What LEM is not

[Skepdick]

Have you ever opened your skull to if there's a brain somewhere inside it?

If not, does that not mean you have no brain?

So you agree that my GPS location is true, even though you haven't looked?

You can't seem to make up your mind what your skepticism means.

[Magnus Anderson]

So, your definition for the term "proposition" is indeed physicalist.

And why does it matter whether it's physicalist or not?

Why are you so focused on these popular categories?

This thread isn't about these philosophies.

[Magnus Anderson]

So you agree that my GPS location is true, even though you haven't looked?

You can't seem to make up your mind what your skepticism means.

Stop dancing around.

Have you ever opened your skull to see if there's a brain somewhere in there?

If not, does that not mean you have no brain?

[godelian]

So, your definition for the term "proposition" is indeed physicalist.

And why does it matter whether it's physicalist or not?

You're trying to shoehorn me into one of the common philosophies of mathematics: physicalism, platonism and formalism.

A physicalist definition for the term "proposition" is unusable in contemporary logic and in contemporary mathematics.

[Magnus Anderson]

A physicalist definition for the term "proposition" is unusable in contemporary logic and in contemporary mathematics.

That's not true. But most importantly, it's irrelevant. The thread is about what LEM means, not what people want it to mean.

[Skepdick]

Stop dancing around.

Have you ever opened your skull to see if there's a brain somewhere in there?

If not, does that not mean you have no brain?

So follow your own advice, cupcake.

SInce you haven't actually investigated the GPS coordinates I gave you does that mean I can't be located there?

I am not the one doubting it's true - you are. So it's your problem, not mine.

[Magnus Anderson]

SInce you haven't actually investigated the GPS coordinates I gave you does that mean I can't be located there?

Do I have to investigate the GPS coordinates that you gave in order to conclude that you exist?

And have you ever opened your skull to see if there's a brain somewhere inside it?

[Skepdick]

SInce you haven't actually investigated the GPS coordinates I gave you does that mean I can't be located there?

Do I have to investigate the GPS coordinates that you gave in order to conclude that you exist?

And have you ever opened your skull to see if there's a brain somewhere inside it?

Why do you continue conflating location with existence? What's wrong with your brain? Does it even exist?

[godelian]

A physicalist definition for the term "proposition" is unusable in contemporary logic and in contemporary mathematics.

That's not true. But most importantly, it's irrelevant. The thread is about what LEM means, not what people want it to mean.

Concerning your take on the LEM:

"Every physicalist proposition is true or false."

ChatGPT: Does logical truth appear in physical reality?

Logical truth, such as tautologies in formal logic, exists in the realm of abstract reasoning rather than physical reality. While physical reality can exhibit patterns that align with logical principles, such as causality and consistency, logical truths themselves are not contingent upon physical phenomena. They provide frameworks for understanding and reasoning about the world but do not manifest as physical entities.

Again, your physicalist view on the LEM is unusable in logic.

[Magnus Anderson]

Again, your physicalist view on the LEM is unusable in logic.

That's neither true nor relevant. This thread isn't about the usefulness of LEM. It's about what LEM is. You keep confusing the two.

ChatGPT: Does logical truth appear in physical reality?

Logical truth, such as tautologies in formal logic, exists in the realm of abstract reasoning rather than physical reality. While physical reality can exhibit patterns that align with logical principles, such as causality and consistency, logical truths themselves are not contingent upon physical phenomena. They provide frameworks for understanding and reasoning about the world but do not manifest as physical entities.

Well, as I said before, the statement "2 + 2 = 4" means "If you take 2 apples and add to that 2 apples, you will have 4 apples".

That's a statement about what will happen under particular conditions, namely, if you start with 2 apples and add 2 more apples to that.

That's a conditional statement. It's not about what is. It's not about what was. It's not about what will be. It's about what will be under certain conditions.

So, even though it isn't expressed in the form of "A is B", it is expressed as "Under circumstances C, A will be B". And that is similar enough.

You can verify that statement through a physical experiment. You can take two apples, add to that two more apples and then count how many apples you have.

But due to the concepts involved, you can also verify it through a mental experiment. You don't need any actual apples, you can just imagine the entire thing in your head.

But most importantly, you can verify the statement entirely through conceptual analysis.

That's why "2 + 2 = 4" can also be expressed as "The relation between the concept attached to the symbol '2 + 2' -- where '2 + 2' does not represent the operation itself but its result, similar to how 9.25 does not represent the operation "9 + 2/10 + 5/100" but its result -- and the concept attached to the symbol '4' is that of equality, i.e. they are the same concepts."

We now have have an English statement in the form of "A is B". We managed to translate a conditional statement into a non-conditional statement about the present, an "is" statement.

The referred portion of reality is the relation between the concept attached to "2 + 2" and the concept attached to "4".

Are concepts physical entities?

Are you going to argue that they are not?

Or are you going to follow in the footsteps of Skepdick and argue that we can't know that something is a physical entity if we don't know its GPS coordinates?

[Skepdick]

That's neither true nor relevant. This thread isn't about the usefulness of LEM. It's about what LEM is. You keep confusing the two.

LEM is the claim that ALL propositons are bivalent e.g the truth-value of ALL propositions is in the set {true, false}
LEM is the claim that negation is involutive e.g (¬⊥ ≡ ⊤) ∧ (¬⊤ ≡ ⊥)
LEM further implies that (¬¬P ≡ P)

It holds in a bivalent logic with involutive negation.
It does NOT hold in non-bivalent logic with non-involutive negation.

https://en.wikipedia.org/wiki/Involution_(mathematics)

The End.

Or are you going to follow in the footsteps of Skepdick and argue that we can't know that something is a physical entity if we don't know its GPS coordinates?

That is not my argument. That is your strawman of my argument.

My argument is that IF X is physical THEN X has knowable location (of which GPS coordinates are one instance)
IF X has no knowable location then X is NOT physical.

Having knowable location s is a necessary property of physical things.

If you don't know the location of something you claim is "physical" then you asserting its physicality is justified via some other means.

Your reasoning is NOT "I know location of LEM therefore LEM is physical"
Your reasoning is "???? therefore LEM is physical"

What is your justification for asserting LEM's physicality?

[godelian]

Well, as I said before, the statement "2 + 2 = 4" means "If you take 2 apples and add to that 2 apples, you will have 4 apples".

That's a statement about what will happen under particular conditions, namely, if you start with 2 apples and add 2 more apples to that.

You can verify that statement through a physical experiment. You can take two apples, add to that two more apples and then count how many apples you have.

The referred portion of reality is the relation between the concept attached to "2 + 2" and the concept attached to "4".

Mapping to physical reality is possible for only some very small part of mathematics. It cannot be done for pure mathematics.

For example:

Galois correspondence. The tower of radical field extensions for the roots of a polynomial is isomorphic with the composition series of the normal subgroups of its associated automorphism group.

Where did you ever see a thing like that in physical reality?

The Galois correspondence does explain, however, why there are no solutions possible in radicals for the quintic, i.e. Abel-Ruffini theorem. It took centuries to discover this, exactly because this concept has no direct physical counterpart.

Are concepts physical entities?
Are you going to argue that they are not?

The Galois correspondence is a concept that has no direct physical manifestation, even though it may very indirectly govern some.

So, the simplest concepts may have a physical incarnation but most of mathematics does not.

[Magnus Anderson]

LEM is the claim that ALL propositons are bivalent e.g the truth-value of ALL propositions is in the set {true, false}

Well, if you're saying that LEM is claiming that every truth value is either true or false, i.e. that it can either be classified as "true" or as "false", then that is true.

If that's the case, can you name us one truth value that is not true and that is not false?

Are you going to say that 0.5 is neither true nor false?

Remember that "false" means "not true" rendering "Not true and not false" a contradiction in terms.

LEM is the claim that negation is involutive e.g (¬⊥ ≡ ⊤) ∧ (¬⊤ ≡ ⊥)

That's absolutely false. LEM says absolutely nothing about negation.

It does NOT hold in non-bivalent logic with non-involutive negation.

Consider Godel logic. That's a non-bivalent logic with non-involutive negation, isn't it?

The truth values in that logic are real numbers between 0 ( completely false ) and 1 ( true. )

Every truth value in that logic is either true or false. "1" is true. All other values are "false".

The end.

The fact that it uses non-involutive negation is IRRELEVANT.

The End.

You wish.

[Skepdick]

If that's the case, can you name us one truth value that is not true and that is not false?

Sure.

Fuzzy-logic. Continuous values between 0 and 1.
Three-valued logic: {true, false, undefined}

Are you going to say that 0.5 is neither true nor false?

Sure. In fuzzy logic that would mean half-true/half-false

Remember that "false" means "not true" rendering "Not true and not false" a contradiction in terms.

That's not generally true in all logics.
That's ONLY true in a bivalent logic with involution.

That's absolutely false. LEM says absolutely nothing about negation.

Contradiction. P is true or the NEGATION of P is true.

Consider Godel logic. That's a non-bivalent logic with non-involutive negation, isn't it?

The truth values in that logic is a real number between 0 ( completely false ) and 1 ( true. )

Every truth value in that logic is either true or false. "1" is true. All other values are "false".

The end.

Contradiction. Real values between 0 and 1 are degrees of truth.

You are claiming that 1 is true, and <1 is false.
That's not true.

The fact that it uses non-involutive negation is IRRELEVANT.

Contradiction. Involutive negation directly implies double negation elimination.

[Magnus Anderson]

That is not my argument. That is your strawman of my argument.

Bullshit.

My argument is that IF X is physical THEN X has knowable location (of which GPS coordinates are one instance)
IF X has no knowable location then X is NOT physical.

You were asking me tell you to the location of the concept attached to the word "is".

In fact, you went so far to ask me to tell you its GPS coordinates.

Obviously, you were suggesting that this is necessary to do in order to prove the physical existence of a thing.

You didn't ask, "How do you know it's physical?" You asked, "Where is it? Tell me its GPS coordinates."

An extremely imbecilic thing to do. But then again, you ARE an extreme imbecile.

What is your justification for asserting LEM's physicality?

So you disagree that concepts are physical?

Do they exist at all?