Given the form of the TLP, you can imagine why Witt would have thought about it. — macrosoft

Yes, I can see why you would say so. But care to expand?

Lots of debate about math involves infinity. How does infinity exists? It is certainly a symbol in the calculus. Can we apply the LEM to infinite sets? Is math eternal? Or does it actually get constructed a bit at a time. Are mathematical statements true or false? Or is there a third state not of unknown but rather not-yet-created-either-way. Does the system of real numbers capture our intuition of the continuum? Is logic really the heart of math? Or does logic follow behind a separate mathematical intuition? Can real numbers be truly real if 'most' of them contain an infinite amount of information (cannot be compressed into a algorithm that generates them to arbitrary precision)?

The machine of math can get along fine without answers to such questions. It is more or less grounded in the consensus about what constitutes a proof. As a rough approximation, I'd say that Wittgenstein would approve of any calculus as a calculus, but he is skeptical about the addition of mental entities and would ground math more in practice and applications. Have you seen the diagonal proof of uncountable infinity? It's fairly short for such an exciting result. And the idea can be repeated an infinite number of times, giving rise to a sequence of richer and richer infinities. I like to obsess over the set of all infinite sequences of bits (closely related to the real numbers and also thinkable as the set of all infinitely long files.) For instance, 10101010101... would be (correspond to a ) rational. But most possible sequences have no compressible pattern. We could of course never write them out or even find a finite description of them. In what way do such sequences exists? We can grasp them to some degree. Such sequences (an ungraspable background that takes up most of the space on the line) are my metaphor for what the later Wittgenstein is trying to point at. Whatever can be said can be said clearly is clearly wrong, IMV.

Yes, I'd say so. And I'd say that WIttgenstein is an anti-Platonist in some sense. He's hard to pin down. He just writes lots of remarks.

The problem, as Wittgenstein sees it, is that mathematicians, especially foundationalists (e.g., set theorists), have sought to accommodate physical continuity by a theory that ‘describes’ the mathematical continuum (PR §171). When, for example, we think of continuous motion and the (mere) density of the rationals, we reason that if an object moves continuously from A to B, and it travels only the distances marked by “rational points”, then it must skip some distances (intervals, or points) not marked by rational numbers. But if an object in continuous motion travels distances that cannot be commensurately measured by rationals alone, there must be ‘gaps’ between the rationals (PG 460), and so we must fill them, first, with recursive irrationals, and then, because “the set of all recursive irrationals” still leaves gaps, with “lawless irrationals”. — SEP

All actual calculation uses a finite alphabet (is discrete.) Even the proofs about infinities are just strings of symbols that satisfy certain rules epistemologically. So the question is 'what are these proofs about'? Some thinkers just say that math is the science of such systems of rules. On the other end, we have intuitive access to some kind of timeless realm that the rules are like the shadow of. In my opinion, there is indeed some kind of shared meaning space, but we can't make it explicit except through 'mechanical' rules if we want reliable consensus about progress. To say that this meaning space is 'here' or 'there' (just human or some Heavenly stuff) is beside the point. What matters is how these things exist for us --and that seems to be largely a personal matter, since math is economically grounded in applications.

This is maybe a good taste:

What arithmetic is concerned with is the schema ||||.—But does arithmetic talk about the lines I draw with pencil on paper?—Arithmetic doesn’t talk about the lines, it operates with them. — W

Yeah, as I said. Heavy stuff to talk about. I don't have much to comment otherwise.

Yeah, as I said. Heavy stuff to talk about. I don't have much to comment otherwise. — Posty McPostface

It's of more interest to someone with training in math, but it's of general interest as a critique of the one uncontroversial metaphysics we have: math. Especially in this highly normalized discourse the problem of meaning or being emerges. This teaches us something about the metaphysical dream. We can line up our concepts very nicely and build spiderwebs of eternal truth. At the same time, we don't know what we are talking about, and we mostly don't know that we don't know what we are talking about. Epistemology dominates ontology. The mystery of meaning sleeps.

At the same time, we don't know what we are talking about, and we mostly don't know that we don't know what we are talking about. — macrosoft

Ah, known knowns, known unknowns, and unknown unknowns. Interesting stuff.

Ah, known knowns, known unknowns, and unknown unknowns. Interesting stuff. — Posty McPostface

Yes. IMV both WIttgenstein and Heidegger are pointing at an unknown known, the actual ground of our doings and believings which is inconspicuous for the atomizing theoretical gaze obsessed with clear and distinct ideas and objects with rock-like constant presence. This ground is not clear and distinct, and yet it makes the quest for a clear and distinct description of experience possible. I don't know that I have hands. 'Know' is the wrong word here.

Philosophy almost exclusively deals with known unknowns and unknown unknowns. I think go about this issue epistemologically is the only way forward. Once known unknowns and unknown unknowns become known then the issue is settled through dialogue or in a dialectical manner, and hopefully Rogerian agreement. Am I sounding pragmatic?

Philosophy almost exclusively deals with known unknowns and unknown unknowns. I think go about this issue epistemologically is the only way forward. Once known unknowns and unknown unknowns become known then the issue is settled through dialogue or in a dialectical manner, and hopefully Rogerian agreement. Am I sounding pragmatic? — Posty McPostface

For me the question is right there in what it means to 'become known.' What is it for something to become known? Before we can plug a thesis into the argument machine, it has to born in someone's mind. And then the argument machine can't just be a dead machine operating on syntax. So how does what we argue about exist for us? How we can argue about the 'same thing' from different skulls. What I have in mind in the mystery of language, the 'house of being.' We tend to obsess over building the right machine, a sort of god surrogate as method. That's fine, but it's mostly politics in disguise, a play for authority and utility.

I am steeped in pragmatism, but I think there is something in humans that is not so interested in utility or consensus. We are the 'animals' that throw our lives away for causes, etc. What does it mean that we can commit suicide in cold blood? How does this complicate utility? Even if we explain it away in genetic terms, there is still the issue of how being human exists for us, from the inside. A predictive model is not what we are looking for inasmuch as we don't just want utility.

Before we can plug a thesis into the argument machine, it has to born in someone's mind. And then the argument machine can't just be a dead machine operating on syntax. So how does what we argue about exists for us? — macrosoft

So, your talking about understanding, having a mind, and intention here? Have you heard of the Chinese Room Argument?

So, your talking about understanding, having a mind, and intention here? Have you heard of the Chinese Room Argument? — Posty McPostface

Yes, and Yes, I like it.

I have been told that the concept of having a "mind" in philosophy, generates more problems than it solves. What's your take on the Chinese Room Argument?

On Certainty is fantastic. Every time I came back to it, I'm blown away. The sensitivity with which Witty approaches language is just unmatched in it. — StreetlightX

I feel the same way but for whatever reason the book, which is taken very seriously by epistemologists, seems to be totally ignored by mainstream philosophy of language. I guess it's just not "technical" enough for those folks?

Hi John Doe. Do you recommend any particular companion to use for this reading group of the Investigations. Your last suggestion in the Tractatus reading group was very helpful.

Sorry to bother otherwise.

Heh, I guess it is a pretty elliptical piece of writing, one that does more to circle around its object(s) in various ways than approach them directly. It's not very scholarly. But probably all the better for it.

Glad to hear the Tractatus suggestions worked out! I'm sorry I didn't participate in that group more. As far as the PI is concerned, honestly, I don't think there's a great companion that doesn't put an onerously heavy interpretative spin on the material. It's really a shame because there's such an abundance of great material on e.g. Being and Time. I think this might be due to scholarship on analytic philosophers generally tending to be a very boring affair.

There is a tendency, though, to break the PI up into chunks according to what Wittgenstein had in his notes / as the book gets sectioned off in The Big Typescript. So the "metaphilosophy" section, the "rule-following" section, etc. So one thing you might think about doing is reading the seminal works which correspond to these sections. For example, Stanley Cavell has a lot to say on the opening aphorisms (1-89). You could do Kripke versus McDowell on rule-following. Etc. But you would definitely need someone smarter than me to organize that sort of chaotic approach.

Yeah so this is something I've been wondering about for a long time, though. It strikes me as pretty bizarre that the current experts on Wittgenstein's primary topic of interest have so little interest in him. And I can't figure out if it's because there genuinely are a lot of highly problematic ideas in his writings that I fail to pick up on due to lack of specific expertise or - this being the default theory that all of us dismissive continental types are quick to grab hold of - it's just typical old pedantic formalists unable to engage with any living creature whose mind happens to be more creative than boiler-plate academic paper-writing. Of course, none of this would affect my deep admiration for L.W.

I'm sorry, but I have an aversion to reading groups of any kind. Don't know why.

Shucks, and here I was hoping Bitter Crank would lead the reading group. :)

Which reading guide? Do you have a pdf?

I'm still unsure which reading guide to pick. Once some consensus on what reading guide should we use I'll upload it to be shared by other participants in the reading group.

Are we assuming people have already read Philosophical Investigations?

That doesn't really matter. Ive skimmed the book but haven't read it cover to cover. Preferably if someone had already read it, they might do a better job at managing this reading group.

If you're looking for something simple and straight-forward why not just go with the relevant Routledge Guidebook?

If you're looking for something simple and straight-forward why not just go with the relevant Routledge Guidebook? — John Doe

I think I will. Any pointers? Is it available also for free?

I have been told that the concept of having a "mind" in philosophy, generates more problems than it solves. What's your take on the Chinese Room Argument? — Posty McPostface

I think Searle is just pointing at meaning. Such meaning generates problems because the fantasy is that one can create a explicit system that does not break down. We are trying to capture our capturing itself. We are tying to trap a mist in a spiderweb. This mist is trying to trap itself in a spiderweb. This spiderweb is a small set of words ripped out of their living context and somewhat naively interpreted as little containers of exact meaning with which we can do 'math.' We can't say exactly what we mean by 'meaning,' but we 'are' this meaning and live in this meaning. We know that others live in this meaning in the same that we know that we have legs when we are walking. It is sub-knowledge, pre-knowledge, ur-knowledge, just like our knowledge that there is a world. This 'world' that we have ur-knowledge of is not explicit for theory. Every explicit account of it simultaneously depends on it and fails to capture it, hence the endless debate, since each account trips on its own atomic approach in relation to other atomic approaches. Theory speaks from a dark place that dimly assumes this world in which others are listening. The others too are not fundamentally explicit. 'I think therefore I am' is spoken from a dark place that 'primordially' under-stands itself to be hear-able. What is this 'I'? Does it not point at the dark place from which we speak and listen?

How can I prove such assertions? If they are true, you and anyone else must already have access to this knowledge. Just as we ignore our feet as we are walking across the street to meet a girl we are thinking about, so we mostly ignore our ur-knowledge, especially if we demand that experience fit an erotically charged method that assumes the real must exist sharply, as the output of an argument.

*I don't think it is impossible that a computer could somehow be made to experience meaning, but I think that humans doing so would be their most spectacular and eerie achievement. Lesser forms of AI (and I work with some) are really 'just' complex computable functions. A much more complex alien might say the same thing about us, but we can't sincerely do so, IMV. We have would to mean something in the saying of it.

I think Searle is just pointing at meaning. Such meaning generates problems because the fantasy is that one can create a explicit system that does not break down. — macrosoft

What's wrong with this pursuit? There's no other way to address the issue, then treating it explicitly.

What's wrong with this pursuit? There's no other way to address the issue, then treating it explicitly. — Posty McPostface

There's nothing wrong with it. Indeed, I myself am trying to make the inexplicit more explicit --in its very resistance to being made explicit. I'm pretty sure this is what Witt was getting at in On Certainty, but I'll need to reread it to check my memory against what I didn't understand at the time.

It's not that different from Hegel's realization that thoughts tend to contain internal contradictions. Basically the same kind of thing is tried hundreds of ways (squaring the circle) until someone figures out why this is impossible. Even after that proof was available (that squaring the circle was indeed impossible), many kept trying, some mistakenly thinking they had done so. As I see it, W and H have truly advanced philosophy.

What's wrong with this pursuit? There's no other way to address the issue, then treating it explicitly. — Posty McPostface

Also I think you are missing out on something. I'm guessing all this knowing business is not making sense. But that's at the center. I won't make sense to you unless you grasp the basic idea --or rather phenomenon point at by the idea.

I won't make sense to you unless you grasp the basic idea --or rather phenomenon point at by the idea. — macrosoft

What do you mean by that?

I’ve read Philosophical Investigations and own a copy. Not forking out for a guidebook though. I’ll try and chip in when I can.

When you starting this?