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Post by Eugene 2.0 on May 4, 2021 17:23:32 GMT
Here's a fragment of his ideas. (I'll paraphrasing him):
Each concept or a notion has one unique symbol. Synthesis or a composition of notions symbolizes via algebraic adding or with a sing "+"; analysis or a decomposition either using algebraic addition symbols, or with a sign "−". A judgment signs as equations; to the left of the equation a subject puts, and to the right of the equation a predicate places. If this judgment is negative, a sign "−" should be placed in front of the predicate. Two or more predicates conjunct with each other via the sign "+", because mostly there's no one-to-one correspondence between a subject and a predicate in the judgments.
For all x, [Px=>Qx] For all x, [Px=>~Qx] There's x s.t. [Px&Qx] There's x s.t. [Px&~Qx]
becomes:
S = P + M S = −P + M P = S − M −P = S − M
So, the modus Barbara would be:
T = P + Z S = T + N S = P + (Z + N)
and if Z+N=W, then:
S = P + W
One of the really good point in his system was an introduction of the undefined terms in any universal judgment. It's the same to say that a general universal judgment is:
There's y s.t. for all x, [Sx = Px & y]
It's like to introduce an individual with no certain property or attribute. It may sound weird - how non-variables might have no properties at all? In the most practical way to mention
For all x, Px
is to mention indeed:
For all x, xєD, Px
where D is some class. And with no class it would seem as there would be a blank - an empty. So, it's one of the reason why Friedrich Castillon's logic tries to get over some of such problems.
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Triangle
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Post by Triangle on May 14, 2021 20:09:37 GMT
Well, nothing in semantics is impossible, so I think that can be a mathematical semantics, but never a semantics of mathematics. Math language is univocal, so there is one value in each operation for the number one or the plus signal. So, if I understood you correctly, you're not against formal semantics, right? About "there is one value in each operation for the number one or the plus signal": is it the axiomatic method, i.e. (x) (x=y`) (F)(x)(y)[(x=y)⇒(Fx=Fy)]right? Perfect, I am not against any semantics. There is a incongruence is that reasoning, but I am not familiarized with math language suficient to argue with you. I am only saying that 2 is a univocal, 2 is 2 and not 3, for example.
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Post by Eugene 2.0 on May 14, 2021 21:04:19 GMT
So, if I understood you correctly, you're not against formal semantics, right? About "there is one value in each operation for the number one or the plus signal": is it the axiomatic method, i.e. (x) (x=y`) (F)(x)(y)[(x=y)⇒(Fx=Fy)]right? Perfect, I am not against any semantics. There is a incongruence is that reasoning, but I am not familiarized with math language suficient to argue with you. I am only saying that 2 is a univocal, 2 is 2 and not 3, for example. I apologize for using the math language. Not being a mathematician (while being familiar with it), I just use it time to time to explicit some of the views. And usually I expect that my vis-a-vis or any other members are more or less in analytic philosophy. Unfortunately, but even the one precise meaning doesn't make the situation with math language clearer. I mean at least there are two attempts in understanding math: a) kantian one; b) frege's one. Or a) a posteriori VS b) a priori. I think the arguments of Frege that we can define numbers just using analytic strictly procedures enough to determine what numbers is (mostly taking as the base - the set theory axioms); while a posteriori kantian programm - in Bauman's interpretation ( H. Behmann's Article) - 1) relation access, 2) linking with axioms. Brifely, no math concepts are non-related: for any x, if x is a math concept, then it is in some relation with y via c, where c is a context, and y - some other parameter (or parameters). And axioms here - is the explanation of why postulating something is connected with some outlook views of the present world, i.e. we can claim that any quadrilateral has four right angles - comes from our observation, because Riemann's or Lobachevsky's geometry doesn't guarantee such a result. By the way, you wrote previously about of non-conceptual side of numbers, but if to apply this to the formulas we may encounter some problems, because: the formulas in math are something to be, at least, a tiny different (if not completely), than the numbers; and a process of creation of the formula, or the process of its acceptation is also something most outer or beyond the math. That's why we should be - I suppose - more accurate in our claims about math deities. Our careful attitude to it might begin from our differentiation of the numbers and the formulas in math. Anyway, thank you for the interesting discussion!
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