I sometimes get the feeling that analytic philosophers hide that they're talking about anything interesting by talking about language. So my eyes often glaze over when they shouldn't. I will read your notes on them, though.

I sometimes get the feeling that analytic philosophers hide that they're talking about anything interesting by talking about language. — fdrake

I sometimes get this feeling too, but have seldom gotten it while reading either Kripke, Putnam, Evans or Wiggins. They are quite adept at navigating between the formal and the material modes of speech, as Carnap might have put it. Pondering over how things can sensibly be said to be (philosophy of language), and how things can sensibly be thought to be (metaphysics and philosophy of thought), often are one and the same inquiry.

Since you've already primed me to think of this in terms of the creation of the synthetic a priori and how that creation interfaces conceptually with the world, it's interesting. Maybe my new mantra reading on similar topics should be: 'they're talking about how we interface with the world through language'. Your prose in the first note isn't making my eyes glaze, though, so thank you for that.

Maybe my new mantra reading on similar topics should be: 'they're talking about how we interface with the world through language'. — fdrake

Yes, and when they fail to do so, then, maybe, they're just passing off linguistics as philosophy of language, or they are falling prey to psychologism in the sense Husserl and Frege warned against. (Not that there is anything wrong with pure linguistics or scientific psychology, per se, but it's not philosophy.)

Just for reference, Michael Luntley's Contemporary Philosophy of Thought: Truth, World, Content, Blackwell, 1999, is a very good introduction to the philosophy of language qua philosophy of thought.

It will be added to the list. Thank you for the reference.

[transposed from Hard Problem thread]

But math doesn't depend on objects. — Manuel

Absolutely. And that it doesn't seem to depend on the universe, somehow. Utterly baffling. — Manuel

It's a question I'm very interested in. One point I've often raised is that numbers (and logical laws and so on) are not dependent on your or my mind, but can only be grasped by a rational intelligence. So they're mind-independent in the sense that they're the same for anyone, but mind-dependent in the sense they can only be grasped by an intelligence capable of counting. This clashes with the empiricist view that numbers (and the like) must be considered a product of the mind. It implies they are real but in a manner different to empirical objects of perception. And mainstream philosophy has no way to accomodate different kinds of real - for it, something is either real or it's not.

See the essay What is Math? in the Smithsonian magazine. James Robert Brown puts the Platonist argument for the reality of number. But the objections are that if numbers are not empirical objects, then you're opening the door to all kinds of 'mystical nonsense':

The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.

Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” ....

Massimo Pigliucci...was initially attracted to Platonism—but has since come to see it as problematic. If something doesn’t have a physical existence, he asks, then what kind of existence could it possibly have? “If one ‘goes Platonic’ with math,” writes Pigliucci, empiricism “goes out the window.” (If the proof of the Pythagorean theorem exists outside of space and time, why not the “golden rule,” or even the divinity of Jesus Christ?)

These objections speak volumes, in my opinion.

I'll check that article out, thanks for sharing.

Empiricism goes out the window if empiricism is construed as implying "publicly observable phenomena". But if you include experience in empiricism, as one must, if any empiricism is going to make any sense at all, then it remains as a method of investigation.

I agree with what you say about math being independent but requiring a mind to comprehend it. Mathematics is extremely strange and may be one of the reasons why Plato required knowledge of geometry to enter his academy, aside from its timeless otherwordly nature.

Apart from the fact that most mathematicians (including me) don't spend any time contemplating the possible Platonic nature of their subject, a more intriguing question is what makes a math subject or result "interesting"? Wikipedia lists around 25,000 math articles, so it's impossible for a single person to be more than superficially aware of more than a small percentage of these. What is it that drives these peculiar people to spend hour after hour pushing the boundaries of math further and further out? :chin:

Apart from the fact that most mathematicians (including me) don't spend any time contemplating the possible Platonic nature of their subject, a more intriguing question is what makes a math subject or result "interesting"? — jgill

What made it interesting to me was the (I thought) simple observation: that numbers (and the like) are unlike phenomenal objects, in that they're not composed of parts (strictly speaking that is only prime numbers) and they don't come into, or go out of, existence (i.e. they're not temporally delimited.) So they exist on a different level, or in a different sense, to objects, all of which are composed of parts and temporally delimited. But then, the idea that there can be different levels of existence, or different senses of existence, turns out to be a metaphysical question.

This was the subject of my first post on the predecessor forum to this one. An excerpt from that was as follows:

I started wondering, this (question, i.e. reality of number) is perhaps related to the platonic distinction between 'intelligible objects' and 'objects of perception'. Objects of perception - ordinary things - only exist, in the Platonic view, because they conform to, and are instances of, laws. Particular things are simply ephemeral instances of the eternal forms, but in themselves, they have no actual being. Their actual being is conferred by the fact that they conform to laws. So 'existence' in this sense, and I think this is the sense it was intended by the Platonic and neoplatonic schools, is illusory. Earthly objects of perception exist, but only in a transitory and imperfect way. They are 'mortal' - perishable, never perfect, and always transient. Whereas the archetypal forms exist in the One Mind and are apprehended by Nous: while they do not exist they provide the basis for all existing things by creating the pattern, the ratio, whereby things are formed. They are real, above and beyond the existence of wordly things; but they don't actually exist. They don't need to exist; things do the hard work of existence.

And no, I don't think it's anything to do with the pursuit of maths as such. There are excellent mathematicians, I have no doubt, who are inclined towards a Platonist view - Roger Penrose and Kurt Godel being two - but there are doubtless very many who don't. And you don't have to know much about maths to understand the major issue, that being the reality of intelligible objects.


//I guess in hindsight that excerpt is a bit over the top. I hadn't planned it, I just sat down to say something and that is what I came up with. I still think it's OK, though.//

Hi Streetlight. I hope you are well. As for Carlo Rovelli ... I have a short story for him:

Six Fools
One day, six fools from a certain village set out for pilgrimage. On their way, they had to cross a river swimming. After crossing the river, one of them counted them, not counting himself. He counted five. They were very upset at losing one of them. To be sure, each one of them counted again in the same way that the first one did and counted five. They informed the matter to a passerby. The passerby was amused at their stupidity. He agreed to produce the lost man. He took a stick and gave a blow on each head until he counted six. The six fools thanked him again and again for producing the lost man ‘miraculously’.
Moral : The stupid are stock of laughter.

Hi Streetlight. — Agent Smith

Long gone. I revived this thread because it was relevant to the point I was making elsewhere. Prior to that the last post was 4 years ago.

After crossing the river, one of them counted them, not counting himself — Agent Smith

"Materialism is the philosophy of the subject who forgets to take account of himself" ~ Arthur Schopenhauer.

My guess is your parable was intended to make this point.

"Materialism is the philosophy of the subject who forgets to take account of himself" ~ Arthur Schopenhauer — Wayfarer

Idealism is the philosophy of the subject who forgets to take account of being a body. :eyes:

Bodies always perish in the end.

Bodies always perish in the end. — Wayfarer

Thus, the a priority of the material (fundamental) and a posteriority of the ideal (emergent).

A pity. Streetlight had interesting things to say but he was a bit brusque in his conduct.

Anyway, as for your comment on different kinds/levels of existence, there's Meinong and his jungle to consider.

The senses and real
You can't see nor smell nor taste air, but it is real.
You can't hear a spanner fall on the moon, but it is real.
You can't touch a radio wave but it is real.

If so, just because you can't see, smell, hear, taste or touch a number, it doesn't mean numbers are not real.

As per Meinong, multiplicities are real (i.e. exist) and numbers are only abstractions (i.e. subsist), no?

As per Meinong, multiplicities are real (i.e. exist) and numbers are only abstractions (i.e. subsist), no? — 180 Proof

Yes, subsists is correct in Meinong's universe. Speaking for myself, I posit that are there are two universes, a) the physical universe and b) the mental universe and numbers exist in the latter while rhinos, the Eiffel tower, etc. exist primarily in the former.

:ok: I think Plato & Peirce (at least) agree with you.

I think Plato & Peirce (at least) agree with you. — 180 Proof

Universe + Ideaverse. We're explorin' the latter here aren't we? You seem to have visited many worlds from what I can gather from your writings and thoughts. I on the other hand have just begun my voyage. My ship was damaged and my navigator died. I'm low on fuel - crash landing on the nearest world. Wish me luck. Out! Hiss ... Crackle .... Crackle :rofl:

:strong: :sweat:

Isn't it a kind of pleasure which deepens desire rather than satisfying desire?

I think philosophy is like that for me.

It's an intrinsically satisfying activity which always leads to something more, unfinished.

Long gone. I revived this thread because it was relevant to the point I was making elsewhere. Prior to that the last post was 4 years ago. — Wayfarer

This is just a reminder of how good Streetlight was and how much he contributed to the forum.

:up:

numbers (and the like) are unlike phenomenal objects, in that they're not composed of parts (strictly speaking that is only prime numbers) and they don't come into, or go out of, existence (i.e. they're not temporally delimited.) So they exist on a different level, or in a different sense, to objects, all of which are composed of parts and temporally delimited. — Wayfarer

And yet the concept of number would be incoherent without the prior construction of the concept of a multiplicity , which itself implies the concept of persisting self-identical empirical object.

Husserl, in Philosophy of Arithmetic, describes a scenario for the stages of development of the modern consort of number:

“Let us transport ourselves into the early stage of the development of a people. The repeated interest in sensible groups of objects the same in kind had already led to the apprehension of a certain analogy, and therewith of a shared characteristic founding it; and thus it had led to the concept of multiplicity, which at this level, of course, being much less abstract than on our own, restricted itself to multiplicities of homogeneous and sense per-ceptible contents. The drive to communicate concerning the events of practical life, in which determinate groups of such objects played a great role, led here (when circumstances were particularly favorable) more easily than in other areas to the thought of an imitation by sensible means of the things repre-sented.

This thought would be immediately suggested by the hands. These visibly prominent organs, which the individual chief-ly employed in both serious and playful activities, and which (depending upon the position of the fingers) presented varying sensible group formations (the clusters of fingers), must accord-ingly have come immediately to mind for the imitation and sym-bolization of corresponding groups of arbitrary other objects? Thus the "finger numbers" arose within sign language as the first number signs. Indeed we can very well claim still more: it is as a rule only on this path of the sense perceptible that a sharp differentiation and classification of the determinate number forms could first come about at all.

In a certain manner one of course already possessed the number concepts when the analogy of different groups equinu-merous to one another and to groups of fingers was grasped. But only through a constant back-reference from groups of the most various types to the finger groups, sharply distinct in sensible appearance, did the finger numbers rise to the level of Representatives of general concepts, of general characteristics of groups classified in terms of more and less. Without fear of paradox we can say: the concepts 1, 2, 3, ... as the species of the general concept of multiplicity, as specifications of the "how many," first came to a more determinate consciousness in the conceptual signification of number signs on the fingers.”

And yet the concept of number would be incoherent without the prior construction of the concept of a multiplicity , which itself implies the concept of persisting self-identical empirical object. — Joshs

Of course, but I don't see any particular conflict with what I'm saying. I had the idea that arithmetic and geometry developed greatly with the establishment of the first agrarian cultures in the Nile delta and Fertile Crescent, used for calculating parcels of land and tallying grain harvests and the like.

(I'm quite interested in the basics of Husserl's philosophy of number but it appears daunting.)

Carlos Rovelli appears in the article I mentioned when I re-started this thread.:

Rovelli [calls into] question the universality of the natural numbers: 1, 2, 3, 4... To most of us, and certainly to a Platonist, the natural numbers seem, well, natural. Were we to meet those intelligent aliens, they would know exactly what we meant when we said that 2 + 2 = 4 (once the statement was translated into their language). Not so fast, says Rovelli. Counting “only exists where you have stones, trees, people—individual, countable things,” he says. “Why should that be any more fundamental than, say, the mathematics of fluids?” — What is Math

It's fundamental because of the way the world is, because we are indeed embodied beings and the world is constrained to exist in certain ways. But according to this argument, there are no necessary facts, everything just happens to be the case - everything is in some basic sense arbitrary, it could just as easily be otherwise. This, I think, is ultimately a form of nihilism.

Elsewhere Rovelli appeals to the Buddhist philosopher Nāgārjuna to justify his 'relational quantum mechanics' but he neglects the ethical dimension of Nāgārjuna philosophy, without which it would indeed be merely nihilistic. Rovelli appears to interpret Nāgārjuna to be saying that 'nothing really exists', which is the common, but fallacious, charge made against Nāgārjuna and the Madhyamika generally. See Bernardo Kastrup's Here I Part Ways with Rovelli:

What Rovelli seems to be now saying is that, although the physical world is constituted of no more than relationships, there is no underlying, non-physical world to ground those relationships. This is problematic for a number of reasons. For one, it immediately runs into infinite regress: if the things that are in relationship are themselves meta-relationships, then those meta-relationships must be constituted by meta-things engaging in relationship. But wait, those meta-things are themselves meta-meta-relationships... You see the point. It's turtles... err, relationships all the way down. — Bernardo Kastrup

See the essay What is Math? — Wayfarer

That article ends in a way not at all incompatible with the article from Street's OP.

Maths is a construction, matching the way the world is for much the same reason that a glove "just happens" to match a hand - it was made to fit.

Those mathematical objects are constructed, as the statue is constructed from Michelangelo’s Stone.

The idea that the mathematics that we find valuable forms a Platonic world fully independent from us is like the idea of an Entity that created the heavens and the earth, and happens to very much resemble my grandfa- ther. — Carlo Rovelli

I get it. After all, as Piggliuci says in that article, '“If one ‘goes Platonic’ with math, empiricism “goes out the window.” (If the proof of the Pythagorean theorem exists outside of space and time, why not the “golden rule,” or even the divinity of Jesus Christ?)"' And we certainly can't risk that, can we! Imagine the nonsense threads alone. (I did seek out and buy, at some expense, Brown's book Platonism, Naturalism, and Mathematical Knowledge, but it's a difficult read.)

And you don't have to know much about maths to understand the major issue, that being the reality of intelligible objects. — Wayfarer

I agree. That takes it to the realm of the meaning of words: reality.

↪jgill
Isn't it a kind of pleasure which deepens desire rather than satisfying desire?
I think philosophy is like that for me.
It's an intrinsically satisfying activity which always leads to something more, unfinished. — Moliere

:up: :up: Spot on, my friend! It's an ongoing exploratory adventure.

:fire: