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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 10, 2021 1:03:14 GMT
But why each concept or notion have a unique symbol?
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Post by Eugene 2.0 on May 10, 2021 8:09:53 GMT
But why each concept or notion have a unique symbol? What do you mean? Is it about this Castillon's logic? Well, he'd better be asked first :) I guess for to escape of some confusions. But I really don't know. |
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Triangle
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Post by Triangle on May 10, 2021 14:54:34 GMT
But why each concept or notion have a unique symbol? What do you mean? Is it about this Castillon's logic? Well, he'd better be asked first  I guess for to escape of some confusions. But I really don't know. A mathematical language have the need of unique symbols, but all concepts? If he say that about mathematical language, I agree. But a number can be the same? If a number only can be represented by a unique symbol, there are no need to consider a number as a concept. |
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Post by Eugene 2.0 on May 10, 2021 15:56:51 GMT
What do you mean? Is it about this Castillon's logic? Well, he'd better be asked first I guess for to escape of some confusions. But I really don't know. A mathematical language have the need of unique symbols, but all concepts? If he say that about mathematical language, I agree. But a number can be the same? If a number only can be represented by a unique symbol, there are no need to consider a number as a concept. Of course, only the natural language is an object that requires to have special names for each separate and quite unique things. I think here Castillon didn't mention this operation; I guess it was my fault to chaos some of his thoughts, or I just said it in a wrong way. Anyway, type/token case could happen even in logic when we're dealing with something like 'sense' or 'meaning'. In a famous example of Phosphorus VS Hesperus it can be, or in this example: "It's necessary for 9 to have three dividers" "The number of planet in the Solar system = 9" ∴ "It's necessary for the number of planet in the Solar system to have three dividers". (From one of W. V. O. Quine's works ) |
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Triangle
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Post by Triangle on May 10, 2021 17:09:31 GMT
The number 1000 is a concept? How it can be?
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Post by Eugene 2.0 on May 10, 2021 17:58:15 GMT
The number 1000 is a concept? How it can be? Depending on how we use words, I think it's not impossible. A legion or an army can be what '1000' means. If for a number – without any cultural references – '1000' isn't a concept. I guess we can't just consider anything as concepts. But I don't understand where are you're heading to? Why did you ask it? |
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Triangle
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Post by Triangle on May 10, 2021 19:59:12 GMT
A number cannot be considered as a concept. A quantity is a concept, but the quantity cannot be a concept. You can illustrate a argument about the concept of numbers by numbers, but is impossible to turn a number a concept.
I am noticing only the difference between a quantity, like 1000, and the quantity of 1000. A certain quantity is a concept, but the quantity itself cannot be considered as a concept.
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Post by Eugene 2.0 on May 10, 2021 20:54:04 GMT
A number cannot be considered as a concept. A quantity is a concept, but the quantity cannot be a concept. You can illustrate a argument about the concept of numbers by numbers, but is impossible to turn a number a concept. I am noticing only the difference between a quantity, like 1000, and the quantity of 1000. A certain quantity is a concept, but the quantity itself cannot be considered as a concept. Well, I mentioned exactly this thought – a quantity can; the one – can't. I haven't heard about 'a/the' quantities before, that's why my "a legion" and "an army" can be taken as "a quantity" example. Also, we can use substitutes for any things whichever are they. In the example: ∀xFx x can be anything including shadows, parts of wheels, barbarians, ties, and so on. I see no real reason to barrier any analysis, especially for (the) logic, because its limits are where the formal side of the question. Instead, it's not less important to pay attention to the predicates or the notions for the purpose of operating them. Anyway, and what it gives to us? Perhaps the numbers can't be conceptualised, and what? |
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Triangle
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Post by Triangle on May 10, 2021 21:12:18 GMT
The number can be conceptualizated if we consider as a certain number, not a number as a concept.
We can think the concept of number without thinking in a specifical number. So I conclude that the concept of number is relative to his essetial notions which componds the concept of number. Because, obviously, a number aren't exclusively a quantity, but have some others notions, which I called essential, who can make us think numbers as a thing and not only as a quantity.
The notion of space, as topology talks, and creates the topological psychology. So, there are mathematical notions who gives not a mathematical use for that same notions. Mathematics is essentially numbers, but the concept of number is not a close concept, and can be developed, and we can discover in the concept of number new things, because these same openess.
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Post by Eugene 2.0 on May 11, 2021 16:28:32 GMT
The number can be conceptualizated if we consider as a certain number, not a number as a concept. We can think the concept of number without thinking in a specifical number. So I conclude that the concept of number is relative to his essetial notions which componds the concept of number. Because, obviously, a number aren't exclusively a quantity, but have some others notions, which I called essential, who can make us think numbers as a thing and not only as a quantity. The notion of space, as topology talks, and creates the topological psychology. So, there are mathematical notions who gives not a mathematical use for that same notions. Mathematics is essentially numbers, but the concept of number is not a close concept, and can be developed, and we can discover in the concept of number new things, because these same openess. Thank you for the informative answer. I see that math isn't about culture, and so on. Surely, probably I misconcepted those things or wrongly wrote about it. Anyway, I didn't lead to a thought that math was dealing with wide or fat notions. What do you think about the math's semantics? |
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Triangle
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Post by Triangle on May 14, 2021 3:55:58 GMT
The number can be conceptualizated if we consider as a certain number, not a number as a concept. We can think the concept of number without thinking in a specifical number. So I conclude that the concept of number is relative to his essetial notions which componds the concept of number. Because, obviously, a number aren't exclusively a quantity, but have some others notions, which I called essential, who can make us think numbers as a thing and not only as a quantity. The notion of space, as topology talks, and creates the topological psychology. So, there are mathematical notions who gives not a mathematical use for that same notions. Mathematics is essentially numbers, but the concept of number is not a close concept, and can be developed, and we can discover in the concept of number new things, because these same openess. Thank you for the informative answer. I see that math isn't about culture, and so on. Surely, probably I misconcepted those things or wrongly wrote about it. Anyway, I didn't lead to a thought that math was dealing with wide or fat notions. What do you think about the math's semantics? 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. |
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Post by thesageofmainstreet on May 14, 2021 17:59:40 GMT
A mathematical language have the need of unique symbols, but all concepts? If he say that about mathematical language, I agree. But a number can be the same? If a number only can be represented by a unique symbol, there are no need to consider a number as a concept. Of course, only the natural language is an object that requires to have special names for each separate and quite unique things. I think here Castillon didn't mention this operation; I guess it was my fault to chaos some of his thoughts, or I just said it in a wrong way. Anyway, type/token case could happen even in logic when we're dealing with something like 'sense' or 'meaning'. In a famous example of Phosphorus VS Hesperus it can be, or in this example: "It's necessary for 9 to have three dividers" "The number of planet in the Solar system = 9" ∴ "It's necessary for the number of planet in the Solar system to have three dividers". (From one of W. V. O. Quine's works ) THE CHIEF JUSTICE ("JUST US") INTERPRETED THE CONSTITUTION AS GIVING THE COURT THE RIGHT TO INTERPRET THE CONSTITUTION
5 + 4 = 9. So the assumption is wrong, not just the way the conclusion was reached.
Academic logicians don't dare use real-life examples, or they would expose Marbury v Madison as begging the question, thereby making judicial review invalid and getting rid of SCROTUS tyranny. But then how would the pseudo-intellectual products of university fake education dominate and humiliate the American people, taking away our right to self-determination? |
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Post by Eugene 2.0 on May 14, 2021 18:32:27 GMT
Thank you for the informative answer. I see that math isn't about culture, and so on. Surely, probably I misconcepted those things or wrongly wrote about it. Anyway, I didn't lead to a thought that math was dealing with wide or fat notions. What do you think about the math's semantics? 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? |
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Post by Eugene 2.0 on May 14, 2021 18:39:49 GMT
Of course, only the natural language is an object that requires to have special names for each separate and quite unique things. I think here Castillon didn't mention this operation; I guess it was my fault to chaos some of his thoughts, or I just said it in a wrong way. Anyway, type/token case could happen even in logic when we're dealing with something like 'sense' or 'meaning'. In a famous example of Phosphorus VS Hesperus it can be, or in this example: "It's necessary for 9 to have three dividers" "The number of planet in the Solar system = 9" ∴ "It's necessary for the number of planet in the Solar system to have three dividers". (From one of W. V. O. Quine's works ) THE CHIEF JUSTICE ("JUST US") INTERPRETED THE CONSTITUTION AS GIVING THE COURT THE RIGHT TO INTERPRET THE CONSTITUTION
5 + 4 = 9. So the assumption is wrong, not just the way the conclusion was reached.
Academic logicians don't dare use real-life examples, or they would expose Marbury v Madison as begging the question, thereby making judicial review invalid and getting rid of SCROTUS tyranny. But then how would the pseudo-intellectual products of university fake education dominate and humiliate the American people, taking away our right to self-determination? Most of academics are being afraid of having been revealed. It's simple: even some theoretician do that. According to Aristotle's "Metaphysics" Ch. 1: many theoretician fail in practice, although they know more about things in general. I studied logic, but it didn't help me to fix my phone charger, and I guess it's explainable: to fix it I had to be enough experienced in it. I mean no theoretical studies won't learn me how to drive a bicycle or a car with no experience driving. However, some skills and talented ones are able to do it. I saw some fighters who never learn a move in fights, but they kept their knuckles up, and they beat down many other warriors. I mean the talent or an inner genius can be presented. If I have no talents in fixing electronics, nobody help me except for myself to learn how to do it. And I guess that I must break some techniques at first to be able to get some required experience. |
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