice to intend being therefore a free choice. Of such beings, they either are or are not - this simpler than may seem at first. If it is, then there are applicable predicates: it is. If it is not, then no predicates apply, and it is not. — tim wood

I cannot follow this dialectic. I don't see the relation between intention and being which you start with. Nor do I see the relation to freedom. And the rest seems right out of place.

Can we agree that "intention" is the cause of purpose? Wherever we find purpose we can conclude that there is intention as the cause of that purpose.

We know that human beings have intention, and their acts are known to have purpose. So every time we observe a human act which appears to be purposeful, we conclude that there is intention behind the act, as the cause of the purposeful act. The intent is not necessarily evident to us. Do you agree, that anytime we distinguish purpose, there must be intent behind the thing we observe as having purpose, like the screw in the machine? And do you agree that the intent is not necessarily the intent of a human being, there could be other sources of intent? Therefore we cannot associate intent with "being" as you propose. We do not have the evidence required to limit "intent" in that way.

Freedom/choice important because without it, purpose dissolves into operation according to law. The engine maker doubtless has many intentions, and purposes many things for the parts of his engine, but the parts themselves (presumably) operate in accord with laws appropriate to them themselves. — tim wood

Freedom/choice have a special relationship with intention, I agree. But I think we need to make one more step of separation now, to include the agent itself. The agent (not necessarily a being, as explained above) has freedom/choice, and the agent also has intention, but these two (freedom of choice, and intention) are distinct. They must be distinct because intention is toward a particular end, will freedom of choice is directed toward no particular end. So the agent has both, freedom to choose an end, and also already chosen ends, as intentions.

Now to jump ahead into what I think the issue is. Does every free being have a purpose? Trivially yes, many. Ultimately, only as self-legislated. By "self-legislated" I mean arrived at by a process of reason. Absent which, the being has no (ultimate) purpose. — tim wood

So, I suggest you try looking at things this way, tim. Let's consider an individual human being as an agent. This type off being has many wants, needs, and desires. It also has freedom of choice. As a manifestation of these two distinct features, desires, and freedom of choice, the being develops intentions, which are particular goals or objectives. Intentions are derived from a combination of desires and of freedom of choice. But the being is hindered by things which are impossible.

Let's start with the human being as a baby. The baby wants all sorts of things, and some, like walking and talking are immediately impossible, but the baby, through intention and will power can learn and earn the capacity to talk and walk. Other things, like flying, are recognized as more absolutely impossible, due to physical constraints. So the freedom of the human individual is restricted by physical constraints, though some may be overcome. However, there is also social constraints like laws, which restrict one's freedom in a different way.

Consider that the human person grows to respect these different constraints as different forms of impossibility. Now the adolescent is free from many social constraints, in many ways, not being constrained by many responsibilities that adults get into, like a chosen career, a mortgage, credit card debt, a family to support, etc.. So the adolescent has much freedom to chose, and formulate intentions in a wide variety of ways. The intentions, goals and objectives are the property of the individual, and the individual's actions have purpose relative to those intentions. This is principle #1, what the individual does, has purpose relative to the individual's intentions, and the individual has freedom to choose one's intentions (being influenced by various desires, wants, and needs, as well as impossibilities).

Principle #2 is that the individual has a desire or need for relations with others. This puts the person into the context of a part of a larger "whole". The larger whole being a family, a team, a business, company, or society in general. As a part of a larger whole, the person has purpose in that relation. Now, not only does the person's actions have purpose in relation to that person, but also the person has purpose in relation to this larger entity.

The person is intermediary now. One's actions have purpose in relation to the person, and the person has purpose in relation to the larger organization. When we say that human beings are "rational animals" it is implied that the person will prioritize the purpose one has in relation to the larger entity over the lower purpose one gives to one's actions through one's own intentions.

But this presents a significant problem. Strictly speaking, the person's actions have purpose relative to the person's intentions, and that's how we understand purpose, as relative to intention. So when we understand that the person has purpose relative to a larger organization, it is more proper to understand the purpose in relation to the intention of the larger organization. But how do we understand this intention? An entity such as a family, a team, a company or business, or society in general, is not the type of thing (a being for example) which we would think of as having intention. Because of this, the way that a person gets purpose from a higher organization is very perplexing.

No word games, please! I am quite sure the screw itself possesses zero purpose. — tim wood

It seems you're the one playing word games, attempting to put an unnecessary restriction on the use of "purpose". Do you agree that "purpose" means "thing intended"? And do you not understand that there is something intended for the screw in relation to the machine that it is a part of? Therefore the screw has a purpose, and is purposeful.

If you are talking about some sort of inherent purpose, which would be intrinsic to the screw, I've already told you that purpose does not exist in that way. It exists in the thing's relation to something else. In this case, the screw has purpose in relation to the machine. Be careful in understanding this relation, because it is not invertible. Purpose exists in the relation of a part to a whole, and not in the relation of the whole to the part. We cannot say that the machine has purpose in relation to the screw.

As to our screw, no doubt a someone or someones intended it for something, which we can call its purpose. But that "its" cannot be used to attribute anything to the screw itself - being just language of convenience. — tim wood

You're very wrong here. The part of the whole, which is named "the screw", has a very particular purpose assigned to it, and only it. Therefore the purpose is attributable to that part, and it alone. It does not matter that the manufacturer chose one particular screw from millions of similar possible choices, the purpose is assigned to that particular one, through the actions which followed from that choice.

You can call this "language of convenience" if you want. But since it is the only way that we have to talk about the intention which is responsible, as cause, for that particular screw's position in the world, it is a way of speaking truth about the object's context within a larger environment. The screw was put there as part of an intentional act, and the purpose is in the part's relation to the whole, not the whole's relation to the part, therefore we attribute "purpose" to the part.

But I think you do use and understand teleology to do just that, attribute to things and beings themselves that which they do not and cannot have. — tim wood

It's very clear to me, that the screw, as a part, has purpose, in relation to the machine, as the whole. If you insist on denying the truth and reality of this predication "the screw has purpose", then how would you propose that we could proceed toward understanding the intention behind the relationship between the parts and the whole?

OK. So I guess measuring an object would count as "distinguishing different parts" of it even if the line that I draw does not correspond to any pre-existing difference or discontinuity in the object. — Ludwig V

I don't understand this at all.

The poster claimed that I equivocate about this. On the contrary, I am clear of quite clear of the distinction and none of my comments employ any equivocation regarding it. — TonesInDeepFreeze

The problem is, that when we divide a material object such as a pie, in half, it is never a perfect division with two perfectly equal parts. There is always some degree of approximation. Dividing in half in mathematics is perfect, no approximation. Therefore "half" has a different meaning in the theories of mathematics, from the meaning it has in practical usage. So your example of dividing a pie, which necessarily involves an approximation, to demonstrate "half" in the context of theoretical mathematics, which is necessarily a division of perfect precision, is simple equivocation.

The paradoxes discussed don't require splitting material objects. — TonesInDeepFreeze

This is exactly why your example of dividing a pie in half, is a case of arguing through equivocation.

We're going to need your definition of "cause." — tim wood

That which produces an effect, where "effect" is the result or consequence of a cause. In other words, when something occurs as the result of, or consequence of another thing, that other thing is the cause.

Also you appear not to distinguish between purpose and purposeful. A screw in a machine has a purpose, but it would be a kind of animism to suppose it - the screw - to be purposeful. — tim wood

I don't understand the distinction you\re trying to make. If a thing has a purpose then obviously that thing is purposeful. A screw in a machine, was put there for a purpose. It has a purpose, therefore it very clearly is purposeful, "purposeful" meaning "having purpose". And this is not "animism".

And I would appreciate it if you would provide your distinction between function and telos. — tim wood

"Function" is the activity by which a thing fulfils its purpose. We can say that "function" is the means to the end, and "purpose" is the end. Both are subjects of teleology.

To me, function is what-it's-for, and if we're lucky, how it does it. — tim wood

Put it this way, "what-it-is-for" is its purpose. How-it-does-it is its function. Can you see how the purpose is the end, and the function is the means to the end? The goal, or end, (the purpose), is the object, or desired state, while the means (function) is the activity which is supposed to bring about the realization of that object,

Above you have telos being about relation and thus not being in the thing, the relation being "between" the thing and its purpose - not sure exactly what that means, or what you're trying to say. If telos is just another word for purpose, and if by purpose is meant function, then it should not be too difficult to note where the words are used beyond their sense. If telos is somehow the purposefulness - intention - of something able to have such a thing, then that is imho, the issue - what would be that thing. — tim wood

I didn't speak of "telos", I provided a definition of "teleology".

Eh? How does this work? How or why is efficient cause deterministic? — tim wood

I think the nature of efficient cause is irrelevant at this point, and a different subject altogether, so I'll leave this question.

..the materialism pushed by the so-called 'ultra-darwinists', which sees everything as being explicable in terms of physical laws... — Wayfarer

And, I might add, when it comes to the difficult question of what is at the bottom, the foundational cause, "physical laws" always fails in explanatory capacity. So, they end up falling back on chance, with concepts like random mutations, abiogenesis, symmetry-breaking, etc..

But disagreement here. Going North didn't cause anything. Being North, they either adopted or died. Nor did I say that the going caused anything. And their choice incidental. — tim wood

Of course going north was causal. It caused them to be in those conditions. The conditions you describe as required to be "either adopted or died". You appear to be refusing to acknowledge that animals choose which direction they go, and their is purpose behind their travels. Since animals are in general, free to wonder, there must be a reason why they would choose to put themselves in an 'adapt or die' situation. This reason for them doing this is causal, though you deny it.

That's correct: teleological explanations explain phenomena in terms of their purpose, rather than in terms of their antecedent causes. It seems a minor difference but a lot hinges on it. — Wayfarer

I think that this is a misrepresentation. Teleology looks at purpose as causal. This is final cause. To portray a dichotomy between teleology and causality is to fall into the determinist trap of scientism, in which final cause, intention, free will etc., is excluded from the category of "causal". This restricts "cause" to efficient cause, making the world deterministic.

.

I said that the two painted halves do not become objects in their own right, meaning separate, distinct objects. You may argue that this is not dividing the pipe, or that each half becomes a distinct object. I don't mind what you choose. This shouldn't be too difficult for you, since you said earlier:- — Ludwig V

Oh, I misunderstood. You are painting the pipe without dividing the pipe. I guess we don't mean the same thing with "divide". I think of "divide" as "separate or be separated into parts; breakup; split". This is why I say that to divide something in two makes two distinct objects, because they are separated, each with its own centre of gravity.

But painting the pipe shows that it depends what you mean by "divide" and/or "object". — Ludwig V

I would say that painting a pipe two different colours is not a case of dividing the pipe. To use your terminology, you are distinguishing two halves without separating them. This does not qualify as "dividing". When I look at an object I can distinguish different parts of the object, and even draw lines on its surface, and all this is done without dividing the object.

I've learned from past experience that you get annoyed when I do not answer your banal questions. So I'll give it a go.

"I should like to start by asking," what, exactly, you think teleology is. In particular I'm interested in whether you will say that the telos of a thing a) is a (some)thing, and b) is in some way intrinsic to but separate from the thing. — tim wood

Teleology is a way of studying things which looks at things in relation to purpose, reason for being. Accordingly, the telos of a thing can never be intrinsic to the thing, as purpose is defined by the thing's relation to something else, for example its function in a larger whole.

My bias is that for individuals becoming what they are is just the operation of law with occasional mutation - the kitten becomes a cat and never a horse. As for the evolution of species, that the operation of both law and chance, with occasional mutation. This group goes North and develops characteristics favorable for living in cold, that group South, and for hot. And those that do not, die.

Or are we in agreement, with just different words? — tim wood

I don't think we are in agreement. You've left out the teleological aspect. Why did this group go north, and that group go south? See, you say that going north, or going south, caused these groups to develop "characteristics favorable" to those areas, but you neglect the fact that they choose to go in those directions, so they already had characteristics which made them favour those areas, prior to going.

And that if I paint half the pipe blue and half red, the halves do not become objects in their own right, but remain halves of the same pipe, even though they are of different colours. — Ludwig V

Why do you say that the two gutters are not distinct objects. A gutter is an object. Or do you not think so? Even if we call them halfpipes, the two are still separate objects. And if we can't even think of a name for them, we acknowledge that they are no longer united as one object, but are now two separate objects. Division of an object does not necessarily produce two new objects that are of the same type as the original, in fact it often does not. So there is no need to think that dividing a pipe ought to make two pipes. However, dividing an object in two always produces two new objects (as well as the waste material). The "waste" becomes an important feature often overlooked in systems theory and the conservation energy, as energy lost to inefficiency or entropy. But the fact of waste in any act of division nullifies the validity of the supertask.

@TonesInDeepFreeze
This is the issue which Ludwig and I have been discussing. "One half" in practise does not have the same meaning as "1/2" in theory.

The pie is cut in half and placed in two different wrappings, as two different things, going to two different places. That these two different things were at one time united in a single source is irrelevant to the fact that after division they are two distinct things with two distinct centres of gravity.

The fact that we call the two things "halves" is just a feature of common vernacular. We know that they are not really each exactly a half, by any strict logical principles. It's just an approximation. Likewise, if we measure two things as 420 kg, we say that they are "the same weight", even though there is a discrepancy of a few grams here or there.

You argue by equivocation, confusing common vernacular with the logic of mathematics. If 1/2 in mathematics was allowed to be imprecise, as the baker cutting the pie in half is allowed to be imprecise, the problem of the op would not arise.

I see no place for formal or final cause in the context of science. — Janus

If we want to understand our own existence, it is necessary. The trend, when Darwinist evolutionists separated themselves from Lamarckian evolutionists, and ridiculed Lamarck, was to ignore the purposefulness of living actions as a cause of evolutionary change, accepting instead "chance" as a proper cause of variation in living beings. However, these biological assumptions create the rift of understanding between conscious intentional actions of human agents, and purposeful actions of other living creatures.

Now, intentional activity is relegated to the social sciences, and there is a separation between these social sciences and the proper science of biology. The rift has been created by the way that empirical evidence is valued and assessed, which dates back to Darwinism. "Purpose" is effectively excluded from science proper, as unobservable. However, it is a necessary subject of social science. This creates the separation between "purpose" in the actions of human agents, and "purpose" in the actions of other living creatures, which I referred to in my last post. We place human beings on a pedestal, being "agents of intent", subject to law and social conventions, separating them from other creatures, and in doing this we provide no principles to show how conscious intention along with laws and social conventions, are just an evolutionary progression from, (an extension of), the purposeful acts of other living beings.

Then, must mathematics not allow smaller numbers? — TonesInDeepFreeze

Smaller numbers are not needed. This idea simply produces unnecessary complications. When you divide one thing into two, you get two things, not two halves. The idea that you get two halves when you divide one thing into two, rather than getting two new whole things, causes the problem being discussed in this thread

So, if someone claims that the mathematics is to blame, then we would ask whether the mathematics itself (which holds that there is no smallest number) needs to be rejected, or whether the way in which the mathematics is applied needs to be rejected, or both. — TonesInDeepFreeze

Yes, I do believe that the mathematics needs to be changed, for the reason given above. The issue, (as I stated earlier in the thread), is that division presupposes an entity or object to be divided. And, divisibility is dependent on the type of thing to be divided. Therefore, when it comes to division one standard does not fit all things, and the principles of division must be specifically designed for the different type of things to be divided.

Maybe some mathematicians like to think that "a number" is a type of thing, or object, and that there is no limit to the way that this type of object may be divided. But I think that's just a mistaken idea.

It is unusual to say that difference proves theory to be wrong. — Ludwig V

Why do you say this? Doesn't science proceed through the falsification of theories?

I would be happy to say, I think, that Zeno's application of the theoretical possibility of convergent series to time and space and the application in Thompson's lamp is a mistake. — Ludwig V

You don't go as far as me then. I say that infinite divisibility is a mistake.

But calculus does have uses in applied mathematics, doesn't it? — Ludwig V

Of course, we need to distinguish between truth as our goal, and pragmatics, which doesn't have any specific goal. Usefulness is relative to the goal, and the goal could be anything. I don't deny that calculus is extremely useful, but that usefulness may be misleading relative to the goal of truth.

Non-dimensional points which have a dimensional separation? H'm. — Ludwig V

Don't you agree, that this is the only way in which one point may be distinguished from another point, through a spatial, or dimensional, separation?

But then a boundary (between your property and your neighbour's) doesn't occupy any space, even though it has a location in the world and will consist of non-dimensional points. — Ludwig V

This is the way I understand boundaries between two pieces of private property. The boundary exists in theory as lines of two dimensions, or sometimes even three dimensions because elevations need to be accounted for. In theory, the line occupies no space. In practise though, the boundary becomes a fence, a disputed sliver, or something like that, and ends up actually occupying space.

So if you and I had a shared boundary, on paper the boundary would be described as occupying no space, you on one side, I on the other, and that would be the theoretical boundary. But in practise, there would be an area, known as the place of the boundary. Even if there is pins, and we stretched a string from pin to pin, the string occupies an area. And so does the pin occupy an area.

Isn't the difference that one is consciously intended, and the other isn't? Isn't there a valid distinction to be drawn between conscious purpose and the autonomic system? One does not have conscious control over how fast your hair grows or your peristalsis. — Wayfarer

I would say that this is acceptable as a proposal worth reviewing; i.e., the proposition that there is a valid distinction between conscious intention and an "automatic system" of a living creature. However, I would also argue that upon analysis such a theoretical distinction cannot be upheld in practise. This is because the supposed separate activities of the nonconscious (automatic), and the conscious, are constantly interacting as is well known to psychologists.

The brain creates patterns of activities which we might associate with 'habits', and even though they may originally be produced through conscious intention, these patterns, in the process of habitualization, become automatic. So there is a very close relationship between the supposed conscious and non-conscious, which makes it impossible to actually separate the intention of one from the intention of the other (intention acting in a hierarchical way as described in Aristotle's Nichomachean Ethics). There are all sorts of examples to support this.

From the side of conscious intention leading the way, consider that you decide on an activity like walking. Once the decision is made, and the act initiated, the habit (automatically) kicks in, and your legs start working in the way that you've learned. From the side of the nonconscious leading the way, consider dreaming as nonconscious. Then look at the way that sensations, sounds heard for example, may enter into the dream. Are you familiar with lucid dreaming?

Now, the issue is that since intention is hierarchical, if we propose a distinction between conscious and nonconscious intention, which one actually leads the way? The conscious mind thinking about this problem might be inclined to assign ultimate authority to itself, and this I believe is the perspective of libertarian free will. A scientist though, is inclined to observe from the outside in, seeing causation in the determinist way, making nonconscious automation the highest principle. It's a conundrum now. Therefore, I conclude that this proposal, to make a distinction between conscious and nonconscious intention is misleading, creating an unresolvable conundrum, and in reality the supposed two must be reduced to one general intention, as the guiding principle. The nonconscious is actually, in reality, prior, higher, and this may be revealed in mystical experiences.

Anyway, here's the 'meta-philosophical' point. That as our culture is individualist, we tend to conceive of purpose and intentionality in terms of something an agent does. Purposes are enacted by agents. This is why, if the idea of purpose as being something inherent in nature is posited, it tends to be seen in terms of God or gods, which is then associated with an outmoded religious or animistic way of thought. I think something like that is at the nub of many of the arguments about evolution, design and intentionality, and the arguments over whether the Universe is or is not animated by purpose.

This Forbes Magazine article just came up, on Dennis Noble’s quest to have purpose admitted back into biology — Wayfarer

This is exactly the problem. Our society has revolted against religion, attempting to remove any principles seated in religion from its codes. This has disassociated the intention (purpose) of conscious action from the intention (purpose) inherent within other living creatures. We cannot associate "intention" with other living beings, because that intention would be sourced from God. So the modern trend is to associate "intention" with the moral responsibility of conscious agents only. This I believe is actually quite modern because standard definitions of "intention" refer only to purpose, but the idea that "intention" is associated only with conscious acts is very pervasive in common usage.

The result is that now we have created a separation between the intentional acts of conscious agents, and the "purposeful" acts of other living creatures. But in truth, to understand biology and all the various activities of the multitude of living beings, along with the process of evolution, we need that continuity, between the purposeful acts of other living creatures, and the intentional acts of human agents. In reality, the intentional acts of human agents are just an extension, another specific incidence, of a purposeful act of a living creature.

The surfaces of the objects around me look as if they are continuous. — Ludwig V

Isn't that surface itself an edge, a discontinuity? And isn't it true, that what you see (sense) is actually a discontinuity, and you think it to be a continuous surface? I suppose, that you might think that within the confines of the edge, there is continuity, but look closer, and you'll see colour changes, texture changes, and other deformities which indicate discontinuity within the surface.

Only if space is infinitely divisible and they are not physical sensors. And you say in the quote below that a sensor is a material object. — Ludwig V

Is this directed at me, or Michael? I maintain that a sensor is a material object consisting of components. The proposition of a non-physical sensor is incoherent.

What do you mean by "actually"? Take any natural number. It can be divided by any smaller natural number. The result can be divided by that same number again. Without limit. — Ludwig V

What I meant by "actually", is what can be carried out in practise. Your example is theory. Anything is infinitely divisible in theory. You see an object and theorize that it can be endlessly divided. But practise proves the theory to be wrong. That is the point in me asking the question of whether you know of anything which is actually infinitely divisible. This would provide evidence that the theory is not false. However, in reality, all attempts have led to a falsification of that theory of infinite divisibility. So what you have stated as your example is just a false theory.

Whenever concepts are defined in relation to each other, they can be distinguished but not separated. Distinguishing is in the head, separation is in the world. Examples of inseparable distinctions are "up" and "down", "north" and "south" (etc.), "convex" and "concave", "clockwise" and "anti-clockwise", "surface" and "object" (in cases such as tables and chairs). — Ludwig V

Aren't you making a category mistake here? If separation is in the world, and distinguishing is in the head, then your examples up/down etc., are examples of distinctions, not separations. It is a category mistake to talk about these as "inseparable" by the terms of your definitions, separable and inseparable would apply to the category of things in the world, while distinguishable and indistinguishable apply to what's in the head.

Here is your statement again. I'll ask the question in a different way, using the definitions you've provided.

And when we describe the principle of distinction between non-dimensional points on a line, we find that our counting is endless. The surprise is entirely due to mistaking non-dimensional points for a physical object - thinking that we can separate them, rather than distinguish them. — Ludwig V

What is "the principle of distinction between non-dimensional points on a line"? How would you distinguish one point from another, except by location? But location is dimensional, and actually a separation. There actually is no distinction between one point and another, they are all exactly one and the same, by definition, each point is the very same point as another point, if they are supposed to be things. The only thing which makes them not the same is a dimensional separation, the idea that they are supposed to be at different locations in the world.

What empirical data do you have in mind? — Ludwig V

The physical evidence, is that we cannot just keep dividing something forever. There is nothing which provides us with the capacity to keep dividing it. The continuum of mathematics is not consistent with any sense evidence.

You seem to be saying in the first quotation that the assumption that space and time are continuous gives rise to the problem of infinite divisibility and in the second that the problem of infinite divisibility gives rise to the problem of infinite convergent series. — Ludwig V

I would say more, that the assumption of infinite divisibility gives rise to the idea of continuity, and the idea of continuity supports the idea of an infinite convergent series. So, to state it simply, the infinite convergent series is the result of, or produced by, the way that calculus deals with continuity. And we need to deal with continuity because we assume that some things (space and time) are infinitely divisible.

The root problem, I claim, is infinite divisibility. From this is derived the concept of "continuity", "continuum", and calculus deals with the continuum by applying the infinite convergent series. Since infinite divisibility is a bogus concept, the whole thing is a problem.

But I agree with you that the convergent infinite series is a possible representation of certain situations. (I would call it an analysis, but I don't think the difference matters much for our purposes.) All I'm saying is that it doesn't give rise to any real problems unless you confuse that representation with the cutting up of a physical object. — Ludwig V

It's not an analysis, but a hypothesis. Infinite divisibility is a theory. And, it does give rise to real problems, as is the case when the representation is not true,

Because the cheese is a physical object and the space is not an object and not physical. You seem to be saying the same thing here:- — Ludwig V

The point is that "space" as a concept, and "time" as a concept, are both derived from our experiences of sensing the world. Kant was wrong to say that these concept are somehow prior to, as necessary for sense experience. Since these concepts are derived from our experiences, then whenever they differ, or are incompatible with our experiences, they are faulty.

I recognize and uphold the difference between the physical things, and the concept, but I also affirm that when the concepts do not conform, there is a problem. So, cheese is like any other physical object, it is not infinitely divisible. The concept of "space" allows for infinite division, but that's inconsistent with the physical world, which "space" is supposed to provide a representation of, so there is a problem.

By the way, nobody is worrying about the fact that we cannot picture an infinitely divisible continuum. — Ludwig V

Speak for yourself.

The surprise is entirely due to mistaking non-dimensional points for a physical object - thinking that we can separate them, rather than distinguish them. — Ludwig V

What do you mean? What is this difference between distinguishing and separating?

Although I don't agree there is a problem with "infinite divisibility"... — jgill

Well.do you know of anything that's actually infinitely divisible?

It was claimed that certain ideas in physics are mixed up because of importation of certain mathematics. What are some specific examples of published work in that regard? — TonesInDeepFreeze

Th Fourier transform and the resultant uncertainty principle.

We frequently (in the context of sf fiction, for example, imagine faster-than-light travel between the stars. — Ludwig V

I would not call that "imagining". Like the "round square" it's simply a case of saying without imagining. An author can say that the space ship moves from here to there in a time which implies faster than the speed of light, but to imagine faster than the speed of light motion requires imagining a material body moving that fast. That body moving that fast, could not be seen, and therefore cannot be imagined.

Or consider Michael's two-dimensional sensors? — Ludwig V

Much of what is said in this thread, and supertasks in general, involve this problem, saying things which cannot be imagined. It's easy to say things which cannot be imagined, and we justify these things through logical possibility, but when logical possibility conflicts with empirical principles, then we have a problem.

The problem for me, then, is that I do not see a relevant difference between "+1" and "<divide by>2" or "divide by>10". (The latter is embedded in our number system, just as "+1" is embedded in our number system). — Ludwig V

They are completely different principles. You're comparing apples and oranges, and saying 'my comparison is relevant because they are both fruit'. We are not talking about "our number system" in general, because that is not the problem. We are talking about a very specific problem which is infinite divisibility, not the general "fruit" (number system) but the specific apple (infinite divisibility).

I agree with you that the problem arises in applying mathematics to the physical world, specifically to space and time. — Ludwig V

The problem is exactly what @Michael has been insisting on, the assumption that space and time are continuous. This supports the principle of infinite divisibility. The problem though is that space and time are conceptions abstracted from empirical observation, how material things exist and move, and the (unimaginable) mathematical conception of an infinitely divisible continuum is not consistent with the empirical data. Hence the Zeno type paradoxes.

But if that's your problem, you ought to have a difficulty with "+1", because there are an infinite number of non-dimensional points between my left foot and my right foot whenever I take a step. Or are you thinking that "+1" involves adding a physical object to a set of physical objects? — Ludwig V

Why does "+1" need to imply anything other than counting? There is nothing between one and two in the act of counting, yet they are distinct. We need to account for that distinction. What separates one from two? When we describe this principle of separation we also provide ourselves with the basis for division.

If you don't have a problem with that, I can't see why you have a problem with a infinite convergent series. — Ludwig V

The problem is not "infinite convergent series". That is a misrepresentation which has occurred over and over again on this thread. The "infinite convergent series" is a particular mathematical idea which has emerged from a proposed solution to the problem of infinite divisibility. The problem arises when people believe that the infinite convergent series is the necessary outcome of the problem of infinite divisibility instead of seeing it as one possible representation.

If you don't have a problem with that, I can't see why you have a problem with a infinite convergent series.
There are real practical difficulties with the idea that a cheese can be cut up into an infinite number of pieces (which could then be distributed to an infinitely large crowd of people). I don't deny that. But dividing the space that the cheese occupies into an infinite number of pieces is a completely different kettle of fish. — Ludwig V

Why do you say this? The cheese is an imaginable, sensible object. The conception of "the space that the cheese occupies" is completely dependent on, and therefore abstracted from that empirically observed cheese. Why therefore, do you conclude that we can do something more with the space than we can do with the cheese?