I say it does. I think you're splitting hairs for the sake of argument. — Wayfarer

Are you serious? As human beings, you and I are equal, based in a principle of equality. Clearly we are not the same. A judgement of equality is based in a principle of measurement, volume, weight, temperature, species, whatever. It allows that two distinct things are equal, by the precepts of the principle. They are the same volume, or the same weight, the same temperature, or the same species. Notice how in the concept of "equal", "the same" is qualified so that it is what is attributed to the thing, volume, weight, etc., which is said to be the same, not the thing itself. Under the law of identity, a thing is the same as itself. So it is impossible that two distinct things are the same thing, as we say that two distinct things are equal. By that law, we can only use "the same" to refer to one and the same thing, the very same thing. This is not a matter of splitting hairs, there's a fundamental difference between two distinct things which are the same in some way (equal by that principle), and one thing, of which no other thing can be said to be the same thing as.

My mind has blocked them out as traumatic experiences. — fishfry

On the basis of that statement I am concluding that proceeding with any discussion with you on this matter is pointless because your mind is liable to block out anything I write.

What's incoherent is you objecting to 4 = 4 as an instance of the law of identity — fishfry

You obviously do not know the law of identity. I had to spell it out for you already. You objected, and offered some axiom of equality which is obviously not the law of identity. This statement above, indicates that you clearly did not take the time to learn it yet. From what I learned last time, until we agree as to what the law of identity stipulates, further discussion on this issue is pointless.

In a given mathematical context, a given symbol holds the exact same meaning throughout. — fishfry

So the issue is, in the context of mathematics, does = mean equal to, or does it mean the same as? I'm sure you can grasp the fact that you and I are equal, as human beings, but we are not the same as each other. Therefore, I'm sure you can accept that equal to has a different meaning from the same as. Which does = symbolize in the context of mathematics?

Hard to believe there are two people who assert this nonsense, not just you alone. — fishfry

Reason is contagious, it tends to catch on. Notice that the op agrees with me as well. And, I think jgill agreed with me on this point in that other thread as well. I don't understand why the obvious appears as nonsense to you. It's very clear, that if 1 always referred to the same object we could not make 2 out of two instances of 1, we'd always have just one object symbolized.

By the way there is a standard formalism for obtaining multiple copies of the same object, you just Cartesian-product them with a distinct integer. So if you need two copies of the real line RR, you just take them as R×{1}R×{1} and R×{2}R×{2}. It's not that mathematicians haven't thought about this problem. It's that they have, and they have easily handled it. As usual you confuse mathematical ignorance with philosophical insight. — fishfry

It doesn't matter how you formalize it, the point is that it violates the law of identity. "Multiple copies of the same object" is exactly what is outlawed. You can rationalize your violation of any law however you like, but it doesn't change the fact that you violate the law. You can show me a thousand objects, and insist that according to your axioms they are all one and the same object. So what? All this indicates is that your axioms are faulty.

In any event, you avoided (as you always do when presented with a point you can't defend) my question. If set theorists are not only wrong but morally bad, is Euclid equally so? You stand by your claim that set theorists are morally bad? Those are your words. Defend or retract please. — fishfry

Did I say set theorists are morally bad? No, it was an analogy. The analogy was that if I saw set theorists doing something I thought was wrong (bad), I might be inclined toward explaining to them how I thought what they are doing is wrong, just like if I saw someone behaving in a greedy way which I thought was morally wrong, I might be inclined to explain to them why I thought what they were doing is morally wrong. The point being that it really doesn't make very much difference to me, in my life personally, if these people, either the set theorists, or the greedy immoral people, continue along their misguided pathways. Nevertheless, I might take it upon myself to make an attempt to point out to them how their pathways are misguided.

Particulars are real insofar as they're instantiations of the idea, which is their unchanging form; that is the sense in which the ideas 'lend being' to particulars, or particulars are said to 'participate in' the form. — Wayfarer

This is where Aristotle parts from Plato. In Plato's Timaeus particulars are supposed to be in some way derived from universal forms. But Plato is incapable of describing the mechanism by which a universal form could create the existence of a particular individual. He found the need to posit "matter" as the recipient of the form, in order to account for the particularities of the individual. The peculiarities of the individual are due to the matter. But when Aristotle developed this idea he discovered that matter itself cannot account for any of the properties of an object, and so each individual thing must have a unique form proper to itself. That's his hylomorphism

This was the fundamental question of his metaphysics, why is a thing the unique thing which it is, rather than something else. He said the commonly asked question of why there is something rather than nothing cannot be answered, and is therefore a fruitless question. So he suggested the proper question to ask of being qua being, is why is there what there is instead of something else. Why is each thing the unique and particular thing that it is, instead of something else. This led him to the conclusion that there is a unique and particular form which is responsible for each thing being the particular thing which it is. Hence the law of identity as formulated, each thing has a unique identity, it is the same as itself, and nothing else. For Aristotle, this is the reality of the particular.

The important thing to understand is that the whole
construct system functions integrally as a unified whole in the construing of events. This is important in understanding how Kelly treats affect. For Kelly the aim of construing is to anticipate what lies ahead. The construct system is wholly oriented around anticipation. It is not designed this way by some arbitrary inner mechanism or evolutionary adaptation. Anticipation is an a priori feature of subject -object interaction in time. — Joshs

I believe the role of anticipation is very important, yet not well understood. It is not well understood because it falls outside the possibility of observation and scientific understanding. If what is anticipated is a future event, and if the anticipation affects the way that one perceives what is presently happening, then we have to account for how a future event acts as a cause at the present. So you describe a system of construing which acts in a way such that future events have causal power over what is presently occurring, through the means of anticipation.

But, the point about universals is that they're universally applicable, isn't it? They're applicable in any context. Think about scientific laws, which I think must in some sense be descended from such ideas. Water doesn't sometimes flow uphill, for instance. Think also about Kant's deontological ethics, which individuals are obliged to conform to if their actions are to be ethically sound. — Wayfarer

I agree, but the universality of universals is exactly what makes them incompatible with identity which is what particulars have. This produces a hole, or gap in human understanding, because the material reality, to which we apply these universals in our attempts to understand, consists of unique particulars. This means that there is always a deficiency in human understanding. The point in enforcing a "law of identity", is to recognize and adhere to this understanding, that this gap exists, so that we do not push Platonism to its extremes, claiming that the physical universe is composed of mathematical objects. This is impossible, because mathematical objects are universals, but the universe is composed of unique particulars. The gap of incompatibility between these two demonstrates that such extreme Platonism, better known as Pythagorean Idealism, cannot be true.

Furthermore, I can't arbitarily designate the rules of math or the laws of logic, I have to conform to them, as much as I'm able (which in my case, is not very much). I can adapt them to my situation, I can use them to advantage, but I can't change them. (Again, the clearest exposition of these ideas are in the Cambridge Companion to Augustine, on the passage on Intelligible Objects.) — Wayfarer

This goes both ways. There are people who literally make up, or create axioms of mathematics, it's what fishfry calls pure mathematics. We must ensure that the mathematical axioms which we employ conform to reality or else they will lead us astray. Therefore it is actually necessary that we do change mathematical axioms as we try and test them. And if you look at the history of them you will see that they evolve, just like knowledge evolves, and living beings evolve. This implies that we must accept such things as evolving properties of living beings, rather than eternal immutable objects.

That the rules of math, and laws of logic appear to you as something which you cannot change, is the result of many years of usage by many different people. They are tried and tested so they are what we use. If, in your occupation there are rules which must be applied in order for you to fulfill your job, then you cannot change those rules or else your job would not get done. However, the world is full of innovative and creative people who could come up with new rules, which fulfill an end different from what you are doing, but is judged to be better than yours, and renders yours obsolete. Therefore this idea of "I can't change them" is just an illusion. Yes, if you want to keep doing what you are doing, you cannot change them, but if you quit what you are doing, and adopt other rules which are conducive to something else instead, which renders what you were doing before as obsolete, you really do change them.

Modern thought treats everything as a thing. (Who's paper is it, 'What is a thing'? Heidegger, I think.) Anyway, the point is, the modern mentality is so immersed in the sensory domain, that it can only reckon in terms of 'things'. Things are 'what exists' - which is what throws us off about mathematical concepts, they're not things, but they seem real, so 'what kind' of reality do they have? In our world, real things can only be 'out there', the only alternative being 'in the mind'. But in reality, 'out there' and 'the mind' are not ultimately separable - hence, as I say, the logic of objective idealism. But it takes a shift in perspective to see it. — Wayfarer

This I completely agree with, but again we have to be aware of where things go the other way. Philosophers looking toward the reality of Ideas describe them in terms of objects to facilitate understanding. However, we can see that thinking is an activity and it doesn't really exist as objects. On the other side of the coin, we see physicists who look at objects and use mathematical ideas to describe them in terms of activity. So we can see that the world of physical objects gets reduced to the activity of energy, because this is compatible with the realm of thought, mathematics. Now we have no adequate principles to separate objects from activities, and it's an ontological mess.

But now you say, "it's incorrect to call mathematical objects "objects" at all, because they do not fulfill the requirement of identity." When a while back you disagreed that 2 + 2 and 4 represent the same mathematical object (regarding which you are totally wrong but nevermind), that was one thing. But now you seem to be saying that 4 = 4 is not valid to you because mathematical objects don't fulfill the law of identity. Am I understanding you correctly? Do you agree that 4 = 4 and that both sides represent the same mathematical object? Or are you saying that since there aren't any mathematical objects, 4 = 4 does not represent anything at all? — fishfry

I guess you don't remember the key points (from my perspective) of or previous discussions. What I objected to was calling things like what is represented by 4, as "objects". I made this objection based on the law of identity, similar to the op here. You insisted it's not an "object" in that sense of the word, it's a "mathematical object". And I insisted that it ought not be called an object of any sort. So you proceeded with an unacceptable interpretation of the law of identity in an attempt to validate your claim. What I believe, is that "mathematical object" is an incoherent concept.

4 = 4 is true by the law of identity, yes or no? — fishfry

This depends on what = represents. Does it represent "is the same as", or does it represent "is equal to"? From our last discussion, you did not seem to respect a difference between the meaning of these two phrases. If you're still of the same mind, then there is no point in proceeding until we work out this little problem. This is why I say context of the symbol is important. When the law of identity is represented as a=a, = symbolizes "is the same as". But when we write 2+2=4, = symbolizes "is equal to". If we assume that a symbol always represents the very same thing in every instance of usage, we are sure to equivocate. Clearly, "is the same as" does not mean the same thing as "is equal to".

Do you at least accept that math can be regarded as a formal game without regard to meaning? — fishfry

No, of course not, that's clearly a false representation of what math is. That would be like saying that 2+2=4 could be considered to be valid regardless of what the symbols mean. That's nonsense, it's what the symbols mean which gives validity to math.

But, are you claiming that 4 means one thing to you today and other thing tomorrow? — fishfry

Yes, that is exactly the case it can even mean something different in the same sentence. When some says "I reserved a table for 4 at 4", each instance of 4 means something different to me. And, as I explained to you already, when someone says 2+2=4, each instance of 2 must refer to something different or else there would not be four, only two distinct instances of the very same two, and this would not make four.

So axioms don't qualify as "statements" in the article of the op? They get a special exemption? See why I reject this interpretation?

OK, you said that the statement can't be verified and it can't be falsified, yet it doesn't classify as level 4 by the standards of the op. How does it classify then? Surely it is in some way influential.

Well, mathematical objects are abstract objects. But I agree that numbers aren't like rocks. That doesn't mean that numbers don't exist. It only means that numbers are abstract. And, per structuralism and Benacerraf's famous essay, What Numbers Cannot Be, numbers are not any particular thing. They're not actually sets, even though they are typically represented as sets. Numbers are the abstract things represented by sets. I suspect you and I might be in violent agreement on this point, but I'm not sure. — fishfry

Well, I wouldn't go so far as to call it a violent agreement. The point of the op I believe, is that it's incorrect to call mathematical objects "objects" at all, because they do not fulfill the requirement of identity. And so, if we start talking about them as if they are objects, and believe that they have identities as objects, and treat them that way, when they do not, there is bound to be problems which arise.

Where we agree is that they are "abstract", but the problem is in where we go from here.

We're just saying that the membership relation holds between the abstract things represented by the symbols. — fishfry

Here is where the difference between us appears to arise. You are saying that there are "abstract things represented by the symbols". That's Platonism plain and simple, the "abstract things" are nothing other than Platonic Ideas, or Forms. See, you even allow that there are relations between these things. But from my perspective, a symbol has meaning, and meaning is itself a relation between a mind and the symbol. So I see that you've jumped to the conclusion that this relation between a symbol and a mind, is itself a thing, and you then proceed to talk about relations between these supposed things which are really just relations, and not things at all, in the first place.

You can, if you like, view the entire enterprise as an exercise in formal symbol manipulation that could be carried out by computer, entirely devoid of meaning. It would not make any difference to the math. — fishfry

If you can follow what I said above, then I'll explain why there's a real problem here. The relation between a symbol and a mind, which is how I characterized the abstract above, as meaning, is context dependent. When you characterize this relation, the abstract, as a thing, you characterize it as static, unchangeable. This is what allows you to say that it is the same as manipulating symbols devoid of meaning, the symbol must always represent the exact same thing. But here is where this thing represented, the abstract, fails the law of identity, the meaning, which is the relation between the mind and the symbol, is context dependent and does not always remain the exact same.

We could go down a rabbit hole here but just tell me this. Do you believe that if E is the set of even positive integers, then E = {2, 3, 4, 6, ...}. Do you agree with that statement? Or do you deny the entire enterprise? I'm trying to put a metric on your mathematical nihilism. — fishfry

I think we've discussed this enough already, for you to know that I denounce all set theory as ontologically unsound, fundamentally. It doesn't mean a whole lot though, only that I think it's bad, like if I saw a bunch of greedy people behaving in a way I thought was morally bad, I might try to convince them that what they were doing is bad. However, if it served them well, and made their lives easy, I'd have a hard time convincing them.

The Platonist explanation is that these 'things' - they're not actually things, which is part of the point - are discerned by the rational intellect, nous. — Wayfarer

I think that modern Platonism treats the abstract as things. This is what allows them to define static relations between these things, as fishfry describes in set theory. But if the abstract is not really things, then this static nature is unsupported, and so are the static relations unsupported.

They transcend individual minds, but they're constituents of rational thought because thought must conform to them in order to proceed truly. — Wayfarer

It appears, that what you are saying here is that there are some sort of ways of thinking, which thought must conform to in order to be rational. I would agree, but the specifics of the correct way is something to be determined. So I will ask you a question to see if you might have an answer. Wouldn't the way of thinking, which would be judged as the rational way, be itself dependent on and therefore determined by the particular situation, or context? So for example, there is some sort of way of thinking which is the correct way for a particular situation, and this transcends all individual minds, making it the correct way for any mind, in that situation. But that correctness, and the way of thinking itself which is correct, is determined by and specific to the particular situation itself. Would you agree with this? And what about the inverse? Is it possible that there is one correct way of thinking which transcends all situations as the correct way of thinking no matter what the situation?

I think that part of the complicated of understanding how inner and outer levels of experience work together is that while we may perceive others as aspects of outer reality, these others also experiencing their dialogue between inner and outer reality. — Jack Cummins

The problems arise when we try to establish a boundary between inner and outer. We say that other people, and all sorts of external objects are definitely outer. So I tend to think that anything outside my body is outer. However, when thinking with the conscious mind as the point of perspective, I start to see my hands and feet, and things like that as outside my mind. And I see them with my eyes and this only tends to confirm that they are outside. Then I start to get inclined toward dualism and see my whole body as outside my conscious mind. Now I have no place to draw the boundary, because I've lost track of where the inner could possibly be, and I need something to validate the very idea of a distinction between inner and outer.

All that means is that you are misusing the term "unfalsifiable". — Banno

Uh huh, so you say. But you're not interested in any interpretation which is not consistent with yours, so it really doesn't say very much.

It can't be, nor has anyone claimed that it can be. — Banno

Do you agree then, that these sorts of mathematical axioms, which are fundamental to the mathematics which is commonly used in scientific endeavours, are what the op refers to as Level 4 statements?

So, you're a relativist after all? — Wayfarer

No, not necessarily, I just recognize that it is impossible for a word to have a meaning before that word exists.

Can you name one such? — fishfry

I think we've been through this before. You insisted on an unreasonable separation between "objects" and "mathematical objects", such that mathematical objects are not a type of object.

We could start with the axiom of extensionality. Any axiom which treats numbers as elements of a set, treats the numbers as objects.

It doesn't matter if you call sets "beer mugs" as Hilbert pointed out. It's the properties and relations that matter, not the nature of individual things. — fishfry

The issue though, is that set theory treats them as "individual things", therefore Platonism is implied. Set theory relies on Platonism because it cannot proceed unless what 2, 3, 4, refer to are objects, which can be members of a set.

My interpretation of evolution as bottom-up design is compatible with human Free Will. — Gnomon

I agree with your bottom-up interpretation of reality, in principle, and also I agree that it is compatible with free will.

Natural Laws : Laws of Nature are to be distinguished both from Scientific Laws and from Natural Laws. Neither Natural Laws, as invoked in legal or ethical theories, nor Scientific Laws, which some researchers consider to be scientists’ attempts to state or approximate the Laws of Nature, . . . Some of these implications involve accidental truths, false existentials, the correspondence theory of truth, and the concept of free will. Perhaps the most important implication of each theory is whether the universe is a cosmic coincidence or driven by specific, eternal laws of nature. — Gnomon

I don't understand this part. Are you making three classifications, scientific laws, laws of nature, and also natural laws. As you can see, I would only have 2 classes, scientific laws which are inductive descriptions, and supposed natural laws which are moral conclusions about how we ought to behave. People justify ethical principles by referring to natural laws. In the case of "laws of nature", I think that some people want to justify scientific laws as true by claiming that they are representations of the laws of nature. But you can see, as I've argued, that I don't believe we're justified in even calling what is represented by these laws as "rules' or "laws" or anything like that.

Perhaps you are thinking of the New Age interpretation of "Holism". But my usage is that of the guy who literally wrote the book. It's only "mystical" in the sense that Einstein called "spooky action at a distance". :nerd: — Gnomon

I do not see how you can make bottom-up mechanisms consistent with holism. If an individual agent has free will to act as one pleases, then on what basis is there a whole composed of numerous individuals. How can individual parts, acting freely, bottom-up, be said to comprise a whole?

But the most succinct formulation of 'the law of identity' is 'a=a'. So are you saying that 'a' doesn't have an identity? — Wayfarer

You know that this is just a symbolic representation of the law. So the symbols need to be interpreted. What 'a=a' represents is that for any object, represented as 'a', that object is the same as itself.

Therefore it's not saying that 'a' doesn't have an identity, it's saying that the identity of the object represented by 'a', is the object represented by 'a'. In other words, an object is its own identity. Aristotle found it necessary to formulate the law of identity in this way, to recognize the difference between the identity we assign to an object, and the object's true identity. Sophistry had demonstrated that the identity which we give an object is sometimes incorrect. So we need a way to allow that the human assigned identity is incorrect, yet the object still has a true identity which the human beings have not determined. Therefore Aristotle posited that the identity of any object is within itself.

Many things can be triangles, but that is only insofar as those things assume that form. The form itself is not a thing. Only three-sided flat planes bounded by lines constitute a triangle but that covers an endless variety of things. That's the 'thing' about universals. — Wayfarer

Yes, that's a feature of universals. the word "triangle" covers an endless variety of things. But this same feature indicates to us, that a universal is not itself an individual thing. A universal is not a thing because it does not conform to the law of identity. It cannot be identified as a thing, because it has no identity as a thing. But, a thing necessarily has an identity, itself. Therefore a universal is not a thing.

This does not imply that there is no immaterial existence, it just means that in our understanding of immaterial existence we have to get beyond the idea that immaterial existence is in the form of things. That is just a sort of mistake which has developed from human beings relating what they know of the material world, to the immaterial, in an attempt to understand the immaterial. Because the material world consists of things, we want to apply the same principles to the immaterial, and portray the immaterial world as consisting of things. But the law of identity is interjected to demonstrate to us, the fundamental difference between material and immaterial, and that this would be a misunderstanding.

To those throwing rocks at mathematical Platonism (as I do when I'm taking the other side of this debate), was 3 prime before there were intelligent life forms in the universe? If that's too easy (I don't think it is), were there infinitely many primes? Or at least no largest prime? — fishfry

The word "prime" was created by human beings, and has a meaning according to what human beings think. It does not make any sense at all to ask about the meaning of the word "prime", or any word for that matter, at a time before the word existed. (What did the word "prime" mean before it existed?) I'm sure you can understand that. We can however use the word to refer to something that we believe existed before the word. Like "earth" for example is supposed to have existed before the word. Your question therefore asks, whether there was something which we refer to with "3", and something which we refer to with "prime", which existed prior to the existence of these words, and that is a difficult metaphysical question without a straight forward answer.

I don't think it implies necessary truth. For example, the claim that there is some particular configuration of stars and planets beyond the edge of the observable universe. That's unfalsifiable, because we can never check it out, no matter how close to the speed of light we accelerate a probe. But it's certainly not necessarily true. — bert1

I don't agree that such a claim is unfalsifiable. Just because we do not have the means to falsify it right now does not mean that we will not develop the means.

Give an example. — Banno

How about the obvious one then, the axiom of infinity? How would it be empirically verified? How could it be falsified?

Right. So 'identity condition' pertains to individual identity, something unique and particular. What is the source or definition of 'identity condition'? — Wayfarer

I don't know where Pneumenon gets this specific terminology, but I know the identity condition as the "law of identity", which states that a thing is the same as itself. Leibniz' posited the "identity of indiscernibles" which stipulates that each individual thing is unique.

Be that as it may, a triangle will never have other than three sides. — Wayfarer

That's true, but "triangle" does not suffice as a thing's identity because many things are said to be triangles. What I believe to be Pneumenon's point, is that whatever "triangle" refers to, it cannot be a thing, because all things have a distinct and unique identity according to the law of identity, or what Pneumenon calls "identity condition". Pneumenon uses this argument against any Platonists who believe that ideas exists as objects, arguing that ideas such as 'triangle" do not fulfil the "identity conditions to be rightly called "objects".

This is an ontological issue, and I don't think it's meant as a simple attack against dualism. When using this argument we do not mean to imply that immaterial things do not qualify as "objects", therefore we ought to reject the existence of the immaterial. What I believe, is that the argument is meant to elucidate the fundamental, and radical difference between the immaterial and the material, demonstrating that it is a basic misunderstanding to portray the immaterial as objects.

If we accept this perspective, that the immaterial ought not be represented as consisting of objects, there is far reaching consequences. Many mathematical axioms such as those of set theory rely on the assumption of mathematical objects. Further, we can see the trend in physics, to translate the immaterial wave fields to objects (particles), though things like virtual particles appear as immaterial. I see this reduction of the immaterial to objects, as a real problem. It basically says that the immaterial has to be like the material, existing as objects. But when we see that the immaterial does not fulfill the "identity conditions" which is required for existence as objects, we need to move on and recognize that the immaterial is radically different from the assumption of immaterial objects.

You might be interested in Joshs' radical temporality:
https://thephilosophyforum.com/discussion/9913/introducing-the-philosophy-of-radical-temporality

I would have thought that the identity conditions of integers was abundantly obvious. I mean, any integer is distinct from all other integers - how does that not constitute an 'identity condition'? — Wayfarer

How can we say that 2 represents a unique and particular object? That is the identity condition. To have an identity is to be identifiable as a unique and particular individual. But every time that there are two objects, the number 2 is represented, so 2 represents something universal, rather than something unique and particular. Therefore it appears like the number signified by the numeral 2 cannot fulfill identity conditions.

As for the triangle, it's 'a flat plane bounded by three intersecting straight lines'. That applies to any triangle. The 'form' is not the shape. — Wayfarer

We can attempt to provide identity through the means of a definition, but the definition always allows that more than one thing can be identified as fulfilling the identity conditions of the definition. So a definition cannot serve to give us adequate identity conditions because it allows that more than one thing might have the same identity.

So, are mathematical axioms concerning infinity not level 4 statements? Are they verifiable or falsifiable?

From a purely materialistic perspective and in a very basic, almost crude, sense, do we have the power to arrest the motion of particles/molecules in our brain presuming the motions of the particles/molecules determine our choices and the acts that should follow them? — TheMadFool

Yes, that's called will power.

f we do possess such an ability, does it follow, by extension, that we can control the motion of particles/molecules in our brain before and during the making of choices, effectively granting us free will? — TheMadFool

Yes.

The answers to these questions are very obvious, and it's very hard for me to imagine how anyone could realistically doubt the truth of free will.

Question 2: If we can delay acting out our choices after making them then doesn't that grant us some kind of free will or, if you like, pseudo-free-will? The lives of people are full of so-called missed opportunities which, to some extent, consist of times when the delay between a choice and acting out on that choice is longer than the temporal window-period during which our actions would've made a difference. For instance, if the tray with the two cans of Cola were to be offered to me by a waiter who was going to wait only for 5 seconds for me to pick a can up and I delayed the action of picking up the can for 10 seconds, the waiter would leave and I would be left without a drink, precisely what would've happened if I had gone against/defied my pre-programmed preferences. This is pseudo-free-will because I actually haven't gone against my programming, it's just that I failed to act within the allotted time. — TheMadFool

I don't see how you reach the conclusion now that free will is "pseudo".

Here's an experiment you can try. Hold an object (preferably unbreakable) in your hand, and have your mind made up, that you will drop it to the floor. Allow yourself to drop it at any random time, without any external influence causing you to drop it, such that the time when it is dropped is completely a determination of your will. Does this not convince you of the freedom of the will?

A being can continue to be itself differently. Ain’t that what self-organization implies? A being that continues to be itself over time not identically , but through a system of interactions with an outside. It conserves its manner of functioning by assimilating the world to itself and accommodating or adjusting its functioning to the novelties of that outside. — Joshs

I know that a being continues to be the same being despite changing, but the point is that we need a principle of identity to validate logically, what we know intuitively. If I am different from what I was last year, then logically I am a distinct, or different, being from what I was last year. Intuitively, I know that I am the same being, with the same identity, but how do I support this logically?

I'm in unfamiliar territory but does the type-token distinction seem relevant to the OP? Speaking in terms of the geometrical object triangle, there's a type triangle and all other triangles are its tokens. Quine's notion of Plato's beard seems to ignore/overlook this. — TheMadFool

I think the point is that there are numerous different types of triangles. And if you want to argue that there is only one type, "the triangle", then why isn't the triangle just one type of polygon? And the polygon is a type of geometrical figure, and so on.

I agree that the distinction between outer and inner reality is not absolute. Even when we are alone we can perceive the outer reality of our own body. However, the most simple way of thinking about inner reality is about shutting our eyes and being in silence. Of course, even then, we have memories of sensory world. However, I do believe that there is a significant inner world and an example of this would be the realm of dreams and imagination. — Jack Cummins

I do not believe there is any real or definable boundary between inner and outer, so the attempt to establish such a distinction would be fruitless. However I do believe that there is a valid distinction to be made in direction, towards the inner, and towards the outer. This would mean that there would be some usefulness in classifying actions this way. But we would need some principles as to what constitutes toward the inner and what constitutes toward the outer. I would think that it would be similar to understanding the flow of time. Some actions go with the flow, and some go against the flow.

There's quite a body of discussion on falsifiability. SOme familiarity with that would be helpful. — Banno

You should have noticed, from what I've posted, that I'm not at all interested in the conventional interpretation of "falsifiability". I believe it tends to be way off the mark. So I really don't know why you would make this suggestion to me. If you're content to sink into the quicksand of that interpretation, then so be it.

Apparently, in your strict vocabulary of technical terms, that might be the case. Since I'm not a professional scientist, I tend to use such jargon more loosely. Besides, in psychology, formal "rules" or "laws" are hard to come by. Most behaviors that psychologists take-for-granted are more like rules-of-thumb than empirically-confirmed-natural-laws. That's why The Diagnostic and Statistical Manual of Mental Disorders has to be regularly updated to weed-out definitions of disorders that turn-out to be too broad or too narrow or just plain wrong. :smile: — Gnomon

Don't you see a problem here? If psychologists are referring to "rules' which account for, or cause certain types of behaviour, and there is really no rules there, then what are they actually talking about? They've taken this term, "rules", which has no real referent, and they use it to account for all sorts of behaviours. Since the thing referred to by the word is just a phantom, so also the understanding expressed is just a phantom.

The "language instinct" is a well-known effect, but it's cause is a matter of debate. Stephen Pinker says that "A three-year-old toddler is "a grammatical genius"--master of most constructions, obeying adult rules of language." And he attributes those "rules" to a combination of Nature and Nurture. But he provides lots of observational evidence, so the mechanism behind the human talent for language is not exactly unknown. Some may claim it's a miracle, but Pinker thinks it's a Darwinian adaptation. — Gnomon

See, even Pinker is assuming "rules", but this is just a phantom understanding, the word is used to refer to what is actually not understood, as a coverup, creating the illusion of an understanding. If we dismiss this term "rule", and look at the fact that a human being is a free willing and free thinking human being, then we have a different perspective form which we can ask why is a person inclined to act in such a way as to create the appearance that one is following rules, when really there are no rules being followed.

PS___Shannon's definition of passive carrier "Information" is on the reductive & empirical end of the Science spectrum. But my definition of active causal "EnFormAction" is more towards the holistic & philosophical end, along with Psychology and History. Does that lack of hard evidence invalidate the hypothesis that Enformation might be the driver of evolution --- including the Language Instinct? Maybe. What do you think? — Gnomon

I have difficulty with the "holistic" approach because in my mind it cannot adequately account for the appearance of intention and free choice.

Referring back to the op, I haven't read the article, I confess. But I think we definitely need to consider these as distinct categories, "confirmable" and "influential". If I look for propositions which are as close to being truly unfalsifiable as possible, I am lead toward mathematical axioms which deal with the concept of infinity, or the proposed infinite. Such axioms are extremely difficult to falsify, being a matter of intuition, definition, or maybe as some would say a priori, so the falsifiability of them is very low, yet they prove to be very influential due to their usefulness. The problem is that the status of influential is provided for by usefulness, and this does not necessarily imply confirmation.

But this implies that no proposition is decidable prior to test. Which further implies that for all propositions for which no appropriate test is available, truth or falsity is indeterminable/undecidable. — tim wood

We actually do make propositions which are supposed to be true by definition, therefore not requiring testing, as is the case in mathematical axioms. But I do not consider these axioms to actually be "true", as you might know from my postings on other threads. Further, these axioms do tend to get tested through application and usefulness. However there seems to be confusion on this forum as to how usefulness relates to true. The usefulness of a mathematical axiom does not verify it as true. So these axioms get into a sort of limbo position where they are unverified, and unfalsified, yet heavily used, therefore very influential.

Therefore, if any propositions ought to be represented as unfalsifiable, and unverifiable, these would be mathematical axioms. Our mode for testing them is usefulness rather than truthfulness. So in science we have a clash of these two distinct forms of judgement. We tend to think that scientific hypotheses are judged according to principles of empirical observation. And that is what is supposed to constitute a judgement of truth. However, we rarely take into account how the mathematical axioms which are judged according to usefulness, rather than empirical truth, influence these empirical judgements.

You're forgetting the other half of the picture. If the proposition is also unverifiable, then why should we believe it is true? — Janus

Unverifiable and unfalsifiable are supposed to be two opposing extremes, a proposition which is claimed to be both ought to be simply be an irrelevant subjective statement, of no import to science. However, we have the status of mathematical axioms being "useful" as explained above, which demonstrates otherwise. So we are tempted to believe that such a proposition (like a mathematical axiom) is true because it is useful and influential.

As the article pointed out there are kinds of propositions which are unverifiable: "all x are Y", but falsifiable, and there are other kinds of propositions which are unfalsifiable: "some x are Y", but verifiable. In the latter case your position would entail that it is necessarily true that some x are Y, but that is nonsense; we could not know that until and unless it had been verified. — Janus

You misunderstand what I said. What I said is that the statement "some X are Y" ought not be classified as unfalsifiable simply on the basis of the apprehended human capacity to judge the truth or falsity of it. That would make "unfalsifiable" a subjective judgement without any objective principles by which we might make that judgement. It does not render "some X are Y" as necessarily true, because only propositions which are truly and objectively "unfalsifiable" would be necessarily true, and this proposition is not.

Well I take a rather dialectical view that being is indeed becoming, but not identical with it. For there to be any becoming there must be a being that becomes. I would disagree that it is a passive unchanging sort of thing. and besides, notice how your description 'unchanging' then also denotes an activity, that is if every 'ing' denotes that. — Tobias

The issue here is "identity". If being is actually a becoming, but you then posit the necessity of "a being" (notice the noun now) which is becoming, then that being must have an identity. Therefore we need something to account for its temporal continuity, its temporal extension, its identity as the same being, throughout its changing existence. Without this principle of identity, it's just a different existence, or different "being" from one moment to the next, as it changes.

This problem is well described in Aristotle's "Physics", where he discusses the principles required to account for the nature of change. The underlying identity, by which we say that a thing persists as the same thing (retains its identity) despite having a changing form, is provided for by the concept of matter. This supposed, assumed, or posited "matter" accounts for the notion that "there must be a being that becomes".

and besides, notice how your description 'unchanging' then also denotes an activity, that is if every 'ing' denotes that. — Tobias

Well, to be fair, the 'un' prefix negates the 'ing' suffix, so that what is signified by 'unchanging' is a lack of activity.

Being is a concept, a notion we use to make sense of the world. Pure passivity is actually negated by it, because if 'something' is purely passive, how would we notice it as a certain something, it must have all kinds of categorical qualities for us to be able to make sense of it at all. — Tobias

The point though, now, is that "being", as a concept, implies, in all of its senses of use, an identity. The difficulty in negating "pure passivity", is to do that without negating identity. I do not see how we could remove all passivity from the concept "being", or existence in general, without denying ourselves the capacity for identity.

What is it you think "unfalsifiable" means? — Banno

I think it means exactly what it looks like it means, not possible to demonstrate the falsity of. The point is that the common epistemological usage of this term is unacceptable because propositions are asserted to be unfalsifiable without due justification. Justification requires a defining of the terms, and a logical demonstration, (empirical demonstration in this case being out of the question). If justification is not required, then "unfalsifiable" has no epistemological import and it's application is arbitrary and subjective. It has become a cop-out term, employed in a lazy attempt to avoid logical rigor. The way it is employed, its meaning is basically 'I don't understand the ontological concepts involved here, therefore I designate the proposition as unfalsifiable'. Consider timwoods examples.

Unless there are standards as to what constitutes "justifiably unfalsifiable" the concept ought not be given epistemological status. And if we apply the necessary rigor (well-defined terms), I believe we'll find what I stated, "unfalsifiable" means impossible to be falsified, therefore necessarily true. Otherwise "unfalsifiable" has no objective status, meaning 'I personally, or we as a group, have not the capacity to falsify this (which is in fact falsifiable) due to the deficiencies of our capacities.

Consider statements of the form "there exists an x such that p(x)", those are verifiable but not falsifiable. Why? To verify it, all you need to do is find an example, to falsify it, you need to go out and look at everything ever and evaluate whether there's an x in it such that p(x). "There exists a non-white swan" - go out and find it. You think there isn't one? Have you looked everywhere? — fdrake

Thanks fdrake for the explanation. Notice that there is nothing here to give "unfalsifiable" any real status. So long as we continue to observe every instance of x with an open mind, such that we continue to allow for the possibility that it might be falsified, there is no assertion of "unfalsifiable". Therefore we may leave open the question of whether "there exists a non-white swan", and maintain that the proposition "all swans are white" is still falsifiable.

The appearance of "unfalsifiable" is just a symptom of ill-definition. If we define "swan" so as to exclude the possibility of a non-white swan, we exclude the possibility of the proposition "there exists an x such that p(x)", as an invalid (contradictory) proposition. Such a creature could not be a swan by that definition. But Banno would reject this as "essentialism", not realizing the damage which rejecting essentialism does to the human capacity for deductive logic, by allowing ill-definition and its consequent assertion, "unfalsifiable". "Unfalsifiable" which really means I am certain that we will not find an off-coloured swan, but I'm not certain enough to define "swan" in that way, really just allows for uncertainty to gain a foothold in epistemology. The alternative, to maintain that "there exists an x such that p(x)", has the status of falsifiable, until we are satisfied that it is a proven fact, then define "p" in this way, such that it is an empirical certainty, thereby avoiding the unnecessary middle position of "unfalsifiable", provides a much more reasonable epistemology.

I think I'm beginning to see your objection to the notion of "rules" in communication. Apparently you are thinking of imposed "explicit" formal rules, while I'm talking about innate "implicit" informal commonalities. As a rule (i.e. normally) humans are born with something like a mental template for language. — Gnomon

Isn't a "rule" necessarily formal though? That's the point, to talk about Innate, informal commonalities, as if they are rules, appears like a mistake to me.

My position on inherent human behaviors (instincts) is basically that of cognitive psychologist Stephen Pinker in The Blank Slate. He calls it "the language instinct", which gives humans an advantage, over most animals, in social communication. Anyway, I doubt that our concepts of communication are very far apart. It's just another failure to "first define your terms". — Gnomon

That might be the case, if we both see this "instinct" as an unknown concerning its true nature, then we have commonality here.

OK. I'll try to avoid using the term "rules", since it seems to trigger your indignation. Instead, I'll use something like "norm". The human language instinct is not a "law of nature" or a "man-made rule", but it is common enough to view it as "the rule rather than the exception". :cool:

Rule : If something is the rule, it is the normal state of affairs. — Gnomon

The problem now, is that with the switch from "rule" to "norm" we jump from the cause of the behaviour (following a rule, instinct, or whatever the cause is), to a description of the behaviour. Then all we are saying is that it is common, or normal for people to act in a particular way, but we have no approach to the cause of that commonality. If we say that the person is following a rule, we create the illusion that we know why the person is acting in that particular way. That is why I objected to that use of "rule".

Each of my three propositions above is unfalsifiable. And according to you, necessarily true. How do you reconcile the nonsense? — tim wood

They only appear as "unfalsifiable" because you have not defined your terms, "God", "exist". Once you provide clear definitions you'll see what I mean. That "unfalsifiable" could mean something other than true is only the case when terms are ambiguous.

Hmm. God exists. Therefore God exists? Or to round out, God does not exist. Therefore God does not exist? Or even, God either exists or does not exist. Therefore either God exists or does not exist? — tim wood

None of these qualify as an "unprovable" inductive conclusions, or universals, which is the substance here. One could make up all sorts of nonsense and insist that its both unprovable (due to inadequately defined terms) and also unfalsifiable (due to the impossibility of testing what is inadequately defined), but that's not really relevant.

What is relevant is that valid inductive conclusions are rejected under the pretense of "unfalsifiable".

Banno seems to think that a proposition can be claimed as "unfalsifiable" without proving that it is unfalsifiable. But this is just a ploy to avoid having to answer whether the proposition is true or not. In reality, either the proposition is truly unfalsifiable, therefore necessarily true, or else "unfalsifiable" is just being asserted in an attempt to avoid the issue of whether the proposition is true or not.

Unprovable and unfalsifiable. — Banno

As I explained, these two are contradictory. Unfalsifiable means impossible to falsify, which implies necessarily true, therefore proven.

Determinism: Every event has a cause. This has the form given for Level 4 statements, an existential statement nestled in a universal. Hence, if Watkins is correct, it can not be proved - doing so would require the impossibility that we examine every possible event and determine its cause; nor can it be falsified; that we have not so far found the cause of some given event does not imply that there is no such cause. — Banno

This is how the problem of induction is resolved. It appears like an inductive conclusion cannot be proven. But an inductive truth is impossible to falsify, and if it is impossible to falsify it is necessarily true. Therefore demonstrating such an impossibility is what actually proves the truth of the inductive conclusion, thereby resolving the problem of induction.

Since I am not an authority on the subject of Semantics and Syntax, I was referring you to some authorities that do see evidence of commonalities, if not formal "rules", in human communication. If you are really interested in the evidence, you can click on the links. But, it seems that you have something against the idea of natural logical structure in communication. And I'm not quite sure what that objection is. — Gnomon

I have nothing against "natural logical structure in communication". But we cannot conclude that natural logical structure implies rules, just because artificial, or formal logic consists of rules. In fact, that's what I see as the difference between formal logic, and natural logic, the former consists of rules, the latter does not.

Well, except for some picky-picky philosophers, most people don't have to establish formal rules before they communicate. — Gnomon

Then, very clearly, your proposal that people must agree on rules in order for communication to be possible, is false. That's the point, agreeing on rules is not necessary for communication, so why assume that rules are essential to language?

Instead, most of us learn the rules informally at our mother's knee, and just by growing up in a particular culture, or may even inherit some mental structure biologically. That's what I referred to as "Intuition". — Gnomon

I really do not see how you can portray learning how to talk as a matter of learning rules. Have you ever seen children learn to talk? If so, what part of it looks like an instance of learning rules to you? Furthermore, this learning how to talk cannot be a matter of following rules which one already knows (innate grammar), otherwise one would not need to learn how to talk, already knowing the rules which make talking possible. It seems very clear from the empirical evidence, that talking is not a matter of following rules. So this type of theory appears to be inconsistent with reality.

But the "rules" of Semantics (meaning) are partly subjective & personal, yet may also be embedded in Jung's Collective Consciousness, or in Freud's Unconscious, or Chomsky's Deep Structure. Don't take those metaphors literally. They merely indicate that part of what-we-know-intuitively, and the rules-of-behavior we follow, are inherited with the human body. Hence, such standards, while important, are not inherently formal or rational. :nerd: — Gnomon

As I said, I don't believe there is such a thing as the rules of semantics. You can keep talking as if you believe that there is, but that won't change my mind. You need to show me some evidence of the reality of what you are saying, justify it. The appeal to authority is insufficient until you bring out the evidence presented by those authorities.

semantic rules make communication possible. They are rules that people have agreed on to give meaning to certain symbols and words. — Gnomon

I don't see that people agree on rules before communicating with each other. Don't you see that agreement requires communication? So this proposition seems to be really impossible, and at best a vicious circle.

I assume that by "excluded", you are referring to "discarding, all that meaning which falls in between, as neither 0 nor 1". But that's not how I understand the digital compression process. Instead, it's similar to Quantum Superposition, in that all values between 0 and 1 are possible, but not actual, until the superposition is "collapsed" by a measurement. The original Intention is still in-there, but un-knowable until the meaning is "measured" by a mind that "resonates" with the intent. In other words, the receiver must already know something about the significance of the communication. — Gnomon

The point remains the same, even if you express it in this way. All that meaning between 1 and 0 cannot be expressed in the digital system.

I'm not into all the technical details, but some Information theorists view the secret to compression as, not either/or, but as all-of-the-above. — Gnomon

Right, that's why all that meaning (information) ends up being contradictory and "un-knowable".

Besides there is no actual Meaning transmitted in a Shannon communication --- only abstract mathematical symbols, that can be used to define conventional relationships, which the receiving mind interprets as Meaning. — Gnomon

That's why the Shannon use of "information" is distinct from most common usage.

Perhaps he is referring to the rules of Syntax, which are conventional, and the rules of Semantics, which are mostly intuitive. — Gnomon

The point being that I don't see any evidence of rules of semantics, and the rules of syntax need to be interpreted.

How can you call them symbols if they don't already represent something? Meaning is inherent in symbols. — Harry Hindu

This is not my preferred terminology, to say that there is a "symbol" which does not represent anything. But that's what they do in examples of logic, they separate the symbols from all meaning, to demonstrate a procedure which uses symbols and the symbols used don't represent any thing. I agree that this is contradictory, and I don't really believe that these things ought to even be called symbols.

Maybe "rule" isn't the most appropriate term. Does natural selection "select rules" by which some organism interprets the information it receives via its senses? Is "selecting rules" an adequate phrase to refer to how certain characteristics are favored by natural selection for the organism to be more in tune with their environment? What is selected is better interpretations of sensory information. These ways of interpreting sensory information are what become instincts, or habits. — Harry Hindu

Right, I'd prefer to call these actions habits rather than instances of following rules.

Habits are memorized rules, or rules that have been engrained in the genetic code thanks to natural selection. — Harry Hindu

I see no reason to believe that habits are memorized rules. If an habitual action is dependent on certain nervous system activity, why would you characterize this nervous system activity as memorized rules. I think we need to reverse this outlook. Memorizing rules could form a particular type of habit, as we find in mathematics, but not all habits are instances of memorizing rules.

Self organization seems to be the answer, as this is the activity the entire universe and hence all of its component parts are constantly involved in. — Pop

The entire universe is involved in self-organization? I thought only living things did this.

This ambiguity of the word information needs to be emphasized in trying to grasp what Shannon's theory says and what it does not say. Shannon was talking about transmission of data over a neutral but imperfect channel not what that data means to a sender or to a receiver. — magritte

Right, that's why I said what "information" refers to in information theory is something completely different from what "information" refers to in much common usage. So for example, if we distinguish between symbols and what the symbols represent (meaning), in information theory the symbols are called information, but in common usage information usually refers to what is represented by the symbols, the meaning.

In a more complicated case perhaps the channel or method of transmission is not neutral. In the verbal transmission of rumors some content is lost, embellished, and added as the content is passed from person to person. Here, content is not the letters, words, or sentences but a human intelligible meaning with both cognitive and emotional elements. — magritte

When we start to consider content now we need to be wary of a potentially similar distinction with respect to "content". In information theory, symbols are transmitted, and we could call this the content. But in speaking about natural language, the content is the meaning.

Now there is an issue of whether any content (meaning) is actually transmitted in natural language use. It may be the case that only symbols are transmitted between us, and all the content (meaning), is created in the minds which transmit and receive the symbols. If this is the case, then information in the common sense of the word, as meaning, is not transmitted in natural language use. This would imply that we need to look for some process other than language use, to understand how information (as meaning) is shared by human beings.

Harry Hindu is speaking of this as a matter of following rules, but I don't see any evidence of any such rules. And the idea of "rules" does not deliver us from the ambiguity. We generally understand "rules" to exist as an expression of symbols. But these rules would need to be interpreted for meaning. So we'd be stuck in a vicious circle here, of requiring rules to interpret rules.

Interpretting words and behaviors entails discovering the rules (beliefs) that the sender used to encode the message. Only by discovering the rule (belief) can you then decode the message. — Harry Hindu

I really do not believe that there are any such rules, just habits, so I think we're on a different page here Harry.

If that is your view, and belief, how do you account for all that meaning which is excluded as not meaningful, by that position, as I explained above? Do you believe that it is acceptable to exclude any meaning which cannot fit into the digital representation, as not meaningful? Isn't that contradictory?

At least the point of Descartes for me is the identification of thinking and being and therefore pointing metaphysics in a certain direction, namely the relationship of being and thinking. — Tobias

I really don't believe that thinking can be identified with being in this way. This is because "being", though the "ing" signifies an activity, is really a passive, unchanging sort of thing, a temporal continuity of the same identified thing. If a thing is changing, it is better described as "becoming" and so we have the ancient dichotomy between being and becoming. Since thinking is better described as an activity of change, it is better classified as a sort of becoming, and Descartes would have been more accurate to say I think therefore I am becoming (as changing). Now, in modern philosophy we have much conflation of being and becoming, such that we have numerous understandings of "being", one supporting the logic of "what is", and another supporting the existence of a growing living being, which is more like a becoming. This makes it very difficult to have any metaphysical discussion of "being", because it's very difficult to know what the participants of such a discussion have in mind by that term.

I'm open to ideas thought. First things first, we all seem to have some hardwired tendencies/proclivities which are very difficult to override - perhaps this reflects brain architectures that tune in to a certain assortment of thought waves (the brain has a preference for certain broadcasting "stations"). — TheMadFool

How would you separate "hardwired tendencies" from conscious thinking habits which are learned at a very young age. Perhaps it's the case that all pre-existent hardwired tendencies are actually overridden at a young age through the training of the conscious mind, by the influencing adults. This would mean that all such broadcasting preferences are actually conditioned, acquired.

Secondly, there's the matter of how we seem to have some control over our thoughts - we can, for instance, decide to close a book we were reading and go out for a walk. This I suppose is what JackCummins means by "self-consciousness" but these instances can be explained in my theory as simply a preset sequence of contents broadcast from the "station" our brains are tuned in to. So deciding to stop reading a book and go out for a walk could simply be the next program in thought wave "station" broadcast. — TheMadFool

If what I said above is correct, then the only true self-control would be to tune out all conscious thought, these being the product of the influence of others. Until you do this, and tune into that radio station which such self-control might give you, you don't have any basis to say what that radio station might be like, because the only time you might have been tuned into it was when you were so young that you couldn't possibly remember it. If such a radio station could actually tell you anything, what do you think it would say?

Digital information is conveyed in the abstract language of binary numbers that have the potential to encode any meaning. — Gnomon

But do they? Or, do you really believe this? What I've been trying to tell you, is that the binary system is really a great restriction to meaning. It is a restriction because any meaning which cannot be expressed in binary therefore cannot be expressed. Consider all the instances where the law of excluded middle does not apply, how could the meaning here be expressed in binary?

Therefore, in order to be meaningful to non-computers, that general (one size fits all) language must be translated (inverted) back into a single human language with a narrowly-defined (specified) range of meanings for each word. — Gnomon

The problem is not translating binary to natural language, but translating natural language to binary. We have in natural language the law of non-contradiction which is very suitable for binary. But by this same principle, binary is much more restrictive, much more specific, than the natural languages which are more general. So natural language consists of generalities, ambiguities, which cannot be captured in the binary. These generalities allow the natural languages wider ranging applicability.

For example, suppose that to fit into binary, the meaning must match the digits, 0, and 1. Anything which does not fit precisely into the designated meaning of 0 or 1 just gets rounded off so that it does fit one or the other. You'd think that this is just making the language more precise. But ask yourself what happens to all that meaning which gets rounded off? It gets lost, simply discarded, as if it's meaning which is not meaningful. So, in weeding out, discarding, all that meaning which falls in between, as neither 0 nor 1 (which would violate the law of excluded middle if it were allowed to remain in between), we end up violating the law of non-contradiction by having meaning which is not meaningful, and therefore discarded as such.