The overlooked part of Russell's paradox
- mystery
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Re: The overlooked part of Russell's paradox
- RJG
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Re: The overlooked part of Russell's paradox
RJG wrote:The Axioms of Simple Logic:
- X=X is true
X=~X is logically impossible
X<X is logically impossible
The "<" operator in the axiom "X<X is logically impossible", refers to "relation". This axiom means that something (X) can't have a relation to itself, because it is itself! (X=X).mystery wrote:um... just overload the < operator to be the same as = and it works.
Therefore, X can't be before (or after) itself; it can't be less than (or greater than) itself; it can't be inside (or outside) itself; etc etc. It can have no relation to itself because it is itself!
- Terrapin Station
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Re: The overlooked part of Russell's paradox
Identity is a relation, by the way.RJG wrote: ↑June 15th, 2021, 6:39 amRJG wrote:The Axioms of Simple Logic:
- X=X is true
X=~X is logically impossible
X<X is logically impossibleThe "<" operator in the axiom "X<X is logically impossible", refers to "relation". This axiom means that something (X) can't have a relation to itself, because it is itself! (X=X).mystery wrote:um... just overload the < operator to be the same as = and it works.
Therefore, X can't be before (or after) itself; it can't be less than (or greater than) itself; it can't be inside (or outside) itself; etc etc. It can have no relation to itself because it is itself!
- Thomyum2
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Re: The overlooked part of Russell's paradox
By selectively responding to just portions of my posts you're missing the points I'm trying to make. Please just try to hear what I'm saying. You don't have to agree, but I'd like you to understand.RJG wrote: ↑June 15th, 2021, 6:02 amIf X represents the word "cat", then X represents the word (not the animal), and vice versa. In logic, X represents whatever it is you are talking about.Thomyum wrote:What does 'cat=cat' even mean? The word 'cat', or an actual cat?...
You are making it much more complicated than it really is. If X represents this cat (specifically identified) or that cat, or the weight, size, or age, then that is what X represents! ...X represents whatever it is you are talking about.Thomyum2 wrote:...Which cat? At what time? Equal how? In weight, size, age? Surely you see what I mean.
I know that a variable can represent anything. But the terms '=', '<', '>', etc. are numerical relationships. If you substitute non-numerical things for the variables, then these symbols become ambiguous. If 'X' can mean a cat, or the word 'cat', or whatever the case may be, then it's no longer clear what it means to be equal to or less than.
My point, in short, is: you're asking us to accept the logical impossibility of this proposition 'X<X' while at the same leaving the door open to assigning any meaning of your choosing to these symbols, e.g. making '<' mean things like 'before', 'inside', 'exists before it exists'. Sorry, I'm not buying into it. Logical arguments require clear definitions.
Let's close this out for now. The thread is about Russell's paradox, which is interesting on its own and this is getting off topic.
— Epictetus
- Thomyum2
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Re: The overlooked part of Russell's paradox
Yes, agreed. Which in turn means something slightly different from 'equality', which is what is usually meant by '='.Terrapin Station wrote: ↑June 15th, 2021, 8:03 amIdentity is a relation, by the way.RJG wrote: ↑June 15th, 2021, 6:39 amRJG wrote:The Axioms of Simple Logic:
- X=X is true
X=~X is logically impossible
X<X is logically impossibleThe "<" operator in the axiom "X<X is logically impossible", refers to "relation". This axiom means that something (X) can't have a relation to itself, because it is itself! (X=X).mystery wrote:um... just overload the < operator to be the same as = and it works.
Therefore, X can't be before (or after) itself; it can't be less than (or greater than) itself; it can't be inside (or outside) itself; etc etc. It can have no relation to itself because it is itself!
— Epictetus
-
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Re: The overlooked part of Russell's paradox
Perfectly possible to do without any compiler errors in a language like C++ but arguably not much use for anything.mystery wrote:um... just overload the < operator to be the same as = and it works.
- RJG
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Re: The overlooked part of Russell's paradox
...and are also logical operators.Thomyum2 wrote:I know that a variable can represent anything. But the terms '=', '<', '>', etc. are numerical relationships.
**********
RJG wrote:The "<" operator in the axiom "X<X is logically impossible", refers to "relation".
Yes, but "identity" has its own special operator "=".Terrapin Station wrote:Identity is a relation, by the way.
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