More accurately, can excluded middle can be applied to identity and non-contradiction?Skepdick wrote: ↑Fri Jun 02, 2023 9:48 pmNowhere.Eodnhoj7 wrote: ↑Fri Jun 02, 2023 9:46 pmAnd where do you stand on the argument I provided?Skepdick wrote: ↑Fri Jun 02, 2023 9:42 pm
None are so blind as those who refuse to understand.
There is an A such that A is the same as itself.
There is a B such that B is not the same as itself.
e.g there are systems of logic in which the "law" of identity is not universal.
Code: Select all
IPython 8.13.2 -- An enhanced Interactive Python. Type '?' for help. In [1]: class Classical(): pass In [2]: class NonClassical(): ...: def __eq__(self, other): return False ...: In [3]: A = Classical() In [4]: B = NonClassical() In [5]: A == A Out[5]: True In [6]: B == B Out[6]: False
Boolean logic with excluded middle amounts to choice.
Sometimes a thing is identical to itself
Sometimes it's not.
Code: Select all
In [1]: from random import choice In [2]: class Random(): ...: def __eq__(self, other): return choice([True, False]) ...: In [3]: C = Random() In [4]: C == C Out[4]: True In [5]: C == C Out[5]: False
Why I Am Neither For Nor Against Aristotelian Thinking
Re: Why I Am Neither For Nor Against Aristotelian Thinking
Re: Why I Am Neither For Nor Against Aristotelian Thinking
Of course. It can be applied to any proposition P.
let P := ¬(a ∧ ¬a)
Either P is true; or not-P is true.
Either non-contradiction is true; or the negation of non-contradiction is true.
Re: Why I Am Neither For Nor Against Aristotelian Thinking
But I am saying either equality (identity) is true or its negation (non-equality (non-contradiction)) is true.
Re: Why I Am Neither For Nor Against Aristotelian Thinking
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
Re: Why I Am Neither For Nor Against Aristotelian Thinking
The negation of identity doesn't violate non-contradiction.
You get a contradiction only if identity is true AND false.
There is no contradiction if identity is either true OR false - that's consistent with LEM.
-
- Posts: 29
- Joined: Fri Apr 28, 2023 5:57 pm
Re: Why I Am Neither For Nor Against Aristotelian Thinking
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 pmThe 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.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.
Let's take your example: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".
- ExistenceOfEodnhoj(x)
- ExistenceOfEodnhoj(@Eodnhoj7) = true
- " Eodnhoj exists in 'Eodnhoj7' "
- ExistenceOfEodnhoj(@Leontiskos) = false
- " Eodnhoj does not exist in 'Leontiskos' "
Re: Why I Am Neither For Nor Against Aristotelian Thinking
Identical(A, A) = true or false?Leontiskos wrote: ↑Fri Jun 02, 2023 10:12 pm Let's take your example: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.
- ExistenceOfEodnhoj(x)
- ExistenceOfEodnhoj(@Eodnhoj7) = true
- " Eodnhoj exists in 'Eodnhoj7' "
- ExistenceOfEodnhoj(@Leontiskos) = false
- " Eodnhoj does not exist in 'Leontiskos' "
Re: Why I Am Neither For Nor Against Aristotelian Thinking
-
- Posts: 29
- Joined: Fri Apr 28, 2023 5:57 pm
Re: Why I Am Neither For Nor Against Aristotelian Thinking
It is perhaps worth noting that the law of identity is subsumed under the law of non-contradiction. The violation of the law of identity is a contradiction. When one violates the law of identity they are effectively making two contradictory predications with respect to the identity or essential properties of some object. Contrary to your OP, if the law of non-contradiction is false, then the law of identity can't be true. They go hand in hand.
Re: Why I Am Neither For Nor Against Aristotelian Thinking
Bollocks.Leontiskos wrote: ↑Fri Jun 02, 2023 10:51 pm It is perhaps worth noting that the law of identity is subsumed under the law of non-contradiction. The violation of the law of identity is a contradiction. When one violates the law of identity they are effectively making two contradictory predications with respect to the identity or essential properties of some object.
I am not the same as myself. e.g I changed - there's no contradiction here.
There would be a contradiction if I am the same as myself AND I am not the same as myself.
Huh?Leontiskos wrote: ↑Fri Jun 02, 2023 10:51 pm Contrary to your OP, if the law of non-contradiction is false, then the law of identity can't be true. They go hand in hand.
Acording to excluded middle either non-contradiction is false and the negation of non-contradiction is true; OR non-contradiction is true and the negation of non-contradiction is false.
-
- Posts: 29
- Joined: Fri Apr 28, 2023 5:57 pm
Re: Why I Am Neither For Nor Against Aristotelian Thinking
The question at hand is whether the law of identity and the law of non-contradiction are the negations of one another.
Re: Why I Am Neither For Nor Against Aristotelian Thinking
No, they arent. By the law of identity itself the negation of identity is the negation of identity.Leontiskos wrote: ↑Sat Jun 03, 2023 6:23 amThe question at hand is whether the law of identity and the law of non-contradiction are the negations of one another.
All of this is trivial. What's non-trivial is whether the negation of negation of identity is the law of identity.
e.g does this hold? ¬¬A ↔ A
It holds in Classical logic.
It doesn't hold in Intuitionistic logic.
https://en.wikipedia.org/wiki/Double_negation
- attofishpi
- Posts: 10012
- Joined: Tue Aug 16, 2011 8:10 am
- Location: Orion Spur
- Contact: