Of course, applications of "+1" include practical applications. The point is that the rule must be applied to each case; it does not reach out to the future and the possible and apply itself in advance.Imagine there is a wedding, and there are 68 guests from one side of the family and 57 from the other side. — Janus
Yes, that's part of W's point. We can apply the rule to imaginary or possible cases, but we have to formulate them first. We cannot apply a rule to infinity. Hence mathematical induction.There is a forward problem of mapping rules — Apustimelogist
.It is natural simply because we can intuitively get the logic — Janus
Yes, that's part of W's point. We can apply the rule to imaginary or possible cases, but we have to formulate them first. We cannot apply a rule to infinity. Hence mathematical induction. — Ludwig V
I think it is arguable that nearly all humans find counting and the basic arithmetical operations intuitive, so it's not arbitrary, Mathematicians have specialized skills that enable them to find things intuitive that the layperson cannot even comprehend because they don't have the requisite training or ability.
It looks like we are going to continue to disagree, but that's OK with me. I believe I would change my mind if given good reason to, but I haven't seen anything approaching such a reason thus far. — Janus
Girard's Ludics is a formalisation of this pragmatic idea of meaning as interaction — sime
But what would you look for in an extraterrestrial signal if you were assessing for rationality? You'd probably want to see intention, right? What tells you that an action was intentional?
Some would say we want to see some signs of judgement. For instance if we would take a sequence of constants as a sign of intelligence, that would tell us that the aliens consciously chose those numbers. Choice entails normativity. They picked this number over that one.
All of this is wrapped up in rule following, which is normativity at its most basic. To follow a rule means to choose the right action over the wrong ones.
If it turns out that there's no detectable rule following in the world, normativity starts to unravel and meaning along with it. Is that how you were assessing the stakes here? — frank
Let me, then, summarize the 'private language argument' as it is presented in this essay. (I) We all suppose that our language expresses concepts - 'pain', 'plus', 'red' - in such a way that, once I 'grasp' the concept, all future applications of it are determined (in the sense of being uniquely justified by the
concept grasped). In fact, it seems that no matter what is in my mind at a given time, I am free in the future to interpret it in different ways - for example, I could follow the sceptic and interpret 'plus' as 'quus'. In particular, this point applies if I direct my attention to a sensation and name it; nothing I have done determines future applications (in the justificatory sense above). Wittgenstein's scepticism about the determination of future usage by the past contents of my mind is analogous to Hume's scepticism about the determination of the future by the past (causally and inferentially). (2) The paradox can be resolved only by a 'sceptical solution of these doubts', in Hume's classic sense. This means that we must give up the attempt to find any fact about me in virtue of which I mean 'plus' rather than 'quus', and must then go on in a certain way. Instead we must consider how we actually use: (i) the categorical assertion that an individual is following a given rule (that he means addition by 'plus'); (ii) the conditional assertion that "if an individual follows such-and-such a rule, he must do so-and-so on a given occasion" (e.g., "if he means addition by '+', his answer to '6S+ 57' should be '125"'). That is to say, we must look at the circumstances under which these assertions are introduced into discourse, and their role and utility in our lives. (3) As long as we consider a single individual in isolation, all we can say is this: An individual often does have the experience of being confident that he has 'got' a certain rule (sometimes that he has grasped it 'in a flash'). It is an empirical fact that, after that experience, individuals often are disposed to give responses in concrete cases with complete confidence that proceeding this way is 'what was intended'. We cannot, however, get any further in explaining on this basis the use of the conditionals in (ii) above. Of course, dispositionally speaking, the subject is indeed determined to respond in a certain way, say, to a given addition problem. Such a disposition, together with the appropriate 'feeling of confidence', could be present, however, even if he were not really following a rule at all, or even if he
were doing the 'wrong' thing. The justificatory element of our use of conditionals such as (ii) is unexplained. (4) If we take into account the fact that the individual is in a community, the picture changes and the role of (i) and (ii) above becomes apparent. When the community accepts a particular conditional (ii), it accepts its contraposed form: the failure of an individual to come up with the particular responses the community regards as right leads the community to suppose that he is not following the rule. On the other hand, if an individual passes enough tests, the community (endorsing assertions of the form (i)) accepts him as a rule follower, thus enabling him to engage in certain types of interactions with them that depend on their reliance on his responses. Note that this solution explains how the assertions in (i) and (ii) are introduced into language; it does not give conditions for these statements to be true. (5) The success of the practices in (J) depends on the brute empirical fact that we agree with each other in our responses. Given the sceptical argument in (I), this success cannot be explained by 'the fact that we all grasp the same concepts'. (6) Just as Hume thought he had demonstrated that the causal relation between two events is unintelligible unless they are subsumed under a regularity, so Wittgenstein thought that the considerations in (2) and (3) above showed that all talk of an individual following rules has reference to him as a member of a community, as in (J). In particular, for the conditionals of type (ii) to make sense, the community must be able to judge whether an individual is
indeed following a given rule in particular applications, i.e. whether his responses agree with their own. In the case of avowals of sensations, the way the community makes this judgement is by observing the individual's behavior and surrounding circumstances.
I think what I'd say is that there are ways of detecting if someone is following a rule, it's only that these ways are not a state of affairs in the world. Rather it's an acceptance by a community. At least this is the solution I see Kripkenstein offering. The conditions of assertability aren't in truth-conditions, but there are still conditions of assertability. You just have to learn what they are. — Moliere
On the other hand, if an individual passes enough tests, the community (endorsing assertions of the form (i)) accepts him as a rule follower, thus enabling him to engage in certain types of interactions with them that depend on their reliance on his responses.Note that this solution explains how the assertions in (i) and (ii) are introduced into language; it does not give conditions for these statements to be true.
So not quite an undermining of all normativity, but possibly a re-adjustment on philosophical interpretations of meaning. — Moliere
Kripke's mind is wild to ride along with. — Moliere
So we still don't have any basis for determining that S followed a particular rule. We just treat certain circumstances as if she did. — frank
Finally, the point just made in the last paragraph, that Wittgenstein's theory is one of assertability conditions, deserves emphasis. Wittgenstein's theory should not be confused with a theory that, for any m and n, the value of the function we mean by 'plus', is (by definition) the value that (nearly) all the linguistic community would give as the answer. Such a theory would be a theory of the truth conditions ofsuch assertions as "By 'plus' we mean such-andsuch a function," or "By 'plus' we mean a function, which, when applied to 68 and 57 as arguments,. yields 125 as value."
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Wittgenstein thinks that these observations about sufficent conditions for justified assertion are enough to illuminate the role and utility in our lives of assertion about meaning and determination of new answers. What follows from these assertability conditions is not that the answer everyone gives to an addition problem is, by definition, the correct one, but rather the platitude that, if everyone agrees upon a certain answer, then no one will feel justified in calling the answer wrong.
And I'm glad I did some of the homework. — Moliere
So we still don't have any basis for determining that S followed a particular rule. We just treat certain circumstances as if she did. — frank
If I'm understanding the argument: in place of truth-conditions Kripke resolves the sceptical problem with the sceptical solution that the community provides assertability-conditions. There's no fact which justifies the assertability-conditions, though. — Moliere
You see, in both cases, the fundamental issue isn't resolved. Answering "habit" doesn't create rule-following facts for us. As with the problem of induction, we still have the gaping hole where we expected empirical data to support our assertions. Obviously, since Hume's problem attracted Kant's approach, we might expect that Kripke's problem would do something similar. Meaning isn't based on objective rule following, so maybe there's something innate about it. Maybe this innateness is a touchstone that meets each episode of communication, including this one. — frank
I think I'm tempted to simply accept the conclusion: there are no rule-following facts. Same with Hume and causation, though I really do admire Kant's attempt to overcome Hume's skepticism towards causation. — Moliere
"How do you know that your present usage of "plus" is in accordance with your previous usage of "plus" ?" — sime
Of course, applications of "+1" include practical applications. The point is that the rule must be applied to each case; it does not reach out to the future and the possible and apply itself in advance. — Ludwig V
But the fact that we mostly agree is not inevitable, not guaranteed. It is a "brute fact", which is the foundation of logic (and other rules). Bedrock is reached. — Ludwig V
The question of intuition is arbitrary because this is about the notion of objective rules or meanings. Why does intuition matter for objectivity? A putatively objective scientific theory should be true regardless of intuition. The truth of thermodynamics doesnt depend on my cats ability to find it intuitive. — Apustimelogist
It's not an epistemic question. It's metaphysics. — frank
The truth of scientific theories is not intuitively self-evident in any way analogous to the truth of basic arithmetical results — Janus
So, scientific theories are never proven. That the math involved in thermodynamics is sound may be self-evident, but that doesn't guarantee that it has anything to do with some putatively objective reality — Janus
So what, some truths are intuitive and some are unintuitive. Their intuitiveness has nothing to do with objective truth. Intuition is a product of your subjective inclinations. — Apustimelogist
And just because a rule is unintuitive doesn't refute it being objectively true. — Apustimelogist
I don't know what you mean when you talk about a rule being objectively true. — Janus
I would say that the only intuitively self-evident truths are logical or mathematical, and I don't see that as being merely a subjective matter. — Janus
That there is a fact of the matter about what rule is being followed. — Apustimelogist
It is a subjective matter because you are appealing to your intuition subjectively and you cannot rule out the other possible rules you can use. — Apustimelogist
Arbitrary rules like quaddition do not yield reliably workable results, or at least I haven't seen anyone showing that they can — Janus
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