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Post by Eugene 2.0 on Apr 3, 2021 11:31:49 GMT
There was an extensive program called logicism, and it was about to find the logical foundations of the math.
It failed.
I wonder what about mathematicism, a view that is about the math as a foundation to logic? In the logicism all the math axioms had to be converted to logical forms. What about to convert logical axioms to math?
Let's take these logical axioms in their metaphysical representation:
a) each something is something; or something equals to something
b) it's not possible that "something is" and that "something is not" at the same time
c) if there are two claims about anything and one of this claims is that "something is" while another is "something is not", then one of these claims must be true
At first we can translate them into more math-look view:
a) (x).x=x
b) (x).~(Px&~Px)
c) (x).(Pxv~Px)
Ok, if we can translate it to more math-look view does it make those logical representations be less math? Don't we do the same with plain number calculations?
I guess all what we can do is to reformulate them into much more math form. I can't say I've done it, but I've tried, here are they:
a) x=x
b) {x|f(x)=y, f(x)≠y}=[xє(x/0)]
c) [{x|f(x)=y}+{x|f(x)≠y}]≠0
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Post by karl on Apr 4, 2021 23:05:40 GMT
Let there be emphasis on "is", for only then is it true that either A or the negation of A is true.
A: "This radioactive atom will decay tomorrow."
B: "This radioactive atom will not decay tomorrow."
Even though B is the negation of A, the truth is neither B nor A.
But rather C: "It is not decided yet whether this radioactive atom will decay tomorrow."
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Post by Eugene 2.0 on Apr 5, 2021 3:46:12 GMT
Let there be emphasis on "is", for only then is it true that either A or the negation of A is true. A: "This radioactive atom will decay tomorrow." B: "This radioactive atom will not decay tomorrow." Even though B is the negation of A, the truth is neither B nor A. But rather C: "It is not decided yet whether this radioactive atom will decay tomorrow." Thanks for the answer. You know, I've been thinking about QM, because to read it and to study it – isn't the easy task for me. And one idea was that QM's logic and QM itself were not the same: QM's logic was a conception, while the real QM was physicists' discovery. And the next one was that there could be no objections that QM wouldn't change in a future. Letting its powerful potential away, we still have got a hope (maybe a tiny one) that it can be different in the future. Moreover, it's not logically impossible to deny a posteriori truths; we're not denying the logical part of QM, because it's just a concept. Considering this idea, for me it's not perfectly obvious that even QM is forever lasting. Maybe one day wefind a tool that will help us to see more tiniest parts of the universe, or some other things will be discovered, and then everything might be different. As long as QM physical part is in a little potential trouble, I can't rely on it. The logical part still works, and your example demonstrates one of the idea of QM. Leibniz would believe in the butterfly effect, because his universe was predictable, and I can't say my intuition is somewhere far away from this view. It doesn't seem to me plain and impossible. |
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Post by karl on Apr 5, 2021 19:16:26 GMT
Let there be emphasis on "is", for only then is it true that either A or the negation of A is true. A: "This radioactive atom will decay tomorrow." B: "This radioactive atom will not decay tomorrow." Even though B is the negation of A, the truth is neither B nor A. But rather C: "It is not decided yet whether this radioactive atom will decay tomorrow." Thanks for the answer. You know, I've been thinking about QM, because to read it and to study it – isn't the easy task for me. And one idea was that QM's logic and QM itself were not the same: QM's logic was a conception, while the real QM was physicists' discovery. And the next one was that there could be no objections that QM wouldn't change in a future. Letting its powerful potential away, we still have got a hope (maybe a tiny one) that it can be different in the future. Moreover, it's not logically impossible to deny a posteriori truths; we're not denying the logical part of QM, because it's just a concept. Considering this idea, for me it's not perfectly obvious that even QM is forever lasting. Maybe one day wefind a tool that will help us to see more tiniest parts of the universe, or some other things will be discovered, and then everything might be different. As long as QM physical part is in a little potential trouble, I can't rely on it. The logical part still works, and your example demonstrates one of the idea of QM. Leibniz would believe in the butterfly effect, because his universe was predictable, and I can't say my intuition is somewhere far away from this view. It doesn't seem to me plain and impossible.
Quantum mechanics just serves to illustrate the problem with excluding the inherent middle if one does not freeze time. Just accepting that reality isn't deterministic, for example if one believes in free will, is enough to state that if A equals:
"I will lift my arm in ten minutes."
and the negation to A then equals:
"I will not lift my arm in ten minutes."
Then it's not correct to assert that either A or the negation of A is true. But rather that either A or the negation of A will be true, but it's not necessarily determined at this point which one it will be.
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Post by Eugene 2.0 on Apr 5, 2021 21:43:32 GMT
Thanks for the answer. You know, I've been thinking about QM, because to read it and to study it – isn't the easy task for me. And one idea was that QM's logic and QM itself were not the same: QM's logic was a conception, while the real QM was physicists' discovery. And the next one was that there could be no objections that QM wouldn't change in a future. Letting its powerful potential away, we still have got a hope (maybe a tiny one) that it can be different in the future. Moreover, it's not logically impossible to deny a posteriori truths; we're not denying the logical part of QM, because it's just a concept. Considering this idea, for me it's not perfectly obvious that even QM is forever lasting. Maybe one day wefind a tool that will help us to see more tiniest parts of the universe, or some other things will be discovered, and then everything might be different. As long as QM physical part is in a little potential trouble, I can't rely on it. The logical part still works, and your example demonstrates one of the idea of QM. Leibniz would believe in the butterfly effect, because his universe was predictable, and I can't say my intuition is somewhere far away from this view. It doesn't seem to me plain and impossible. Quantum mechanics just serves to illustrate the problem with excluding the inherent middle if one does not freeze time. Just accepting that reality isn't deterministic, for example if one believes in free will, is enough to state that if A equals:
"I will lift my arm in ten minutes." and the negation to A then equals:
"I will not lift my arm in ten minutes."
Then it's not correct to assert that either A or the negation of A is true. But rather that either A or the negation of A will be true, but it's not necessarily determined at this point which one it will be.
I guess you know better. As far as I know Aristotle raised this problem in his "De Interpretatione": Chapter 9. Of contradictory propositions about the past and present, one must be true, the other false. But when the subject is individual, and the proposition is future, this is not the case. For if so, nothing takes place by chance. For either the future proposition such as, 'A sea battle will take place,' corresponds with future reality, or its negation does, in which case the sea battle will take place with necessity, or not take place with necessity. But in reality, such an event might just as easily not happen as happen; the meaning of the word 'by chance' with regard to future events is that reality is so constituted that it may issue in either of two opposite possibilities. This is known as the problem of future contingents. [it's from Wikipedia]. And also I find to be strange one thing: why it's not a contradiction to claim that "if a bullet is thrown by 45°, then it will describe the longest trajectory" or something like this "in 4.3 billions of years dissolution of nucl if 238U will be happened". And at the same time it's impossible to claim "tomorrow it's raining" and "tomorrow it's not raining"? Do our predictions depend on micro- or macro-objects? For instance, it doesn't possible that as any tiniest elements of the universe so the whole universe will disappear tomorrow". We can't predict only certain equal of objects?.. |
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Post by karl on Apr 6, 2021 9:37:19 GMT
Quantum mechanics just serves to illustrate the problem with excluding the inherent middle if one does not freeze time. Just accepting that reality isn't deterministic, for example if one believes in free will, is enough to state that if A equals:
"I will lift my arm in ten minutes." and the negation to A then equals:
"I will not lift my arm in ten minutes."
Then it's not correct to assert that either A or the negation of A is true. But rather that either A or the negation of A will be true, but it's not necessarily determined at this point which one it will be.
I guess you know better. As far as I know Aristotle raised this problem in his "De Interpretatione": Chapter 9. Of contradictory propositions about the past and present, one must be true, the other false. But when the subject is individual, and the proposition is future, this is not the case. For if so, nothing takes place by chance. For either the future proposition such as, 'A sea battle will take place,' corresponds with future reality, or its negation does, in which case the sea battle will take place with necessity, or not take place with necessity. But in reality, such an event might just as easily not happen as happen; the meaning of the word 'by chance' with regard to future events is that reality is so constituted that it may issue in either of two opposite possibilities. This is known as the problem of future contingents. [it's from Wikipedia]. And also I find to be strange one thing: why it's not a contradiction to claim that "if a bullet is thrown by 45°, then it will describe the longest trajectory" or something like this "in 4.3 billions of years dissolution of nucl if 238U will be happened". And at the same time it's impossible to claim "tomorrow it's raining" and "tomorrow it's not raining"? Do our predictions depend on micro- or macro-objects? For instance, it doesn't possible that as any tiniest elements of the universe so the whole universe will disappear tomorrow". We can't predict only certain equal of objects?..
It's all about probability. It's incredibly unlikely for even a small visible object to just disappear by chance, far less the entire universe. So on a macro scale, it seems as if the world is ordered and predictable, and in regards to probability, it kind of is. -Although only for small time intervals. For longer time intervals, the butterfly effect applies.
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Post by joustos on Apr 6, 2021 21:31:08 GMT
I guess you know better. As far as I know Aristotle raised this problem in his "De Interpretatione": Chapter 9. Of contradictory propositions about the past and present, one must be true, the other false. But when the subject is individual, and the proposition is future, this is not the case. For if so, nothing takes place by chance. For either the future proposition such as, 'A sea battle will take place,' corresponds with future reality, or its negation does, in which case the sea battle will take place with necessity, or not take place with necessity. But in reality, such an event might just as easily not happen as happen; the meaning of the word 'by chance' with regard to future events is that reality is so constituted that it may issue in either of two opposite possibilities. This is known as the problem of future contingents. [it's from Wikipedia]. And also I find to be strange one thing: why it's not a contradiction to claim that "if a bullet is thrown by 45°, then it will describe the longest trajectory" or something like this "in 4.3 billions of years dissolution of nucl if 238U will be happened". And at the same time it's impossible to claim "tomorrow it's raining" and "tomorrow it's not raining"? Do our predictions depend on micro- or macro-objects? For instance, it doesn't possible that as any tiniest elements of the universe so the whole universe will disappear tomorrow". We can't predict only certain equal of objects?..
It's all about probability. It's incredibly unlikely for even a small visible object to just disappear by chance, far less the entire universe. So on a macro scale, it seems as if the world is ordered and predictable, and in regards to probability, it kind of is. -Although only for small time intervals. For longer time intervals, the butterfly effect applies.
I beg to differ from Aristotle (and other original logicians I have not read). My own stand on contradictories has nothing to do with the present, past, or future. I came to it by analyzing an actual situation: I saw that Genesis-1 ASSERTS that the Elohim [the (Supreme) Gods] created Man in their image, one Male and the other Female, whereas Genesis-2 ASSERTS that Yahweh [one male God] created Man [Adam, from whom he fashioned a female]. Well, I thought, 2 (gods) cannot equal 1(god), and 1 cannot equal 2. The two contradictory assertions cancel each other; the two cited chapters provide NO TRUE knowledge as to the number of creating gods; both ASSERTIONS may be FALSE. //Though from a different perspective, Plato (in "Theaetetus") would agree: If I assert that the house I am looking at is small, and you (standing nearby) assert that it is big, the two contradictory assertions provide no knowledge as to how the house is IN ITSELF (NO TRUE knowledge); both assertions may be false. [ I know there is a semantic issue in this example, which I leave unresolved...] |
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Post by Elizabeth on Apr 7, 2021 7:25:18 GMT
Ok but why exactly did it fail? I actually see potential in this.
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Post by karl on Apr 7, 2021 11:22:39 GMT
It's all about probability. It's incredibly unlikely for even a small visible object to just disappear by chance, far less the entire universe. So on a macro scale, it seems as if the world is ordered and predictable, and in regards to probability, it kind of is. -Although only for small time intervals. For longer time intervals, the butterfly effect applies.
I beg to differ from Aristotle (and other original logicians I have not read). My own stand on contradictories has nothing to do with the present, past, or future. I came to it by analyzing an actual situation: I saw that Genesis-1 ASSERTS that the Elohim [the (Supreme) Gods] created Man in their image, one Male and the other Female, whereas Genesis-2 ASSERTS that Yahweh [one male God] created Man [Adam, from whom he fashioned a female]. Well, I thought, 2 (gods) cannot equal 1(god), and 1 cannot equal 2. The two contradictory assertions cancel each other; the two cited chapters provide NO TRUE knowledge as to the number of creating gods; both ASSERTIONS may be FALSE. //Though from a different perspective, Plato (in "Theaetetus") would agree: If I assert that the house I am looking at is small, and you (standing nearby) assert that it is big, the two contradictory assertions provide no knowledge as to how the house is IN ITSELF (NO TRUE knowledge); both assertions may be false. [ I know there is a semantic issue in this example, which I leave unresolved...]
So let's exemplify this. If someone first states that a radioactive atom will decay tomorrow, and then states that it won't, then he hasn't stated anything meaningful about what will happen. If that's you're point, then I agree.
The statement "The radioactive atom will decay tomorrow." is neither true nor untrue, since its not decided at the time of the prediction whether it will happen or not. One may make a guess about it, and that guess may or may not become true. If one, however, guesses both that it will and it won't happen, then the guess itself is meaningless.
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Post by karl on Apr 7, 2021 11:27:01 GMT
Ok but why exactly did it fail? I actually see potential in this.
It was the project of the logical positivists, and it failed, in my view, because language requires fundamental concepts that cannot be broken down any further, and hence is based on both intuition and logic, not just logic. The logical positivists claimed that only clear, descriptive statements like "The cat lies on the mat." are meaningful, while poetry, for example, is meaningless.
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Post by Eugene 2.0 on Apr 9, 2021 9:39:49 GMT
Ok but why exactly did it fail? I actually see potential in this. For math it was necessary to have propositions or sentences that belong to math. But it appeared that there was no chance to build a system where it could be possible to verify all the propositions or sentences whether they belong to the system. It was discovered that no matter how cool system we can develop each of such a system would necessary have a proposition or a sentence about we could not say whether or not it belonged to math. |
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