• Isaac
    10.3k
    No, its the deflationary view of truthSeppo

    Oh, that's not my understanding of the deflationary position at all (which, for me, is admittedly mostly from reading Ramsey). Do you have to hand any sources you use for yours? For me deflationary positions on truth cannot include the expression ""x" is true iff..." in any sense at all because 'true' cannot be a property of a proposition in a deflationary understanding. Truth not being properly a property of anything.

    this is to miss the point in any case: the point is that not only are these claims/beliefs truth-apt, they are true, for all but the rarest cases (the handful of people who actually have been to the moon, and the people who don't have two hands, for whatever reason).Seppo

    Well, it is if that's the position on truth that Wittgenstein held, yes. As I say, I'm not sufficiently expert in his works to gainsay your assertion, but I always thought he took a more Ramseyan attitude to truth, which would impinge directly on the point of whether hinge propositions are 'true' as Wittgenstein understood the term. That's all I was saying.

    If Wittgenstein did indeed understand 'true' to mean something such that ""I've never been to the moon" is true iff I've never been to the moon", then you're right, but I've never read anything to that effect so I'd be grateful for a pointer in the right direction.
  • Luke
    2.6k
    Could a mathematical proposition that is true be false? No. Could a mathematical proposition be false? Yes.Fooloso4

    What I meant, wrt my post to Seppo regarding the bipolarity of propositions, was: is 12x12=144 susceptible of being false? If not, then it is not a proposition (in Wittgenstein’s view), and neither is it susceptible of being true.
  • Sam26
    2.7k
    The argument is invalid, its conclusion doesn't follow (as has already been pointed out to you) and the "force" of an invalid argument can't really "end the discussion", obviously. If you want to end the discussion, you could venture a reply to my post here.Seppo

    You apparently haven't studied logic. The argument is a hypothetical syllogism, which means that it's valid. What you have to demonstrate is that one of the premises is false, i.e., that it's not sound. So, the valid form of the argument is...

    If p, then q.
    If q, then r.
    Therefore, if p, then r.

    And, since you apparently don't know the difference between a valid deductive argument and an invalid one, I'm not even sure you're qualified to say whether the argument is good or not. And, by the way, your statement that the conclusion doesn't follow is also false, because given the premises, and the validity of the form of the argument, the conclusion follows necessarily. Again, the only way to defeat the argument is to show that at least one of the premises is false.

    So, maybe you should rephrase your statements.
  • Sam26
    2.7k
    If Wittgenstein did indeed understand 'true' to mean something such that ""I've never been to the moon" is true iff I've never been to the moon", then you're right, but I've never read anything to that effect so I'd be grateful for a pointer in the right direction.Isaac

    Wittgenstein had a more pragmatic idea of truth. It was never outlined as some are doing in this thread. It was never, something is true, iff such and such (unless you're thinking in terms of the Tratatus), at least as a general rule. This would be anathema to W.'s later philosophy. For W. one looks at a variety of uses within the context of our everyday lives.
  • Fooloso4
    6.2k
    is 12x12=144 susceptible of being false? If so, then it is not a hinge.Luke

    Are you claiming that a hinge is not susceptible to being false? Or are you making a claim about mathematical hinges?

    Is the concept (I am trying to avoid the term proposition and the confusion it may cause, independent of OC) of the earth revolving around the sun a hinge? Is it susceptible of being false? At one time the sun revolving around the earth was a hinge.
  • Isaac
    10.3k


    Thanks. My reading of Wittgenstein is limited to PI and OC plus a few random papers, I acquired the impression I outlined to @Seppo only from a single lecture given by Cheryl Misak (placing Wittgenstein amongst the Cambridge pragmatists), so I didn't have a lot of textual support. I appreciate the guidance.
  • Luke
    2.6k
    Are you claiming that a hinge is not susceptible to being false? Or are you making a claim about mathematical hinges?Fooloso4

    My immediate point was that the equation 12x12=144, and similar fundamental mathematical statements more generally, are not susceptible to being false. That this can also be extended to some empirical statements was W’s concern in OC.

    Is the concept (I am trying to avoid the term proposition and the confusion it may cause, independent of OC) of the earth revolving around the sun a hinge? Is it susceptible of being false? At one time the sun revolving around the earth was a hinge.Fooloso4

    Yep, hinges can become propositions and propositions can become hinges. I think that today it is incontrovertible that the earth revolves around the sun, so it would be a hinge, unless or until some new scientific discovery were to change that.
  • Sam26
    2.7k
    Yep, hinges can become propositions and propositions can become hingesLuke

    This is an important point I tried to make earlier in the thread, and it's where a lot of confusion happens. Moore's propositions (not really propositions if they are hinges) for the most part are hinges, but W. gave e.g.s, where in some contexts, they are not hinges, and therefore propositions. It's this back and forth that causes many interpretative errors in my view.
  • Fooloso4
    6.2k
    I think that today it is incontrovertible that the earth revolves around the sun, so it would be a hinge ...Luke

    @Sam26

    And therefore not a proposition? And that is because a proposition can be either true or false and a hinge can't? So at one time, the sun revolves around the earth was a hinge and not a proposition? But now it is not a hinge but a proposition?

    Where does Wittgenstein make this distinction between hinges and propositions?

    I think the distinction he makes is not between hinges and propositions, but between propositions that function as hinges and propositions that do not. That is not to say that all hinges are propositions, but to say that the statement "the earth revolves around the sun" is not a proposition because it is a hinge is to make restrictive demands on its usage.

    It reminds me of a quip by Wittgenstein:

    Philosophers use a language that is already deformed as though by shoes that are too tight.

    Just as waking is made difficult in shoes that are too tight, thinking is made difficult by a language that is too restrictive.
  • Sam26
    2.7k
    I think the distinction he makes is not between hinges and propositions, but between propositions that function as hinges and propositions that do not. That is not to say that all hinges are propositions, but to say that the statement "the earth revolves around the sun" is not a proposition because it is a hinge is to make restrictive demands on its usage.Fooloso4

    I have no problem with that view. It's probably a better way to say it.

    I think there are different kinds of hinges too. I believe that non-linguistic actions, like the action of opening a door, shows my belief in the door, my hands, objects, etc. It's the certainty of the background that is the springboard to epistemology and doubt.
  • Banno
    25.2k
    But this is more or less a correspondence view of truth, if the aim is to understand what Wittgenstein was getting at in OC, what do you think using such a non-Wittgensteinean definition of truth brings to that project?Isaac

    Throughout On Certainty Wittgenstein takes great care to keep truth, certainty and knowledge seperate. Wittgenstein also takes care to treat truth as belonging to propositions, but certainty and belief and knowledge as relations between people and propositions.

    Wittgenstein made explicit in the tractates that "the world is what is the case", that what is true is what is the case (for a start see 4.02 and thereafter, 4.06 and thereafter). Now this is not quite correspondence, there is some nuance, but it remains that the world is what makes certain statements true. I am not aware of anything in his subsequent writings that leads this approach into doubt; if you are, point us to them.

    Again, the ani-realist reading of Wittgenstein is relatively recent, and I think unsupported by the text. It's folk reading their anti-realism into his writings.
  • Banno
    25.2k
    A proposition standing alone, i.e., without justification, can have a value of either being true or false, it's a simple claim or belief.Sam26

    Where did you conflate truth and belief? Right there. A proposition standing alone can have a value of true or false; but it is not a claim or a belief until it enters into relation with the person claiming our believing.

    "P is true" is a single-place predicate.

    "A believes that P is true", "A claims that P is true","A is certain that P is true","A knows that P is true","A doubts that P is true" - these are all relations between proposition P and person A.

    Anti-realism denies this.

    (1) If knowledge claims are necessarily about the process of arriving at truth, then Moorean propositions are necessarily about truth claims.
    (2) If Moorean propositions are about truth claims, then necessarily W.'s attack is an attack on the truth of Moorean propositions.
    Sam26

    Again, this not only does not follow, but is not supported by the text. Wittgenstein's attack is very really against the justification of Moore's claim, not it's truth.

    Here's one place he discusses the issue:

    204. Giving grounds, however, justifying the evidence, comes to an end; - but the end is not certain propositions' striking us immediately as true, i.e. it is not a kind of seeing on our part; it is our acting, which lies at the bottom of the language-game.
    205. If the true is what is grounded, then the ground is not true, not yet false.
    206. If someone asked us "but is that true?" we might say "yes" to him; and if he demanded grounds we might say "I can't give you any grounds, but if you learn more you too will think the same."

    If this didn't come about, that would mean that he couldn't for example learn history.

    While §205 might at a glance appear to give support to an anti-realist view, look at §206. It is clear the proposition is true, yet ungrounded. §205 says the grounding is neither true not false, §206 says that the corresponding proposition is true.

    Going back to my previous analogy, it is pointless to argue whether the hinge is part of the door or part of the wall. (§205 is about that part of the hinge that is on the wall, §206 is about that part of the hinge that is on the door?)

    But the hing can be expressed as a propositions and that proposition is true.

    So please reconsider this:
    (2) If Moorean propositions are about truth claims, then necessarily W.'s attack is an attack on the truth of Moorean propositions.Sam26
    Do you really wish to claim that when Moore held up his hand and said "Here is a hand", that what he said was neither true nor false? That strikes me as absurd.

    And again, if basic propositions are to ground our knowledge, then we must be able to set out their logical consequences. But if they have no truth value, they can have no place in any sort of deduction. They are useless.
  • Banno
    25.2k
    It was never, something is true, iff such and such (unless you're thinking in terms of the Tratatus), at least as a general rule. This would be anathema to W.'s later philosophy.Sam26

    Oh, take care here. For example, Kenny lists as one one the elements common to the whole of Wittgenstein's work, including the Tractatus, that "a proposition is true or false in virtue of its relation to reality". The change is what that relation to reality consists in. He also lists "A proposition must be independent of the actual state of affairs that makes it true or false".

    Your anti-realist reading is one of several, and a comparatively recent addition to the exegesis off Wittgenstein. I think it misguided.

    @Isaac, what I have been saying here is not dependent on Davidson's T-sentence, if that is what you are thinking. Davison's considerations mostly take place within the scope of Wittgenstein, as it were. After all, T-sentence presuppose that the right hand side is understood.
  • Banno
    25.2k
    The argument is valid but has a false premise.
  • Banno
    25.2k
    I think the distinction he makes is not between hinges and propositions, but between propositions that function as hinges and propositions that do not. That is not to say that all hinges are propositions, but to say that the statement "the earth revolves around the sun" is not a proposition because it is a hinge is to make restrictive demands on its usage.Fooloso4

    Indeed, the term "hinge proposition" is the source of much of the confusion here.

    A hinge is a way of acting in the world, it is "animal"; but it can also be stated. So Moore acts in such a way that it is beyond doubt that he has a hand. And "Here is a hand" is true.

    And again, it is patently absurd to suppose that since the proposition "Here is a hand" presents a hinge, it is false, or worse that it is not truth-apt. If it is beyond doubt, how could it be considered not to be true? As if something that is neither true nor false could yet be beyond doubt... As if something could be certainly true and yet not truth-apt...? Or is the supposition that we can be certain that this is a hand and yet not certain that "this is a hand" is true?

    Better to consider being a hinge as a role a proposition might play within given language game.
  • Sam26
    2.7k
    Where did you conflate truth and belief? Right there. A proposition standing alone can have a value of true or false; but it is not a claim or a belief until it enters into relation with the person claiming our believing.Banno

    I don't mean by "stand alone"' that it's not connected to a person. Why do you think I said it's a claim or belief? A claim or belief, is by definition, connected to a person. Claims and beliefs don't pop into thin air without people. What I mean by alone, is without justification. A mere belief without justification can be either true or false. It's not true, until there is some kind of justification involved. Otherwise it's just a simple claim or belief - an opinion.

    Do you really wish to claim that when Moore held up his hand and said "Here is a hand", that what he said was neither true nor false? That strikes me as absurd.Banno

    Yes! Because that is what Moore is claiming, that he knows his statements are true. And, that is what W. is arguing against. What is it that Moore is claiming to know, if not the truth of his claims, and that he's justified in claiming they're true. The only thing that's absurd is keeping truth in Moore's statements while W. is saying he doesn't know what he thinks he knows. If he doesn't know that he has hands, then it necessarily follows that he doesn't know that they're true.

    You have completely gutted Wittgenstein's arguments. Moreover, it is supported by the text. In fact, the quotes you took from OC don't support your position.

    If my argument doesn't follow, then you have to demonstrate which of my premises are false, which you haven't done. Simply saying it doesn't follow, doesn't suffice.
  • Banno
    25.2k
    ...it is not a proposition (in Wittgenstein’s view), and neither is it susceptible of being true.Luke

    So your argument, if I understand it, concludes that 12 x 12 =144 is not true.

    Hence why not reject your argument by reductio?
  • Sam26
    2.7k
    I don't give two shits about anti-realists. My reading has nothing to do with anti-realists. Good God, have you lost your mind. Go talk to MU, maybe you'll get you mind back.
  • Banno
    25.2k
    Here you express an anti-realist view:
    A mere belief without justification can be either true or false. It's not true, until there is some kind of justification involved.Sam26
    Then:
    I don't give two shits about anti-realists.Sam26

    Yeah, might have to leave you to it for a while. Cheers.


    Edit: Had you instead said "it is not known to be true until there is some kind of justification" I would agree.
  • Banno
    25.2k
    Because that is what Moore is claiming, that he knows his statements are true. And, that is what W. is arguing against.Sam26

    Wittgenstein is arguing that Moore uses the word "Know" in "I know I have a hand" incorrectly; that what he might instead have said is "I am certain that I have a hand".

    "I know I have a hand" is incorrect because knowledge requires justification.

    "I am certain that I have a hand" is correct because it is not a statement, the truth of which he could doubt.

    In neither case is Wittgenstein entertaining the view that "Here is a hand" might be anything other than true.
  • Sam26
    2.7k
    I don't recognize my thoughts as you repeat them back to me. This isn't going anywhere, so ya, we should move on.
  • Banno
    25.2k
    Sure. Time to clear the air.

    Do you agree with
    Wittgenstein is arguing that Moore uses the word "Know" in "I know I have a hand" incorrectly; that what he might instead have said is "I am certain act I have a hand".

    "I know I have a hand" is incorrect because knowledge requires justification.

    "I am certain act I have a hand" is correct because it is not a statement, the truth of which he could doubt.
    Banno

    If so, then our difference is probably trivial. If not, then where and why?
  • Luke
    2.6k
    So your argument, if I understand it, concludes that 12 x 12 =144 is not true.

    Hence why not reject your argument by reductio?
    Banno

    Perhaps you could if it implied that 12 x 12 = 144 was false. But, according to Wittgenstein, the mathematical equation is nonpropositional, so it is neither true nor false.

    But feel free to present an argument.
  • Banno
    25.2k
    according to Wittgenstein, the mathematical equation is nonpropositionalLuke

    Where does he say this?
  • Sam26
    2.7k
    Do you agree with
    Wittgenstein is arguing that Moore uses the word "Know" in "I know I have a hand" incorrectly; that what he might instead have said is "I am certain act I have a hand".
    Banno

    Here is a quote from one of Moore's papers, A Defense of Common Sense (second paragraph of first page).

    "The method I am going to use for stating it is this. I am going to begin by enunciating, under the heading (1), a whole long list of propositions, which may seem, at first sight, such obvious truisms as not to be worth stating: they are, in fact, a set of propositions, every one of which (in my own opinion) I know, with certainty, to be true."

    He's arguing against Moore's use of the word know, as an epistemological use, and all that entails. For me, that entails justification and truth. Moreover, Moore is stating above, what he knows, viz., he knows these truisms are true with certainty. And, he does use the word certain, as you can see, but certainty has different uses. It can be used as a synonym for knowing as W. points out in OC 8. It can also be used to emphasize my subjective certainty, i.e., as an expression of my conviction. The use of the word know is often used like this too. Of course the use of the word know and certain when used to express the subjective, is not an epistemological use, or an objective use (that I have evidence or good reasons), it's akin to a feeling or maybe an intuition. One often confuses an expression of conviction (e.g., someone might say with emphasis, "I know I'm right." - this is just an expression of a subjective conviction) with actual knowledge, but knowledge, as you know, is established objectively (OC 14, 15).

    There is a kind of certainty that is expressed in our actions, i.e., as we act within the world, our actions show our certainty. However, this use is similar to subjective certainty above, but without the use of language. I act with certainty as I open the door. My actions show that I'm certain there is a door, that I have hands, etc.

    So, again, what is it that Moore knows? He's claiming to know, and also that he has the proper justification (a proof) for, the truth of his propositional claims.

    "I know I have a hand" is incorrect because knowledge requires justification.Banno

    I agree, knowledge necessarily requires some justification. Again, ask yourself, what are we trying to justify if not the truth of Moore's claims? Note in OC 21 W. says that Moore's assertions are more like the concepts of a belief, a surmise, or be convinced of "...in that the statement "I know... can't be a mistake. And if that is so, then there can be an inference from such an utterance to the truth of an assertion." This is the point of Moore's claims, their truth. However, W. argues, it's as if Moore's claims, that aren't justified, force us to the truth, but how in the world do they do that if they aren't justified, i.e., how do we know their truth without justification? Moore's supposed propositions are akin to mere beliefs or mere claims, which maybe true, or they maybe false. The truth of the claims have not been established without justification, which is why they cannot be true or false, neither has been established. Moore's propositions have the potential to be true, but they also have the potential to be false; and without justification one way or the other, we just don't know, which is why they aren't truths. Moore claims they are truisms, but W. argues against this whole view of Moore's. Any claim without justification, is a claim that only has the potential to be true or false. It cannot be said to be true unless there is a justification for that truth.

    There is much more to this, but I'd have to do more exegetical work.
  • Isaac
    10.3k
    Wittgenstein also takes care to treat truth as belonging to propositions, but certainty and belief and knowledge as relations between people and propositions.Banno

    Does he? I defer to your greater knowledge here, but your assertion really surprises me as it upturns a huge portions of my understanding of Wittgenstein's approach to truth (not to mention making a hash of Cheryl Misak's lecture).

    Here's where I'm getting my understanding from, see if you can say where I'm going wrong.

    Firstly in OC...

    The big reveal for me is at 607, which I took to be a complete agreement with Ramsey's deflationary/pragmatist approach

    A judge might even say "That is the truth - so far as a human being can know it." But what would this rider [Zusatz] achieve? ("beyond all reasonable doubt"). — 607

    He seems, to me, to be quite clearly saying that 'so far as a human being can know it' adds nothing to 'truth', that the term already implies the limit of human ability, the asymptote to which our investigatory endeavours approach.

    Then there's

    The truth of certain empirical propositions belongs to our frame of reference.

    Again, placing truth relatively, not absolutely. Same with...

    It is the truth only inasmuch as it is an unmoving foundation of his language-games

    At 108, Wittgenstein answers a question about the objective truth of a proposition with a measure of our certainty about it.

    "But is there then no objective truth? Isn't it true, or false, that someone has been on the moon?" If we are thinking within our system, then it is certain that no one has ever been on the moon. — 108

    Then at 200, he seems abundantly clear (perhaps clearest of all)

    Really "The proposition is either true or false" only means that it must be possible to decide for or against it. But this does not say what the ground for such a decision is like. — 200

    You said earlier that Wittgenstein was clear in PI that neither idealism nor realism were quite right, and yet you seem adamant that 'creeping anti-reslism' be kept out of Wittgensteinean exegesis. If we know Wittgenstein wasn't for full throated realism, then wouldn't 'creeping anti-realism' be exactly what we'd be looking for in finding his meaning?
  • Sam26
    2.7k
    Another point to be made about propositions and Wittgenstein's hinge's, is that propositions, since they have the potential as claims or beliefs to be true or false, allow for doubt. The doubt arises because of the potential for the claim to be other than what we believe. This also extends to knowing, i.e., even if I'm justified in believing that x is true, there is still the possibility that I'm incorrect (W. says we often forget the phrase "I thought I knew." OC 12); and where this possibility doesn't exist, viz, where it is senseless to doubt, then we're dealing with hinge's.

    Given the nature of propositions as claims or beliefs, viz., that they are truth-apt (can be true or false), this is what allows for doubt. If this possibility wasn't part of what we mean by proposition, then there would be no reason to doubt. What would the doubt be about? Other than you are wrong, the proposition isn't true, or you are wrong the proposition isn't false. This is the doorway to doubting someone's claim. There is much more to this though, because I think in some sense W. was trying to go beyond our conceptual framework. He was trying to come up with a conceptual framework that allowed him to talk about hinge's, and their role in our language-games. You can see this in his many descriptions of hinges, which gives rise to some of the disagreements about hinges. In one setting he seems to say one thing, in another setting something else. It's an unfinished and unpolished work. We need to keep this in mind.

    There are hinges (bedrock beliefs) that are so fundamental to our lives that they are non-propositional arational beliefs. Why is this important? You've heard it many times from me and others, but it's important to this particular conversation, because these kinds of beliefs are outside the impetus for doubting. What does that mean? It means that the impetus for doubting, viz., that the belief can be true or false is removed, which is why hinges can't be doubted. Moreover, it's why hinges are neither true nor false. The language-game of doubting has no foothold, no grounding, nothing bedrock to support it. These kinds of bedrock beliefs are needed for our conceptual framework of knowing, doubting, true and false to even function as a part of our forms of life. To doubt such bedrock beliefs, is to doubt that which gives rise to doubting in the first place. If one doubted such beliefs, then as W. has said, one couldn't even be sure of the meaning of our words. Our conceptual framework (including the concepts of true and false) would simply fail to have meaning. The uses of our concepts are reality dependent, viz., they are dependent on the interactions, at a very basic level (in an animalistic sense), that allow for the structure of language, and the many kinds of language-games to evolve (again, the conceptual framework).

    And, @Banno, this is a realist position, a pragmatic look at language from the framework of reality being "...all that is the case." There is no need to point to some ideal to understand what W. is saying, no need for the anti-realist position, in terms of understanding these points. However, one needs to be careful not to put W. into some particular theoretical box, be it realist or anti-realist, there are bits of both in his thinking, but W. does lean heavily in the realist direction, as do I, by the way.
  • Banno
    25.2k
    He's arguing against Moore's use of the word know, as an epistemological use, and all that entails.For me, that entails justification and truth.Sam26

    Indeed, for you.

    That is not how I, and others, read Wittgenstein. We read him, as pointed out, as saying that it is the justification that is faulty, not the truth value. And again, both Moore and Wittgenstein are certain that "Here is a hand" is true. What they are certain of is the truth of the proposition.

    Consider the absurdity of someone being certain that "here is a hand" and yet not certain that "Here is a hand" is true.

    I suppose that there might be something in what you are saying if we remove the quotes; that someone might be certain act this is a hand, and yet not certain that "This is a hand" is true - perhaps they do not speak English, or perhaps they do not speak any language. Is this part of your thinking?

    I don't see this as more than trivial.

    I am puzzled by your approach. More to come.
  • Luke
    2.6k
    according to Wittgenstein, the mathematical equation is nonpropositional
    — Luke

    Where does he say this?
    Banno

    From Moyal-Sharrock's book again:

    For Wittgenstein, to be a proposition is to be bipolar; that is, to be susceptible of truth and falsity. From the first, Wittgenstein’s technical concept of the proposition is internally related to bipolarity: ‘In order for a proposition [Satz] to be capable of being true it must also be capable of being false’ (NB 55); ‘Any proposition [Satz] can be negated’ (NB 21); ‘A proposition [Satz] must restrict reality to two alternatives’ (4.023) [...] In the thirties, Wittgenstein still upholds bipolarity: ‘In logic we talk of a proposition as that which is true or false, or as that which can be negated’ (AWL 101); ‘ “A proposition [Satz] is whatever can be true or false” means the same as “a proposition [Satz] is whatever can be denied” ’ (PG 123); ‘it is a part of the nature of what we call propositions [Satz] that they must be capable of being negated’ (PG 376). The ruling out of the possibility of falsity amounts to the ruling out of propositionality: ‘There is no such proposition as “Red is darker than pink”, because there is no proposition that negates it’ (AWL 208; my emphasis). In other words, so-called analytic and synthetic a priori propositions are not propositions.
    The claim that propositions are essentially bipolar cannot be consistent with accommodating rules, tautologies or anything else which is necessarily true within the propositional fold.

    [...]

    G.E. Moore reports Wittgenstein as asserting both that a proposition ‘has a rainbow of meanings’ (MWL 107) and, of the ‘kind of “proposition” ’ that has traditionally been called ‘ “necessary”, as opposed to “contingent” ’, such as ‘mathematical propositions’,

    ...he sometimes said that they are not propositions at all...They are propositions of which the negation would be said to be, not merely false, but ‘impossible’, ‘unimaginable’, ‘unthinkable’ (expressions which [Wittgenstein] himself often used in speaking of them). They include not only the propositions of pure Mathematics, but also those of Deductive Logic, certain propositions which would usually be said to be propositions about colours, and an immense number of others. (MWL 60)

    However Moore may have taken Wittgenstein’s ‘puzzling assertion that 3 + 3 = 6 (and all rules of deduction, similarly) is neither true nor false’ (MWL 80), there is no ambiguity about Wittgenstein’s ‘declaration’ and ‘insistence’ that mathematical ‘propositions’ are ‘rules’, indeed ‘rules of grammar’ (MWL 79) and that these ‘rules’ are ‘neither true nor false’ (MWL 62, 73). And this cannot be dismissed as ‘early Wittgenstein’. He is still making the same claim in the Remarks on the Foundations of Mathematics:

    There must be something wrong in our idea of the truth and falsity of our arithmetical propositions [Sätze]. (RFM, p. 90)

    It is important to underline that Wittgenstein does not only attribute nonpropositionality to mathematical ‘propositions’ but, as he makes clear in the AWL passage above, and it is worth repeating, to any ‘proposition’ of which the negation would be said to be, not merely false, but ‘impossible’, ‘unimaginable’, ‘unthinkable’ and these

    ...include not only the propositions of pure Mathematics, but also those of Deductive Logic, certain propositions which would usually be said to be propositions about colours, and an immense number of others. (MWL 60)
    — Understanding Wittgenstein's On Certainty, pp. 35-38
  • Deleted User
    -1
    By the same logic, if it is a proposition then it must be justifiable, dubitable and capable of being known, because that is just what a proposition is. Yet hinge propositions are none of these things.Luke

    That's because "hinge-propositions" are a neurological phenomenon. Meaning, the acceptance of a truth value, much like logical validity itself, does not imply the accurate conclusion of truth value one way or the other. But, that such an acceptance must take place before action, and thereby function, can be initiated.
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Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.