What LEM is not

[Skepdick]

It's nothing like that.

It's exactly like that. And yes, it is an equivocation.

Your word against mine.

Like all philosophy. Pointless fucking mental masturbation.

[Magnus Anderson]

Your word against mine.

Like all philosophy. Pointless fucking mental masturbation.

What you put in is what you get out.

[Skepdick]

Your word against mine.

Like all philosophy. Pointless fucking mental masturbation.

What you put in is what you get out.

Great! So put something in..

What is the Boolean-value of LEM?

This is a question for axiology.

[Magnus Anderson]

Great! So put something in..

I did and you ignored it.

I will kindly ask you to leave this thread if you have nothing of substance to add.

[Skepdick]

Great! So put something in..

I did and you ignored it.

I will kindly ask you to leave this thread if you have nothing of substance to add.

Where is this "substance"? You are stuck in a circle.

What is the truth-value of LEM?

LEM itself is either True or False. Which one?
Exactly like TREE(3) itself is either Odd or Even. Which one?

My substance is in rejecting the universality of LEM.

[Magnus Anderson]

What is the truth-value of LEM?

Yes, It's Either True or False. Which one?

First of all, you have to make sure that your questions are relevant and that they are perceived as such. Noone will answer a question they perceive as irrelevant. Not only that, but since you've demonstrated that you don't enjoy proving the relevance of your questions, you won't be asked to do that. You will be simply ignored.

Second of all, your question has been answered more than once here in this thread. Not only that but I am sure you knew the answer long before you opened this thread.

[Skepdick]

First of all, you have to make sure that your questions are relevant and that they are perceived as such. Noone will answer a question they perceive as irrelevant. Not only that, but since you've demonstrated that you don't enjoy proving the relevance of your questions, you won't be asked to do that. You will be simply ignored.

Second of all, your question has been answered more than once here in this thread. Not only that but I am sure you knew the answer long before you opened this thread.

Contradiction.

LEM is relevant to ALL propositions.
LEM is a proposition.
Therefore LEM is relevant to ALL propositions. Including itself.

Q.E.D

What is the truth-value of LEM?

The question is relevant. Even if you are unable to perceive its relevance.

Maybe you don't understand relevance logic?
https://en.wikipedia.org/wiki/Relevance_logic

[Magnus Anderson]

This guy is seriously deaf.

[Skepdick]

This guy is seriously deaf.

Yes you are.

Keep repeating it. Until you hear it....

[godelian]

Imagine that somebody proposes that every proposition is either true or false. Is that proposition true or false?

The proposition is false. Counterexample: Russell's paradox. There are undecidable propositions.

[Magnus Anderson]

The proposition is false. Counterexample: Russell's paradox. There are undecidable propositions.

By definition, every proposition has truth value. That cannot be argued against.

Russell's paradox has nothing to do with that and concerns itself solely with non-propositions, i.e. propositions that aren't really propositions, such as "The set of all sets that do not contain themselves is a member of itself". That is a non-proposition because "the set of all sets that do not contain themselves" is an oxymoron. It's like saying "Square-circles are squares".

[godelian]

By definition, every proposition has truth value. That cannot be argued against.

In my opinion, stating that "every proposition has truth value" is equivalent to stating that "every proposition is decidable".

This is not true.

We do not even need to introduce natural numbers or sets. Logic itself is already generally undecidable:

https://en.m.wikipedia.org/wiki/Decidability_(logic)

In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not.

Many important problems are undecidable, that is, it has been proven that no effective method for determining membership (returning a correct answer after finite, though possibly very long, time in all cases) can exist for them.

Decidability of a logical system

A logical system is decidable if there is an effective method for determining whether arbitrary formulas are theorems of the logical system. For example, propositional logic is decidable, because the truth-table method can be used to determine whether an arbitrary propositional formula is logically valid.

First-order logic is not decidable in general; in particular, the set of logical validities in any signature that includes equality and at least one other predicate with two or more arguments is not decidable.[1] Logical systems extending first-order logic, such as second-order logic and type theory, are also undecidable.

[Skepdick]

...

1. https://en.wikipedia.org/wiki/Rice%27s_theorem

all non-trivial semantic properties of programs are undecidable.

2. https://en.wikipedia.org/wiki/Curry%E2% ... espondence

In programming language theory and proof theory, the Curry–Howard correspondence is the direct relationship between computer programs and mathematical proofs.

Proofs ARE programs.
All non-trivial semantic properties of Mathematical proofs are undecidable.

And that does it for the semantic view of Mathematics. Garbage in - Garbage out.

[godelian]

...

1. https://en.wikipedia.org/wiki/Rice%27s_theorem

all non-trivial semantic properties of programs are undecidable.

2. https://en.wikipedia.org/wiki/Curry%E2% ... espondence

In programming language theory and proof theory, the Curry–Howard correspondence is the direct relationship between computer programs and mathematical proofs.

Proofs ARE programs.
All non-trivial semantic properties of Mathematical proofs are undecidable.

And that does it for the semantic view of Mathematics. Garbage in - Garbage out.

Yes, agreed.

[Magnus Anderson]

In my opinion, stating that "every proposition has truth value" is equivalent to stating that "every proposition is decidable".

This is not true.

"Decidable" and "undecidable" are not truth values, they are epistemic categories.

Moreover, if the truth value of a proposition cannot be known, it does not mean it does not exist. ( Albeit, in practice, everything can be known. All one has to do is randomly stumble upon truth. It's a different question whether something can be deduced by employing certain type of reasoning on certain type of premises. )

But most importantly, you can't argue against the claim that every proposition has truth value because it is so by definition.