My understanding of Wittgenstein's idea that meaning is use is that a word's meaning is not given by a definition which purportedly captures the word's essence but by the context in which it appears. — TheMadFool
I don't know how intuition and "psychological well-being and development" are related but we do feel upbeat when our intuition is right on the money, hits the bullseye — TheMadFool
Perhaps this is related to your attempt to link intuition with "psychological well-being and development" — TheMadFool
). Intuitions can become more and more correct, however (see my 4. below).The fact that we have near-zero knowledge of intuition is a major stumbling block in advocating it as a reliable technique for problem solving. — TheMadFool
A better way to approach it is to forget about meaning and look to use. Knowing what a number is consists in being able to count, to add, to subtract, to do the things that we do with numbers; not with a definition set out in words.
Wittgenstein wrote much regarding philosophy of mathematics, and considered it is more important work. — Banno
You are correct, strictly speaking. Practically speaking, this does not apply to arithmetic anymore, unless you were a raised as a feral child, a.k.a Mowgli style. The formalization of such extremely rudimentary and materially manifest abstractions doesn't happen under spontaneous impetus. Those ideas were internalized, starting long ago, with routine behavior associations in our remote animal ancestors, as @Banno proposed them to be, then they were gradually absorbed into awareness through notions that articulate vaguely aspects of nature, and then finally conceptualized. Conceptualization also follows a historical process of refinement involving the civilizational fabric of society and the formal academic convention, passing through stages of eccentricity that resemble arithmetical theism. So, your spontaneous conception of ideas regarding the basic qualities of nature, such as arithmetic, are relatively unimpactful, because you are entrenched into continuous multi-generational collective refinement of those concepts, spanning many evolutionary stages.I don't see how we can escape from the essential role of a pattern of synaptic firings that results in a subjective feeling of knowing. And then the problem is, as I suggested earlier, that if one day my brain functions differently than it usually does, that pattern might be triggered not by 2 + 2 = 4, but by 2 + 2 = 5. Evolution has guaranteed that such days will be rare, but is a high order of probability the best we can do in trying to prove that 2 + 2 = 4?
If I'm missing something, I hope that someone can pinpoint what that is. — Acyutananda
I have a discussion with another member of this forum in a different thread. I am arguing there that ultimately everything rests on innate conviction, or persuasion, and that it cannot be denied. Of course, one can continuously reevaluate the quality of such persuasion, as they gain new insight and amalgamate their various persuasions, but again, even if a person is wrong about something, one can always hope that nature will decrease their chance of thriving and evolution will replace their erroneous influence. So, don't worry about it. Genocide is a form of logical argument."2 + 2 = 4" (with or without ↪simeonz
's "cyclic group" qualifier) cannot ultimately be known. Its knowledge ultimately rests on a feeling of knowing, which is a kind of intuition, and intuitions are not objective reliable as justifications for knowledge — Acyutananda
Can you think of a non-mathematical use for numbers? — TheMadFool
I don't see the relevance... — Banno
if we should forget about meaning and look to use, it must be possible to use "2" in any way we want. — TheMadFool
1. "2 + 2 = 4" (with or without ↪simeonz's "cyclic group" qualifier) cannot ultimately be known. Its knowledge ultimately rests on a feeling of knowing, which is a kind of intuition, and intuitions are not objective [Edit: objectively] reliable as justifications for knowledge (because, for instance — Acyutananda
Intuitions can become more and more correct, — Acyutananda
There is another sense in which my 1. above is not trivial – the sense that admitting it motivates us to want to know practically how to avoid/prevent occurrence of the "feeling of knowing" neurological event when we are contemplating 2 + 2 = 5, and thus may lead us to learn how to avoid/prevent such occurrence. This is of epistemological significance — Acyutananda
How did you come to the conclusion that "Intuitions can become more and more correct" when you know that "intuitions are not objective [Edit: objectively] reliable"?
The way it seems to me, the two statements made by you (above) don't jibe. — TheMadFool
The meaning of "2" is not set out in a definition, but seen in what we do with numbers. Meaning as use. — Banno
We can. — Banno
An example? — TheMadFool
You have to be kidding me. If meaning is use, we should be able to use "2" in some way different to what it was intended for (counting) or, if we should forget about meaning and look to use, it must be possible to use "2" in any way we want. — TheMadFool
Strings are infinitely dimensional space
— simeonz
I have no idea what that means. — emancipate
Simple materially implied intuitions can become very reliable. When they have been ratified from experience for generations and convention has reached consensus, there aren't a lot of variables left in their definition that provoke further refinement. That is why mathematics focuses on simple pervasive intuitions and builds the rest from them. This is what distinguishes it from physical sciences that are much more susceptible to constant amendment.That is, "intuitions are not objectively 100% reliable." — Acyutananda
It is a counter-example of arithmetic. — simeonz
"2" could be code for my lawnmower. We do look to use to discern meaning. The notion that meaning is identical to use is wrong. Without some predetermined meaning, symbols can't be used for anything. — frank
May I?
"Would you care for another glass of 'Two Barrels'*?"
*it's a brand of Whiskey. — Isaac
The problem is, that you demonstrated that syntax could be abused, not that concepts with strict semantics behind the syntax can be used in innovative ways. Strings can actually be ordered lexicographically, but are something called free monoid, and their ordering is not well-ordering. Natural numers are sigularly generated (by the successor relation) commutative monoids and are well-ordered.So my attempt was successful. — emancipate
An obvious non numerical example: dynamic programming languages tend to treat '+' as a concatenation operator when applied to sequences of 'chars'. So x = '2' + '2'; means that x is equal to (or has the value of) the string '22'. Not the integer value 22 — emancipate
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