Radical Skepticism: All propositions are false

Quoting TheMadFool

First I reject all knowledge which may be expressed in the statement A = All propositions are false. If A is true the A is false because A is itself a proposition. Ergo, A is false which then implies B = Some propositions are true. It is absolutely certain that B is true.

Quoting Wikipedia on Gödel's completeness theorem

Gödel-Henkin model existence theorem.
We say that a theory T is syntactically consistent if there is no sentence s such that both s and its negation ¬s are provable from T in our deductive system. The model existence theorem says that for any first-order theory T with a well-orderable language, if T is syntactically consistent, then T has a model.

Propositions, i.e. sentences, live in an abstract, Platonic world. If its construction logic is syntactically consistent, then this world's theory has a non-empty model, i.e. a set of objects/facts that satisfy the sentences of the theory.

A theory is itself defined as a formal language with formal construction rules. Example: Hofstadter's MU puzzle.

There are still two situations in which all propositions in a theory can be false:

• The empty theory has an empty model, which is equivalent to no model. All its non-existent sentences are false, but all its non-existent sentences are also true. That is indeed ambiguous.
• Any syntactically-inconsistent theory has no model either.

Hence, "In any theory T some propositions are true" is formally false.

The physical universe is a model that satisfies the otherwise unknown theory of everything (ToE). Since the universe exists, the ToE cannot be empty nor syntactically inconsistent.

However, not one known theory has the physical universe as (one of) its model(s). In absence of the ToE, there do not exist logically true and/or provable logic sentences about the physical universe. In that sense, "Some propositions are true about the physical universe" is undefined.

Quoting TheMadFool

B = Some propositions are true. It is absolutely certain that B is true.

What does 'true' mean in this context? What makes you so certain that the statement is 'true'?

At best the statement is not self-contradictory, but that doesn't make it 'true' in any significant way.

Reply to TheMadFool In my philosophy I set out to do something very similar to this. I start out with rejecting two positions that I call fideism and nihilism, the latter of which I take to mean roughly the same thing as saying nothing is true. And the former is something you're probably just taking for granted here: you can't just prove something by assertion. Between the two of those, you get the view that something or another is true, but no claim about what it is can just be taken for true. The result is that everything must be taken as possibly true until we can show that it is false. You can think of this as taking the infinite disjunction of all propositions (A or B or C or D or ...) and then ruling out some of them bit by bit to narrow in on a smaller and smaller disjunction of possibilities. But of course, whittling down an infinite set still leaves you with an infinite set, but you nevertheless "gain knowledge" of what is not the case, even if you will never settle concretely on one specific thing that is the case.

Quoting A Seagull

What does 'true' mean in this context?

I propose to use Tarski's definition for (logically) 'true' as in his semantic theory of truth.

Truth is then a property of a (logic) sentence within a theory T en provenance from an encompassing meta-theory Tm. We therefore disallow a theory T to define the truth of its own sentences.

Quoting Pfhorrest

The result is that everything must be taken as possibly true until we can show that it is false.

Yes, but that is a practical heuristic in absence of knowledge of the truth of a (logic) sentence.

Tarski addresses this problem in another way. Tarski assumes the existence of a meta-theory which knows the truth of sentences in a subordinate, embedded theory.

Tarski's theory of truth is quite relevant in the context of a formal theory, which is in my opinion the context in which OP carries out his approach.

Quoting alcontali

"Some propositions are true about the physical universe" is undefined.

How on Earth did you infer that?

My argument is watertight.

1. Assume A = All propositions are false, is true
2.. From 1, A itself, being a proposition, is false
3. So we have A & ~A, a contradiction
So,
4. A is false
5. If A is false, its contradictory, B = some propositions are not false = some propositions are true, is true
So,
6. I know that Some propositions are true with absolute certainty.

The difficulty lies in discovering these propositions whatever they are. Logic would be a necessity but the premises would be a point of contention; it seems that any body of knowledge (collection of true propositions) will be ultimately axiomatic in character; the other less desirable options being circularity or infinite regress. The question is whether it's possible to find all true propositions with the one we know with absolutely certainty viz. B = some propositions are true, and applying correct principles of logic to it. B would become the one and only one axiom of the system.

Do you think this'll work?

It seems a good method of discovering certain truths is to copy the style of my original argument which is to make it self-referential and self-refuting which allows us to infer their negation.

For instance, begin with C = everything changes. If so, the meaning of C changes and that would be N = some things don't change. N contradicts C, by which we can infer the negation of C and get N = some things don't change.

Similarly, if we say M = everything has mass, then, since M applies to itself, we discover that meaning, being immaterial, is massless, and so M is false or L = somethings don't have mass, is true.

The technique is to construct a universal statement that's self-referential and self-refuting by which we can infer the contradictory particular statement.

Quoting A Seagull

What does 'true' mean in this context? What makes you so certain that the statement is 'true'?

If there's a flaw in my reasoning you're referring to then I didn't get it. For the discussion I think the correspondence theory of truth is adequate and also that whatever proposition is claimed to be true needs a sound deductive argument to back it.

Quoting Pfhorrest

I set out to do something very similar to this. I start out with rejecting two positions that I call fideism and nihilism, the latter of which I take to mean roughly the same thing as saying nothing is true. And the former is something you're probably just taking for granted here: you can't just prove something by assertion. Between the two of those, you get the view that something or another is true, but no claim about what it is can just be taken for true. The result is that everything must be taken as possibly true until we can show that it is false. You can think of this as taking the infinite disjunction of all propositions (A or B or C or D or ...) and then ruling out some of them bit by bit to narrow in on a smaller and smaller disjunction of possibilities. But of course, whittling down an infinite set still leaves you with an infinite set, but you nevertheless "gain knowledge" of what is not the case, even if you will never settle concretely on one specific thing that is the case.

That's very scientific and, in my opinion, applies to empirical knowledge where we're better off relying on falsifiability. As you can see, proving the disjuncts of an infinite disjunction false is hard work and is impossible. The usual way people go about building a belief system is to prove the truth of propositions, plus it's a widely expressed belief that the burden of proof relies on the person making a positive assertion rather than the one negating said proposition. However, the merit of your method is in keeping all options visible and given equal importance as should be the case: it prevents prejudice and bias.

I have rejected that knowledge from human sources, is true, all my life, but I accept them as potentially true.

I don't believe our pool of knowledge is perfect.

I'd rather take what I know from existence, than the word of another person - I have trust issues.

My first realizations from what you have written as 'A = all propositions are false', is that I exist; further, there is existential pheonomena, and how I exist is a structured existential phenomenon.

I don't regard the universe (the structured existential phenomenon) as all that exists, it has not presented itself in this way; I'm aware of existence (as a mental concept).

Therefore, my theory of everything must be existential and not universal; regarding the universe, but not falling too deep within it's contraint.

Thinking out of the box, per se, but not insanely.

I'm aware I exist in the universe, but 'I exist' comes foremostly.

"If this knowledge is true I can use my mind to find out" - a motto I live by.

If we test communicated knowledge through our own science, it helps to filter communicated knowledge, and gain trust with certain sources.

A camel, is a horse designed by comittee. I'm afraid wikipedia is like a camel; which can be good but I'm doing my own computation first.

Quoting TheMadFool

Do you think this'll work?

The video on Tarski's Convention T is only 11 minutes, very short, and it is really clear too.



Logical truth does not exist outside a formal system. So, what is the definition of your formal system? It looks like the empty system. What other system would it be?

Because of Tarski's undefinability of truth theorem, you cannot assess (logical) truth of a statement that belongs to a system from within the same system. That is why Tarski proposes convention T.

In Convention T, you need two theories (meta and object) to assess the truth of statements in the object theory from within the meta-theory. In your case, the object theory seems to be the empty theory. Therefore, I don't think that your conclusion will evaluate to true in the meta-theory. On the contrary, the meta-theory will rather conclude that not one proposition in the empty object theory will be true (nor false).

By the way, it is not allowed to reason within the meta-theory about the meta-theory. The meta-theory can only talk about the object-theory, and never about itself. In your approach, you may actually be conflating meta-theory and object-theory into one single theory, which is exactly what is not allowed.

I do not think that you can do this analysis without something like convention T.

Quoting TheMadFool

First I reject all knowledge which may be expressed in the statement A = All propositions are false.

In fact, it is simple.

According to Tarski's undefinability of truth theorem, a theory is not allowed to proclaim the truth or falsehood of its own propositions. Therefore, statement A is in violation with Tarski's theorem.

Quoting Wikipedia on Tarski's undefinability

The theorem applies more generally to any sufficiently strong formal system, showing that truth in the standard model of the system cannot be defined within the system.

(That is the reason why convention T is needed in which it is the meta-theory that assesses the truth of the object theory's propositions)

Quoting Qwex

Therefore, my theory of everything must be existential and not universal; regarding the universe, but not falling too deep within it's contraint.

Hello Q! Can you expound a bit on that one?

Reply to 3017amen

Hmm.

It's going to be hard for me to expand because it took me a long time to word that paragraph..

Given all information in the universe, a lot of this information can be discarded or categorized, unless the objective is to truly track every object.

When building a theory of everything, you only take what you need from universe experience?

Then, is it fair to say the theory of everything is existential? Relative to existence and not only the universe experience.

Relative to simulation as a whole, maybe?

It can be said that a conscious mind created the universe. I'm not religious but I'm open to the idea.

If that makes no sense, or if there's part missing, as I think there is in line 5, I'm sorry but I'll need thinking time.