Are the fundamental laws of logic true?

[trenton]

I have been exploring the most foundational laws in logic. I have been trying to stress test them to see if they are true. This includes

1. The law of identity 

2. The law of non-contradiction (also known as the law of contradiction)

3. The law of the excluded middle

If you would like to try to refute them you can. The law of non-contradiction in particular seems to be the closest to refuted, though this seems debatable.

Firstly, the law of identity is the most stable one in my opinion. A=A. If it is the case that existence is, then existence is. I haven't come up with a clear counter example.

Secondly, that law of non-contradiction seems to hold in most cases. The closest thing to a test would be "this statement is false." Some argue that it is genuinely both true and false at the same time. Dialetheism is something I would like to check for those who claim contradiction is not an error. The counterargument is that "this statement is false" doesn't give any truth value at all and is completely vacuous. But then would that make this neither true nor false? That is still a third category of truth.

The way I think about contradiction is that there are different types of contradictions that are allowed. Some contradictions resolve by disambiguating. Some by setting a reference point. Some are a difference in perspective. Some may be the result of limited human concepts for explaining reality, and this would be semantic or linguistic contradictions. The contradictions I treat as genuine problems would be self defeating performative contradictions that fail their own test. 

For example, "all statements are meaningless unless they can be empirically verified." Logical positivism has an actually damaging contradiction because it fails by its own standard. This is the same as claiming "nothing is true." The problem is that if that statement is true, then there is at least one truth. It the statement is false, then the truth is that the statement is false. A contradiction is not necessarily an error, but there are specific types of contradictions which are actually problematic for a logical system. Some contradictions are self defeating within a logical system. Beyond this domain, I'm not sure I would say that no contradiction is ever allowed. That can be debated.

The law of the excluded middle appears to hold when formalized in a narrow and specific way. That is that a proposition is either true or false by virtue of the structure of a proposition which thus serves as a truth claim. It seems the liar paradox would be the closest attempt at a counter example.

Self reference is the main source of paradox in these cases. I haven't seen any attempt that isn't self referencing.

Do you think any of the laws of logic are true? If one is false, then which one and why?

[Mixcoatl]

I think the third one is non true in quantum physics. That's why new kinds of logic had to be developed. 

I agree that the first one is the most stable law: It's a squared triangle possible? 

By the way, some people say that God has absolute power. I don't know. I think God can't break the most fundamental laws of logic. A squared triangle is absolutely impossible.

[trenton]

1 hour ago, Mixcoatl said:

I think the third one is non true in quantum physics. That's why new kinds of logic had to be developed. 

I agree that the first one is the most stable law: It's a squared triangle possible? 

By the way, some people say that God has absolute power. I don't know. I think God can't break the most fundamental laws of logic. A squared triangle is absolutely impossible.

By a squared triangle, I assume you mean a three sided shape with four sides. A counter example would be a shape that is both a square and a triangle by having three and four sides. It is a fairly stable example.

I think once you pin down limitations, it creates a situation in which one finite thing cannot be another finite thing. Therefore do long as you have defined parameters, there is by necessity limitations in which the defined thing logically can't be other than what it is given the limitations imposed by the definition. 

From that standpoint a true counterexample involving a squared triangle would probably be non duality. If you and I are one, then a square and a triangle are one. You may or may not accept this, but my point is that in order to break the law of identity, one would have to dissolve the entire concept of identity altogether in order to get to anything remotely resembling a counter example. This isn't really the game logic is designed to play.

One thought I had regarding contradiction would be reality as a whole necessarily operating independently of our human concepts. For example, there is the law of impermanence in which change is unchanging. At that point how do we distinguish between reality being constant change and constant persistence? If there is no real difference between change and not change without human concepts creating ground rules and limitations, then doesn't existence itself have this paradoxical nature which can't be cleanly pinned down without human concepts ultimately collapsing under their self imposed limitations, thus leading to contradictions?

What do you think about "everything except change is changing?"

[Ulax]

Epistemic regress argument makes me say no.

I love the epistemic regress argument so much. There should be a statue dedicated to it in every town and city worldwide.

[trenton]

2 hours ago, Ulax said:

Epistemic regress argument makes me say no.

I love the epistemic regress argument so much. There should be a statue dedicated to it in every town and city worldwide.

That is where I explored when I considered this as well.

If logic can't tell if the premises are true, then logically that applies to the laws of logic as well. From that standpoint it can't be known if the laws of logic are true or false.

I don't think the epistemic regress problem demonstrates that the laws are false, but rather that they are unknowable in their truth value. Logic does concede that it can't tell you if it's premises are true. It therefore limits itself to the specific domain of defined propositions which in turn are structured such that they either are true or false, thus following the laws of logic.

This looks like a circular argument if logic is thus used to justify logic. A proposition which enters that system will not break the system due to the rules that system set up for what counts as a proposition. Logic is therefore a system that succeeds on its terms, but not necessarily on other terms like fuzzy logic among other logic types. Succeeding on its terms does not mean it is true according to logic.

[Joseph Maynor]

The laws of logic are a collective creation, or an artform.  This artform has the relevance it has but no more too.  There is a rhetoric and power aspect to using laws of anything to consider.  And it depends on context too.  Sometimes logic is very clear -- someone got busted with their hand in the cookie jar for example.  Or there is x amount of money in someone's bank account right now, or not.  That is an exclusive or that comes from logic.  

[something_else]

I think Gödel's incompleteness theorem is useful here.

Quote

Secondly, that law of non-contradiction seems to hold in most cases. The closest thing to a test would be "this statement is false." Some argue that it is genuinely both true and false at the same time. Dialetheism is something I would like to check for those who claim contradiction is not an error. The counterargument is that "this statement is false" doesn't give any truth value at all and is completely vacuous. But then would that make this neither true nor false? That is still a third category of truth.

This was Gödel's path to his theorem. He essentially took the statement "this statement cannot be proven" and showed that:

• if the statement is true, then there must exist logical statements which cannot be proven (logic is incomplete)
• if the statement is false, then it means the statement can be proven but that would logic has just proved a false theorem (logic is inconsistent)

The way he did this is really cool, basically getting maths/logic to eat its own tail by creating an encoding system, representing a formula in that system that when decoded says "The formula with code number X has no proof.". But then if you decode what X is, it is the encoding of the exact same formula.

Edited 5 hours ago by something_else