Also, don't forget that quus is only one example of many other possible rules so actually you have been using some other strange rule since you started learning math and you have been using it fine — Apustimelogist
What other "strange rule" have I been using? — Janus
Basic arithmetical procedures are simply the infinite iterability — Janus
I agree that many rules have been extrapolated out of these basics, but the extrapolations are not arbitrary in the kind of way quaddition is — Janus
other rules like quus. there are probably a multitude of them which are consistent with all of the addition you have ever done so far in your life and you can't rule them out. — Apustimelogist
uhhh don't you mean quu-nfinite quu-terability? — Apustimelogist
why should it be that just because a description is general or extrapolatable means it is any more or less true than a description which is specific. Is the fact you are using addition any less true than the more general description of using an operator? is the more general description of being a mammal somehow more true than the more specific description of being a human? — Apustimelogist
And as for people claiming they are following "other rules", there might be some plausibility to that if the other rules yielded the same results. — Janus
It's worth remembering that in geometry, it turned out that rules other than Euclid's (with all their intuitive plausbility) turned out to yield consistent systems, which, in the end, turned out to have "practical" applications.Judging from the ordinary understanding of basic arithmetic and logic I would say their results are self-evident to anyone who cares to think about it. — Janus
I don't think that's a particularly interesting result. Rules are instructions, so they aren't either true or false. That is, the rules of chess are not true or false; but they do yield statements that are true or false, such as "Your king is in check".indeed, it seems that Kripkes proof shows rules are not objectively true. — Banno
Well, I would suggest that what is at stake is the refutation of a certain conception of what rules are - the idea that logic/mathematics is some kind of structure that determines the results of all possible applications in advance. Nothing can reach out to infinity. What we have is ways of dealing with situations as they come up which do not appear to have any limitations to their applicability. (That phrase could be misinterpreted. I mean just that "+1" can be recursively applied indefinitely. What we can't do is apply it indefinitely.)Well, neither is quite right. It's a question about meaning. What do we claim when we say "Jenny can add"? And more generally, what do we claim when we say that someone follows a rule? — Banno
Yes, but that doesn't mean that we cannot have ways of responding to, and dealing with, problems as they come up - if necessary, we can invent them - as we do when we discover irrational numbers, etc. or find reasons to change the status of 0 or 1. In the case of 0, we have to modify the rules of arithmetical calculation.Again, the point is underdetermination so its not about whether one rule is workable or not, any time you use addition it has an underdetermined characterization, and your ability to use it and practise it has little to do with that. — Apustimelogist
How can they be consistent if they don't yield the same results. — Janus
No, I wasn't referring to gibberish. — Janus
All that seems irrelevant. — Janus
I don't think that's a particularly interesting result. Rules are instructions, so they aren't either true or false. That is, the rules of chess are not true or false; but they do yield statements that are true or false, such as "Your king is in check". — Ludwig V
Yes, but that doesn't mean that we cannot have ways of responding to, and dealing with, problems as they come up - if necessary, we can invent them - as we do when we discover irrational numbers, etc. or find reasons to change the status of 0 or 1. In the case of 0, we have to modify the rules of arithmetical calculation. — Ludwig V
other rules like quus. there are probably a multitude of them which are consistent with all of the addition you have ever done so far in your life and you can't rule them out. — Apustimelogist
Kripke's mistake (assuming I am recalling his position correctly), was phrasing the skepticism as a circular question to a mathematician where he asked to defend the validity of his judgements, as in
"How do you know that your present usage of "plus" is in accordance with your previous usage of "plus" ?"
That question is easily viewed as nonsensical, since it is easily interpreted as asking a person to question their own sanity. Similarly bad phrasing, leading to pointlessly circular discussion is found throughout the philosophy literature on private language arguments. — sime
I admire your memory! But isn't it exactly the same as we all (?) do when we memorize the standard multiplication tables and recall what 12x11 is. (It's just a convention that we stop at 12. The table for 13 is no different in principle from the table for 12.) Multiplication reduces to addition, but adding 12 11's by that procedure is long and boring. By memorizing the standard multiplication tables, we have a quicker way of dealing with some questions and of calculating bigger numbers. (Incidentally, how do you deal with 2 to the power of 35?)For example, having worked with digital logic a fair bit, I have all the powers of 2 up to 2^13 memorized and if I see 2048 + 2048 I simply recognize that the sum is 4096 without following any step by step decimal addition rules. — wonderer1
I agree with that. Though Wittgenstein would ask what makes the sign-post point? Again, there's a practice of reading sign-posts, which we all somehow pick up/learn. Perhaps by recognizing a similarity between a pointing finger and the sign-post.rules and explicit definitions are more like signposts than prescriptions on how to behave. — Apustimelogist
I agree with that. It's a pointless difficulty. Like most sceptical arguments. I like Hume's response - essentially that it is not possible to refute the argument but it has no power to persuade me to believe the conclusion. But that's not how the philosophical game is played - for better or worse.I don't think this problem has anything to do with practical problems. The quus issue has no bearing on someones ability to perform math. — Apustimelogist
There's a nest of complications buried in that. In one way, you are just raising the original question again. However, there is a fact of the matter involved - that I gave 125 as the answer to the question. Whether I was following the rule "+1" is another question. In one way, it depends on whether I had that rule in mind when I gave the answer. In another way, it depends on whether we agree with the answer - and that may depends on the wider context (consistency and practical outcomes).Buy "you are following x rule" is factual. — Apustimelogist
Forgive me, I don't really understand what "conditions of assertability" are as opposed to "truth-conditions". Are they facts? In which case, we may be no further forward.It's true because that's the answer we should obtain according to the conditions of assertability, but there are no truth-conditions that make it true. — Moliere
That's an interesting question. In one way, the desired result is to defuse the question so that I don't get bothered by it - that is, don't need to take it seriously. Whether that's interesting or not depends on whether you are philosophically inclined or not.What do you think is the interesting result of this story then? — Apustimelogist
I agree with that. One of the difficulties is that the text is not difficult to understand (contrast Hegel or Derrida). The difficulty is to understand what the point is. That's where the commentators can help - and sometimes hinder, so don't read them uncritically.It (sc. Philosophical Investigationscan be really difficult to read to be fair. Its one of those books where possibly what the book says has not been as influential as what othwrs have said about the book. — Apustimelogist
Forgive me, I don't really understand what "conditions of assertability" are as opposed to "truth-conditions". Are they facts? In which case, we may be no further forward. — Ludwig V
I agree with that. Though Wittgenstein would ask what makes the sign-post point? Again, there's a practice of reading sign-posts, which we all somehow pick up/learn. Perhaps by recognizing a similarity between a pointing finger and the sign-post. — Ludwig V
I like Hume's response - essentially that it is not possible to refute the argument but it has no power to persuade me to believe the conclusion. — Ludwig V
There's a nest of complications buried in that. — Ludwig V
In one way, it depends on whether I had that rule in mind when I gave the answer. — Ludwig V
But I am learning from this. One result is that I now know how to defuse Goodman's "grue". Another is that it seems that Kripke has made the private language argument superfluous. I need to think about that. A third - minimal - result is that Kripke has added to the stock of examples that pose Wittgenstein's problem. The fourth is that I notice that we have all appealed to the wider context, both of mathematics and of practical life to resolve it. Kripke's case is effective only if we adopt his very narrow view, The wider context makes nonsense of it. (I'm not saying that a narrow focus is always a bad thing, only that it sometimes gets us into unnecessary trouble.) — Ludwig V
But isn't it exactly the same as we all (?) do when we memorize the standard multiplication tables and recall what 12x11 is. — Ludwig V
(Incidentally, how do you deal with 2 to the power of 35? — Ludwig V
This is all what I meant when I said that meanings and definitions are so impoverished that language should not be usable, yet it is. — Apustimelogist
therefore it seems weird to me to focus so, on whether some particular rule was used in some specific case. — wonderer1
we impose labels on the world at out own discretion and there are no fixed set of boundaries for those concepts or force us to impose concepts in a particular way. — Apustimelogist
Can you elaborate? — Apustimelogist
I think it'd depend upon how we're trying to judge if someone knows something or not. — Moliere
Yes. There isn't a way of resolving that without going beyond that way of thinking. W's does that. His appeal to games, practices, forms of life etc. is an attempt to explain it. As a general thesis, it is quite unsatisfactory, (cf. God of the gaps) — Ludwig V
That works in some ways. But the picture of the world out there, waiting to be "carved at the joints", is partial. The world reaches in and prods us, tickles us, attracts us and repels us. We do not start out as passive observers but as engaged actors in the world - which does not always behave in the way that we expect. — Ludwig V
I think the intention is to distinguish between a heuristic which may be useful in some circumstances, but not in all, and how we would settle the question whether the output of the heuristic is correct or not. — Ludwig V
Some focus would help — Ludwig V
neurons that are physical enslaved — Apustimelogist
I hope so. It's the only way that we get reliable information - and, in great part, we do.impelling the perceptions forced upon us — Apustimelogist
I'm sure there's a lot of quick and dirty solutions and heuristic dodges involved. Anything remotely like formal logic would be too slow to be useful.making it look like we are acting in these kinds of mysterious ways that seem somewhat messy and underdetermined by our concepts and so can only be described as "games, practises, forms of life". — Apustimelogist
I was only talking about relying on a memorized table, instead of doing the basic calculations. It's an example of a quick and dirty solution.I dunno; I think looking at this way, as I seem to understand what you have said, plays down everything else that Wittgenstein seems to be getting at in philosophical investigations. — Apustimelogist
One result is that I now know how to defuse Goodman's "grue". — Ludwig V
This point is made elsewhere. The complication is that the private language argument does rely on some of the things he says about rule-following, particularly the importance of understanding what does and does not conform to the rules about ostensive definition. But numbers are not sensations, so the cases are not exactly the same.Another is that it seems that Kripke has made the private language argument superfluous. I need to think about that. — Ludwig V
W likes lots of examples. In one way, Kripke's case is just another one, although W does mention the point at PI 201 "This was our paradox: no course of action could be determined by a rule, because every course of action can be brought into accord with the rule. The answer was: if every course of action can be brought into accord with the rule, then it can also be brought into conflict with it. And so there would be neither accord nor conflict here." I had forgotten this quotation. In time, I could no doubt find what he was referring back to. It gives a short answer to both Goodman and Kripke.A third - minimal - result is that Kripke has added to the stock of examples that pose Wittgenstein's problem. — Ludwig V
Isn't that an accurate reflection of what we've been saying about practices?The fourth is that I notice that we have all appealed to the wider context, both of mathematics and of practical life to resolve it. Kripke's case is effective only if we adopt his very narrow view, — Ludwig V
I'm sure there's a lot of quick and dirty solutions and heuristic dodges involved. — Ludwig V
I think the problem with the answers that brains give though is they are finely contextualized by different personal histories, individual differences in brain structure, noise etc. What people learn and the information they store is probably different for everyone, but in places like academia we want to remove all ambiguity. The side effect of neat clean concepts is they lose all the fuzzy non-linearity which makes them exceptionally good at being used in real life. — Apustimelogist
I get that distinction. Indeed, arguably an assessment whether the knower is in a position, or has the capacity, to know p is appropriate in assessing any claim to knowledge. And I can see that final truth will often be distinct from any such assessment. (The jury has a perfect right to find the prisoner guilty or not. Yet miscarriages of justice do happen - and proving that is different from proving whether the prisoner is guilty or not. (A miscarriage might have reached the right result.)) But I still feel that the distinction is quite complicated. After all, the truth would be the best assertability condition of all, wouldn't it? And the assertability conditions would themselves be facts, wouldn't they? Of course, they need not be the same facts as the truth conditions. — Ludwig V
The side effect of neat clean concepts is they lose all the fuzzy non-linearity which makes them exceptionally good at being used in real life. — Apustimelogist
because here we have truths that we arrive at because of the conditions of assertability — Moliere
Yes, that's true. I'm a bit inclined to say the W sees that "fuzzy non-linearity" as inherent in all concepts. — Ludwig V
Can you demonstrate how quus is dealt with by the approaches you have said? — Apustimelogist
logical nihilism or pluralism. — Apustimelogist
Maybe we should distinguish between what brings the rule into effect (I chose that word carefully because after it becomes effective it is correct to say that there is a rule that ...) Can we see conditions of assertability as comparable to the licence conditions for someone to perform a wedding? If so, laying down a rule is or at least is comparable to, a speech act. We then have to explain that in some cases, the rule is not formally laid down, but informally put into effect (as when language changes, and "wicked" comes to mean the opposite of what it meant before). Once the rule is in effect, there is a fact of the matter, as when your king is in check or 68+57=125. — Ludwig V
There are rules for which the process that brings them into effect is quite clear. They are what we call laws, but there are other varieties. They are imperatives, not really different from the order given by the general. Other rules, like mathematical rules about how to calculate are different. There are proofs of such rules. What makes them effective? Which is to say, what justifies them? That's where the sceptical pressure (which W also applied) and his appeal to practices comes in. But that involves saying that the rule doesn't really of itself produce facts; human beings have to carry out the calculations (or psersuad machines to do it for them. Those results are facts, i.e. have the authority of facts? Only the calculation, which can't produce a wrong result. That means that if a result does not fit in to our wider lives in the way it is expected to, we look for the fault in the calculation and the calculator, not the rule.The rule is in effect, and in some sense then it produces facts — Moliere
If you mean a fact that justifies the rule and/or justifies how the rule is applied. I sometimes think that the quickest way to state the problem is to point out that the rule cannot be a fact, because the rule has imperative force and no fact can do that - a version of the fact/value distinction. For the same reason, no fact can, of itself, justify the rule.The skeptic has to be pointing out that we're inclined to believe there's a fact where there is none in order for the skeptic to have a point at all. — Moliere
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