I don't disagree with the private language argument, at least as I interpret it, which is to say that if you tried to construct a private language, you would always be relying on the public language you know in order to tell yourself what your novel language means. So. I'm not seeing the relevance in this context.

It has everything to do with it because you're adamant that even when the situation is underdetermined, you dogmatically lean on plus even though you have no further means that can disambiguate the actual rule was plus. — Apustimelogist

Again nonsense. The logic of addition is not dogmatic, but simple: I can just keep adding forever in principle. Anything indistinguishable from that is just that and nothing more, so neither underdetermination nor dogma have anything to do with it.

But the question is whether it is also quaddition? — Apustimelogist

If quaddition is the same as addition then it's not a different procedure but just a different name. So what? If it differs, then how could it do so without arbitrarily stipulating that iteration must cease at some point?

And that's a problem with both idealism and materialism, each supposing that it alone has priority. — Banno

This is sometimes depicted as a kind of Hegelian dialectic, whereby first one, then the other, are held up as being fundamental.

But I think that Kant's transcendental idealism evades this dichotomy, because Kant acknowledges the harmonious co-existence of both empirical realism and transcendental idealism. — Wayfarer

All just ways of thinking about things. How can we count any of them as being the real thing?

I did.

It only dispells it if you think dogmatism is a valid way to objective truth. — Apustimelogist

Dogmatism has nothing to do with it; there is simply no reason that addition should terminate anywhere.

In addition, your point of view comes to the bizarre conclusion that under the conditions of underdetermination of the thought experiment where there is no fact of the matter that distinguishes someone's past usage of quus vs. plus, someone has to be using plus and not quus. Its impossible for someone to be using the rule quus because it would be too arbitrary. — Apustimelogist

This is nonsense: I haven't claimed that one could not use quaddition or any other arbitrary rule. If some rule of quaddition stipulates that addition must terminate somewhere then it is indistinguishable from addition up to the point of termination. But then it is simply addition up that point, and so what?

Isn’t that analogous to how well science can reconfigure the way that world appears to us though a gestalt shift? — Joshs

No, I don't think so. Science observes, and then attempts to explain what is observed. I see fire, for example, and I explain it in terms of phlogiston, then later I explain it in terms of oxidative combustion. I continue to see the fire the same way; its appearance does not change regardless of the theory about its cause.

Picture a tranquil mountain meadow. Butterflies flit back and forth amongst the buttercups and daisies, and off in the distance, a snow-capped mountain peak provides a picturesque backdrop. The melodious clunk of the cow-bells, the chirping of crickets, and the calling of birds provide the soundtrack to the vista, with not a human to be seen.

Now picture the same scene — but from no point of view. Imagine that you are perceiving such a scence from every possible point within it, and also around it. Then also subtract from all these perspectives, any sense of temporal continuity — any sense of memory of the moment just past, and expectation of the one about to come. Having done that, describe the same scene. — Wayfarer

Are we to imagine perceiving the scene form no point of view (an obviously incoherent request) or from "every possible point within it, and also around it"?

There could be no perception without memory or expectation, so nothing to describe.

If there are butterflies flitting about, there is no possible point of view of them from which they would not be flittering about.

So, I am struggling to see the point of this thought-exercise.

That may be true. — frank

I have seen no reason to think it is not true. I also see that fact as dispelling Kripke's skeptical challenge.

Redundant

An interesting article. Animal calls can be concrete signs, but that is not the same as the abstract signification of a symbol. Mathematics, an abstract elaboration of the basic concrete activity of counting is not possible without symbolic language; that was the point I made. Are you disagreeing with that, and taking this article to be evidence against it?

By that he meant the evidence we receive from the world is a response to the way we formulate our inquiries toward it. It can respond very precisely to different formulations, but always in different ways, with different facts. — Joshs

The way we formulate our enquiries towards the world is in response to the way the world appears to us. We have no control over how the world appears to us.

The question of how mathematical rules are justified is also interesting, but Kripke's challenge is about the use of the English word plus. What fact is there about how you were using it? — frank

The natural logic of addition includes infinitely many iterations simply because in principle there is no reason why you cannot just keep adding. Anything counter to that is a completely arbitrary stipulation.

The various branches of Logic has been used for the real life technology applications by adding the contents into the formulas for a long time. I suppose they are the knowledge for the specialists. — Corvus

The contents themselves are not the stuff of logic. but are merely set out in accordance with its strictures.

And again, regarding my saying that all synthetic philosophy is a creative exercise of the speculative imagination, that was not meant to apply exclusively to Kant, so asking for quotes from Kant is not appropriate.

I was right into Whitehead for a good while. I think process metaphysics is closer to actuality as experienced than substance ontology is. I like speculative metaphysics because it's an exercise of the creative imagination. Whether or not it accords with any absolute reality is unknowable, but I don't think that question matters at all, or is maybe even coherent. Falsification has no provenance when it comes to metaphysics.

A correlationist will say that we cannot imagine how objects exist "in themselves". We can imagine that they do exist in themselves, which is something else, obviously.

The existence of computers based on logical operations says nothing about content. Various logics are formalizations of the rules that are understood to govern thinking; consistency, non-contradiction and so on, and do not themselves mandate any particular view about anything.

t is a characterization of Kant's philosophy that applies to synthetic philosophies in general. Wherever there is creativity, it is a product of the imagination.
— Janus

I would appreciate the direct quotes from Kant's own books supporting your points. Thanks. — Corvus

I haven't claimed Kant said that—I am saying it, so your request for supporting quotes from Kant is not relevant.

Could you please clarify which logic you mean here? There are vast many different types of Logic. — Corvus

None of them provide any content.

Could you please elaborate your points with the relevant quotes from Kant's CPR or any of his own writings? — Corvus

It is a characterization of Kant's philosophy that applies to synthetic philosophies in general. Wherever there is creativity, it is a product of the imagination.

For instance, Kant's Metaphysics arrives at its conclusions via rigorous logical arguments. Aristotle's Metaphysics analyses the abstract concepts and universals again via logic. I don't see any imagination there at all. — Corvus

Logic supplies no content; it consists in procedural rules. Kant's philosophy is the product of logically constrained imagination; that is it consists in imagining the entailments of some basic premises in a logically rigorous, i.e. coherent and consistent, way.

Which animals can count? — Corvus

https://www.bbc.com/future/article/20121128-animals-that-can-count

https://www.newscientist.com/gallery/mg20227131600-animals-that-count/

Anyhow simple counting is not mathematics. — Corvus

I didn't say that simple counting is mathematics, I said that mathematics is an elaboration of simple counting. Perhaps it would be better to say that mathematics is an elaboration of simple arithmetic, which in turn is an elaboration of counting.

Mathematics — Corvus

Yes, mathematics is one example of a symbolic language. I see mathematics as being an elaboration of the basic, prelinguistic ability to count. I say prelinguistic because apparently some animals can do simple counting. Mathematics would be impossible without language, because it relies so much on naming. The numerals are names of quantities.

What have humans got, the other species haven't got? — Corvus

Symbolic language.

:up:

:up: :cool:

I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science recently retired from the University of Toronto. “Working mathematicians overwhelmingly are Platonists. They don't always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”

I have long thought that mathematics is both invented and discovered. If it is embedded in the human understanding of nature, then that is an existential fact about the part of nature that is the human/ environment interaction or relation. So, it is there within at least our natures to be discovered, which from another perspective can be seen as us inventing it.

I don't know where that "empriricist objection" is quoted from, but it is the lamest. most hand-wavy of objections.

My belief has always been that numbers are real but not physical. Of course, that contravenes physicalism, for which everything must be reducible to the physical, so it can't cope with that idea. It has to reject it. So I think those comments are revealing of the real philosophical issue at stake: that mathematical realism, the idea that numbers and mathematical relations are real but not physical can't be allowed to stand. — Wayfarer

Of course, numbers are not physical objects. But it seems unarguably true that number and quantity is everywhere manifest in the physical world. And this would seem to be logically necessary in any diverse world. That numbers are not physical objects does not contravene physicalism, per se, although it obviously contravenes your conception of physicalism.

Any attribute of, or relation between, anything at all would seem to contravene your model of physicalism since attributes and relations are not physical objects. I think it's fine to disagree with physicalism, but it seems to me that the claim that it is incoherent or self-contradictory relies on a strawman version of the position.

Nevertheless it could never have been discovered without mathematics. — Wayfarer

Physics itself would not be possible without mathematics. If, as you agree, it is not the task of physics to find out what nature is, but rather to produce models that present the best human understanding of what is observed and measured, then it doesn't seem to follow that mathematics is embedded in nature at all, but rather that it is embedded in the human understanding of nature. But that mathematics is embedded in the human understanding of nature is hardly controversial.

I know it's a bit of a tangent, but you haven't provided a reference for that passage about Peirce you quoted.

Good question. In the context of Aristotle's philosophy, as well as in biological classification and other systems of categorization, a "genus" is a class or group that includes different species. Note however its ultimate source in Aristotle. — Wayfarer

Right, so a generic concept is the concept of a class of things which share some salient similarities, a class of species. You haven't said what you think a universal concept is, and whether it is the same or different than a generic concept.

This equation incorporated both the principles of quantum mechanics and the theory of special relativity, describing electron behavior at relativistic speeds. — Wayfarer

This is an equation belonging to quantum physics and relativity theory, not pure math.

I'm incllined to agree with Bohr's aphorism 'It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature.' Also Heisenberg's 'What we observe is not nature in itself but nature exposed to our method of questioning.' — Wayfarer

We agree on that.

What he was trying to do was avoid psychologism (which he was accused of in Philosophy of Arithmetic) by grounding mathematical principles in transcendental
phenomenology. — Joshs

It seems to me that maths, based on number, is grounded in immanent phenomenology. We encounter diversity, difference and similarity, everywhere.

As an abstract concept, it's a universal. More to the point, per my earlier posts in this thread, is that mathematics can be used to make discoveries hitherto unknown about nature herself, thereby demonstrating that they are something more than simply 'mental constructs'. — Wayfarer

What is the difference between a universal concept and a generic concept? You are talking about math as an aid to science, right...can you give me an example of pure math being used to discover anything about nature? Do you think any discoveries about nature are about nature as it is in itself or merely as it appears to us?

The same way they do any other ideas - thinking, using intuition, or reasoning. — T Clark

That leaves me wondering what you think thinking or intuition is, other than exercising the imagination.

Numbers are abstract entities, concepts...they are abstracted from number which is concretely instantiated in the material world. It is no different than saying that "tree" is a generic concept, abstracted from actual trees.

I'm not a Kant scholar, but I've read "Critique of Pure Reason." I don't remember it saying anything like "metaphysics is, in fact, indistinguishable from human imagination." I doubt that it did and I doubt that Kant thought it. I can't speak to Leibnitz, but I would be surprised if he felt that way. — T Clark

How do people arrive at metaphysical conjectures if not via imagining them?

"Husserl was interested in the psychological origin of number concepts. He explored how individuals move from concrete individual experiences to abstract generalizations that constitute numerical understanding. For Husserl, numbers aren't just abstract entities; they have their roots in our lived experiences and acts of grouping and collecting. — Wayfarer

This is exactly what I've many times said to you, arguing against your Platonic notion of numbers.

Presumably the only exponents of propositional knowledge we know of are humans, since propositional knowledge requires symbolic language.

I also distinguish knowledge by acquaintance or familiarity, as in "I knew Catherine", and this can be more or less intimate as in "carnal knowledge", good friend or casual acquaintance. And then there is know-how. It seems obvious that animals are capable of both of these forms of non-propositional knowledge.

If your cat could tell you she is mad are you, matters might then be different; as it is you have to guess and allow for the possibility that you are projecting when you think she is mad at you.

Yes, all knowledge is perspectival. As to what the word 'knowledge' can be applied to, I think that is a matter of stipulation, not fact. — Janus

That said, I should acknowledge that it is a fact that there is a range of established stipulations, which hold some normative sway. Novel, creative usages are always possible, but they surely must exemplify something, however minimal, of the logic of established usage, and there is no guarantee that neologisms will catch on.

I think your caveat -- "apart from animal knowledge" -- illustrates the problem of identifying knowledge per se with human knowledge. There would also, traditionally, be the question of God's knowledge. To this day, physicists like to talk about "God's PoV" or "the mind of God" as a shorthand for describing an ideal knowledge of how things are. Why would there be some sort of guarantee that human knowledge must coincide with this? And if you discount a God hypothesis, there are still the non-human animals. What they know is surely very different from our human knowledge. — J

Well, human knowledge is the only knowledge we actually enjoy; animal knowledge we can infer from animal behaviors, and from studying their perceptual organs. "God's knowledge" is the idea of unlimited knowledge, the dialectical counterpart of limited knowledge. We find our own knowledge to be limited, but, we imagine, much more comprehensive than animal knowledge.

The idea of knowledge is the idea of something real; "illusory knowledge" does not make sense. There can be illusory belief, but 'belief' and 'knowledge' are different concepts.

You ask why there would be a guarantee that human knowledge accords with God's knowledge. First, I would say there is no guarantee that there is a God, or any absolute knowledge, and even if there were we cannot know it, so no comparison can be made.

The knowledge that animals possess may be very different than human knowledge, but that would invalidate neither, because knowledge is relational, and it seem obvious that different organisms would have different relations to their worlds.

Perhaps, instead of using words like "contaminated" or "distorted," we could simply speak of "perspectival" knowledge. That way, we avoid the idea -- which I assume you don't advocate -- that the word "knowledge" can only be applied to what humans know. — J

Yes, all knowledge is perspectival. As to what the word 'knowledge' can be applied to, I think that is a matter of stipulation, not fact.

You are begging the Kantian question. You are not allowing yourself to see past Kant's axiom. — Leontiskos

That's a bare statement and fairly useless without some explanation.

There is truth in that, but I'm not sure I would say much different about most of the human-produced graphics I've seen. — T Clark

Right, and I think that is because most of the human stuff is also just robotically imitative.

I have no argument with any of what you've said there, except I would not frame the background as a matter of belief, but as a matter of being, more akin to the idea of a "form of life" or "umwelt" than to the idea of "hinge propositions", That we have hands, mountains, oceans, planets and so on has, primordially speaking, nothing to do with propositions or beliefs, but these are simply attributes of the human-shaped lifeworld.

So it's the idea that knowledge of the world is possible, and this knowledge is not automatically contaminated, distorted, or even conditioned by the human subject. This draws near to classical realism. — Leontiskos

The notion of knowledge being contaminated or distorted by human subjects seems absurd given that we are speaking about human knowledge. So, what could its state of purity or clarity be, such that it could be contaminated or distorted? Even to say that (human) knowledge is conditioned by humans seems redundant.

All that said knowledge (apart from animal knowledge) is human knowledge after all, and as such relates only to the world as it appears to humans, or to put it another way, the human "umwelt".

So… Thoughts? I have no particular agenda here. I guess I’m just looking to clarify for myself how to think about these things. — T Clark

Looks like AI has a Kitch sensibility. It all seems like tasteless crap to me.

other rules like quus. there are probably a multitude of them which are consistent with all of the addition you have ever done so far in your life and you can't rule them out. — Apustimelogist

How can they be consistent if they don't yield the same results.

uhhh don't you mean quu-nfinite quu-terability? — Apustimelogist

No, I wasn't referring to gibberish.

why should it be that just because a description is general or extrapolatable means it is any more or less true than a description which is specific. Is the fact you are using addition any less true than the more general description of using an operator? is the more general description of being a mammal somehow more true than the more specific description of being a human? — Apustimelogist

All that seems irrelevant. I may be missing something to be sure, but if it is so, no one seems to be able to point it out. I've reached burn-out on this...

Thus, it is always "speculative" because, though the human "form of life" so-to-say can never be avoided when conveying these concepts, the content of what is conveyed can be "about" the non-human forms of life, if you will. — schopenhauer1

This is a point that often seems to lead to confusion. Take, for example, modern geology; there is no need to take the observer into account in the theory of plate tectonics. From the perspective of geology the observer is irrelevant. It's not even clear how the observer could be incorporated into the theory.

On the other hand, of course plate tectonics is a theory that seeks to explain phenomena observed by humans; yet that seems to be a trivial factoid in regard to all the sciences bar, perhaps, quantum mechanics.

Also, don't forget that quus is only one example of many other possible rules so actually you have been using some other strange rule since you started learning math and you have been using it fine — Apustimelogist

What other "strange rule" have I been using? Basic arithmetical procedures are simply the infinite iterability of addition and subtraction, and the fact that things can be grouped together in terms of different quantities.

I agree that many rules have been extrapolated out of these basics, but the extrapolations are not arbitrary in the kind of way quaddition is. They just show what can be done with these basic conceptual tools.

So, I don't agree that these basic procedures are "under-determined".

We apparently see things very differently; so much so that I cannot even tell where you are coming from with this.

Arbitrary rules like quaddition do not yield reliably workable results, or at least I haven't seen anyone showing that they can. The logic of addition is that you can keep adding forever, and that logic is based on the fact that there is no reason you cannot keep adding forever. Quaddition is just an arbitrary countermand of that unlimited iteration. What's the point, when it cannot even yield workable results? And as for people claiming they are following "other rules", there might be some plausibility to that if the other rules yielded the same results.