I think that's true for the most part. I don't see any use of mentioning pragmatism again.

What do you think comes after the linguistic turn?

I disagree, most of what pragmatists wanted to accomplish has been already accomplished by linguistic philosophers, or it was some sort of natural tendency for the linguistic philosophers to somehow agree tacitly with the pragmatists(?)

Anyhow, seeing as this is going nowhere, I think, it makes sense to look into some sort of idea about what comes next? What's your take?

Why a new thread? — Banno

That really couldn't really be answered, instead of this one, Banno.

Like, who's going to verify such a statement that the linguistic turn is indeed dead?

If you prefer here then all the better?

...then you have the difficulty of differentiating analytic philosophy and linguistic philosophy. Noether term has a hard and fast definition.

The linguistic turn was a change in method. If it had a goal at all, it was to elucidate philosophical problems by taking care with the language involved. — Banno

This gives me a mental-cramp and creates a ill feeling. Namely, reading this as if it were definitional based, one can claim that this is closer to pragmatism by how you talk about treating it as a method instead of a 'turn' in philosophy.

... and this doesn't even sound wrong on face value!

I'm operating from the counterfactual, that linguistic philosophy was not treated as the mainstay, and instead analytic philosophy had its mainstay much earlier.


Also, what was the grand overarching goal of linguistic philosophy, and did it achieve it?

I have no use for category theory, but it does attempt to generalize areas of math that have similarities. I fear your knowledge of mathematics is so minimal that we are not getting anywhere here. Since I have been a mathematician (over fifty years) the subject has grown so dramatically and is so complex now I understand little of it myself. — jgill

Well, my knowledge doesn't seem to be a deterrent for some kind of discussion. All that I have concluded now is that there's no determined method to quantifying complexity in mathematics.

That said, it can't be denied that logic has its own language consisting of symbols with very precise meanings and instructions on how to use them correctly to cut through all the logically extraneous linguistic elements of discourse and zero in on an argument if there is one. However I still have misgivings about treating logic as just another language - there's more to it than mere words and rules on how to manipulate those words. — TheMadFool

Logic takes care of itself. The other issue is that language does (not) have a universal grammar.

What kind of truth about this whole issue do you think this has in common with category theory or perhaps this is sort of some kind of new logic at play? I mean, is there anything novel about this line of reasoning to the subject matter of mathematics?

Or maybe the act of inquiry and arising insights to sound more pragmatist?

A lot of people are baffled by this topic for some reason, where I see this in a sense very apparent in mathematics nowadays to talk about the sort of lack of categorization, that can even at all begin or take place!

True, but, there's a category of importance or impotence nowadays on every roster.

Totally. It's no mistake nowadays that analytic philosophy has proffered from logical positivism and figures such as Quine and Carnap as well as Schlick and other logical positivists.

I'm not quite sure Quine was a logical positivist or something that came after its advent.

A term invented after the fact for an approach to philosophy that began with critiques of the obscure language of the Hegelian thinking of the 19th Century and the discursive narratives that it produced, seeking a return to analysis. The critics held that philosophy should focus on being clear and coherent. There were two threads to the linguistic turn. One was formal, seeking to use the newly developed logic of propositional calculus to set philosophical issues out clearly. The other used natural languages such as English, seeking to clarify issues of ambiguity by an analysis of the complexity of words.

It's roughly congruent with analytic philosophy. — Banno

Congruent? It's a travesty that logical positivism got shat on and Cambridge wanted to go for common sense philosophy, whilst America steadfast followed the post-war logical positivist boon of philosophers from Europe, invested in or by pragmatisms influence or better stated congruence.

it would be better to say that the linguistic turn is now so ubiquitous that it goes unnoticed. — Banno

What does that mean?

The OP is misguided to say that the linguistic turn is now over; it would be better to say that the linguistic turn is now so ubiquitous that it goes unnoticed. — Banno

Not really, as nothing profound has actually changed in the field of philosophy. Go ahead and read the afternotes of Rorty's The Linguistic Turn.

Metaphysical questions still take place as often as they used to.

What's next? Perhaps a return to pragmatics?

Sure, but this is quite a conundrum towards the notion that everything in mathematics should or is determinate.

I think the OP trite, and hence thoughtless. — Banno

As well as this comment, huh?

I posted this in another thread about logical positivism/atomism/monism being, quite possibly, a precursor to formal languages like programming languages and such?

It's a stretch, and to get back on topic, I suppose that there's some truth to the notion that philosophy in some sense needs innovation rather than criticisms of past philosophers all the time.

What do you think?

Do you think Wittgenstein would like Apple more or PC?

But, but, we're all using the internets, and the computer positivists are smiling in their graves with all this formalism in language with Grammarly!

They gave to the world everything including primitives in your latest logical space Operating System.

From the link above: "So, I don't think anyone has addressed the question posed in the title; but, is complexity in mathematics in your opinion determinate?"

No. No more so than complexity in human thought is determinable. — jgill

I was expecting something like:

Mathematics is deterministic, and yet, this situation arises.

Maybe some stuff in maths can get organized better with this in thought?

Logical simples solves the issue. Just can't find em.

Posted on PhysicsForum also:

https://www.physicsforums.com/threads/is-complexity-in-mathematics-determinate.1000094/

Different times, eh?

Where a unit of a good is defined much more precisely in digital goods, and the brand of a product doesn't influence the quality factor of the good, then the effect of deflation is more apparent in sum total.

I'm not sure cars are a good example, due to the variance and band effect on the final good.

It's interesting that with strict economical analysis of such mercantilist firms like Tesla, that this becomes more apparent.

But, how do you get around variables influencing homoscedasticity of the curve during time evolutions?

Might I suggest that this question is about syntax and not math?
simplicity vs. complexity — Rxspence

Interesting approach. What kind of general syntax applies to proof telling?

Into 3D or possibly 4D? Such as time evolutions?

Do theorems "provide" for proofs? Especially ones that are "least complex" or "more complex"(than what?). And this is "logicizing" logic? — jgill

I seem to have run into issues with describing the part about complexity due to the fact that there's no (extra)-systematic way of formalizing mathematics apart from discerning some form of induction rather than say induction on the part of not logic but rather intuitive reasoning about how one should go about designing a proof for a theorem. What I do try and state, rather poorly is that there's inherent issues with trying to state something of the sort as to whether one can determine the complexity (if it pertains at all in any systematic manner) towards a proof of a theorem. It might be easier to think of this as if the incompleteness theorem were to assert that we just expand the alphabet of a theorems proof until it satisfies some least complexity if at all ever can be estimated.

My attempts seem to be closer to what Hilbert may have been trying to do in his program.

Hope that made sense.

What is "congruent mathematics"? Just curious. — jgill

Geometry, mainly.

Maybe unscramble this — jgill

I think it is better understood in number theory for example. Is every theorem able to provide for a proof that is least or more complex, and what this would itself amount to? I see that there's difficulty in understanding this because mathematicians aren't accustomed to treating logic as much as it used to to be about logicizing it.

Generic psychologies need not apply.

It's a pitiful psychology to find a niche in terms of dangly parts instead of something so much more complex and sophisticated as a computer. Be it as it is, human psychology doesn't seem entertaining to me. It kind of hangs around the same topic all the time. And, to further say that computers or sophisticated Generalized-AI doesn't have a psychology is doubly erroneous.

Solipsism is everything to me.

Isn't it humiliating to think a computer is superior to you in every single regard? As much as you'd like to pitifully think you are better or greater or faster or more beautiful, it just ain't so honey.

Did you have an example of one? — apokrisis

Seemingly, an example cannot be provided since, I think, it cannot ever be determined if it really is conscious or even sentient according to the information processor theory or something?

Of which there are none. Except in every sci-fi work of fiction I guess. — apokrisis

How are you so sure?

Did you misunderstand? I was saying that humans with conscious intent write the programs. The computer runs the program without consciousness or intent. — apokrisis

Ok, makes sense. But, I'm focusing on sentient computers.