Why I Am Neither For Nor Against Aristotelian Thinking

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Eodnhoj7
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Re: Why I Am Neither For Nor Against Aristotelian Thinking

Post by Eodnhoj7 »

Skepdick wrote: Fri Jun 02, 2023 9:57 pm
Eodnhoj7 wrote: Fri Jun 02, 2023 9:50 pm More accurately, can excluded middle can be applied to identity and non-contradiction?
For identity I've already demonstrated.

let P := (A=A)

Either P is true; or not-P is true.

e.g either A=A is true; or not(A=A) is true.

Which one? Whichever one you choose axiomatically

Code: Select all

In [1]: class NonClassical():
   ...:     def __eq__(self, other): return False
   ...:

In [2]: A = NonClassical()

In [3]: not(A == A)
Out[3]: True

In [4]: A == A
Out[4]: False
Ambiguity on my part. Can the statement (A=A) v (A=/=-A) be made when the laws are self applied?
Skepdick
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Re: Why I Am Neither For Nor Against Aristotelian Thinking

Post by Skepdick »

Eodnhoj7 wrote: Sat Jun 03, 2023 6:47 pm Ambiguity on my part. Can the statement (A=A) v (A=/=-A) be made when the laws are self applied?
Sure. That's the law of excluded middle.

P v ¬P ↔ ⊤

Substitute the expression " (A=A)" for P and you get

(A=A) v ¬(A=A) ↔ ⊤
Eodnhoj7
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Joined: Mon Mar 13, 2017 3:18 am

Re: Why I Am Neither For Nor Against Aristotelian Thinking

Post by Eodnhoj7 »

Leontiskos wrote: Fri Jun 02, 2023 10:12 pm
Eodnhoj7 wrote: Fri Jun 02, 2023 9:45 pm
Leontiskos wrote: Fri Jun 02, 2023 9:30 pmBuilding on what I said in my last post, the law of identity and the law of non-contradiction both apply to Aristotelian substances and accidents, but they simply are not mutually exclusive in the way you suppose. It can be true that something is identical with itself while at the same time it is not identical with another thing. For example, I am me (law of identity) and I am not you (law of non-contradiction). They are both true at the same time. Naturally, they refer to different objects, but that is much the point.

As I said in my first post, I don't perceive any clear argument that you have given to the contrary. We can't just stipulate termina for the LEM.
The contradiction depends on where you place the core truth value of the laws discussed, this value can be expressed as: Equality vs. Inequality. This dichotomy results in opposites and yet these opposites depend on each other, remove one and the other one goes. However from another angle each of these laws, identity and non-contradiction, are mutually exclusive just as 'truth' and 'falsity' are mutually exclusive as one is the negation of the other.
This would only be true if your relations (equality and inequality) were being applied to the same set of objects. As noted, they are not, and therefore the argument fails. To predicate 'equal' and 'unequal' of the same pair or set would be contradictory, but to predicate them of different sets is not necessarily contradictory. The latter is the case with the LOI & LNC. The set of things which is identical to an object is distinct from the set of things that is 'contradictory' to an object.
Eodnhoj7 wrote: Fri Jun 02, 2023 9:45 pmAnother way of looking at this:

"Me" and "You" share the relative truth values of "Existence of Me" and "Non-Existence of Me (You)".

Because the laws of identity and law of non-contradiction are opposites in values, equality vs. absence of equality, one is the absence of the other thus it is the same as saying "A" and "-A" when saying "Law of Identity and Law of Non-Contradiction".
Let's take your example:
  • ExistenceOfEodnhoj(x)
  • ExistenceOfEodnhoj(@Eodnhoj7) = true
    • " Eodnhoj exists in 'Eodnhoj7' "
  • ExistenceOfEodnhoj(@Leontiskos) = false
    • " Eodnhoj does not exist in 'Leontiskos' "
The reason no contradiction occurs here is because the predication is made of two different objects. The same thing is true with the relation of LOI & LNC.
However equality and inequality are opposite assertions in themselves as each, no matter how they are expressed (ie the laws), are thetical and antithetical. LI and LNC are opposites because they contrast allowing for the identity of each. Negate one and the other is meaningless. Identity because of contrast.

I am not sure the difference in predication matters as the core "value" is "=" and "=/=". This is what defines the statements. 'Equality' can stand as P and 'inequality' as -P. Equality and inequality can also stand as metapredicates because of LI, Equality is equality and inequality is inequality.

But let's argue your side. A=A is different from A=/=-A. A problem occurs as the values in LNC still require LI in order to exist. This would be the same as saying ((A=A)=/=(-A=-A)) in which LI contradicts itself.
Skepdick
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Re: Why I Am Neither For Nor Against Aristotelian Thinking

Post by Skepdick »

Eodnhoj7 wrote: Sat Jun 03, 2023 9:28 pm This would be the same as saying ((A=A)=/=(-A=-A)) in which LI contradicts itself.
Univalence Axiom: (A = B) ≃ (A ≃ B).
Identity is equivalent to equivalence.

https://ncatlab.org/nlab/show/univalence+axiom

Read the book: https://homotopytypetheory.org/book/

It's way more contemporary than Aristotle.
Eodnhoj7
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Joined: Mon Mar 13, 2017 3:18 am

Re: Why I Am Neither For Nor Against Aristotelian Thinking

Post by Eodnhoj7 »

Skepdick wrote: Sun Jun 04, 2023 8:09 am
Eodnhoj7 wrote: Sat Jun 03, 2023 9:28 pm This would be the same as saying ((A=A)=/=(-A=-A)) in which LI contradicts itself.
Univalence Axiom: (A = B) ≃ (A ≃ B).
Identity is equivalent to equivalence.

https://ncatlab.org/nlab/show/univalence+axiom

Read the book: https://homotopytypetheory.org/book/

It's way more contemporary than Aristotle.
Thanks, will read when I have the time.

Are you right? Yes. But can identity be limited to equivalence? No. Why? Contrast. By comparing equivalence to non-equivalence both stand apart from each other as they are distinct from each other. This can lead to the assertion that identity is not on dependent upon symmetry but asymmetry as well. Under these terms it may be said that the law of identity can strictly just be P (not just P=P).
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