First, I want to praise this with every fiber of my being. I hope that my challenges to your writing have not come across as antagonistic. I am not trying to tear you down, I genuinely want to see if you can produce answers to the questions that have plagued epistemology for years. Knowledge was an absolute passion of mine for many years until I moved onto other things. So if I can help in any way, I will. — Philosophim

You have been a very excellent reviewer. Almost everyone here has proven to be very knowledgeable and sincerely wants an honest dialogue. That is much better than any other Philosophy forum. For example StackExchange severely penalizes every new idea just because it is a new idea.

I do encourage you strongly to read my theory of knowledge paper that I linked towards the top of these forums. — Philosophim

I have no idea how to find this.

Is it the only possible mistake though? And if a theory allows a mistake, does that mean its a complete and good theory? — Philosophim

The forced choice here is either to accept that a space alien perfectly disguised as a duck necessarily must be mistaken for an actual duck or empirical knowledge must be determined to be impossible. There don't seem to be even any other categories of possibility. It seems absurd that expressions of language that are false yet taken to be true could possibly be correctly construed as knowledge.

The actual knowledge itself is contained in a correct verbal model of the actual world. Mapping things in the world to their element in this knowledge tree might not itself be any sort of knowledge.

Lets look again at the statement, "to the best possible extent". What specifically is someone's best possible extent? How do we measure this or note this in any other claim? — Philosophim

When a counterfeit thing has no discernable difference from the real thing then it cannot possibly be correctly construed as a mistake when the counterfeit is (at least tentatively) taken to be real. On the other hand taking a counterfeit to be real remains incorrect.

↪PL Olcott Thank you for the interesting link. — Truth Seeker

I really appreciate all of your feedback. This whole forum seems filled with
people that are knowledgeable of the subject and sincerely want an honest dialogue.

Trying to talk to logicians about the foundations of truth and logic is like trying to
talk to atheists about God. I am very happy that I found this forum.

Banno
21.2k
↪PL Olcott No, it isn't. — Banno

That is the way that I mean it.
If one is aware that one is thinking this proves that thinking exists.
If thinking exists then this refutes the assertion that nothing exists.
This is the most certain thing because it occurs RIGHT NOW.

We can at the very least know that existence exists right now.
— PL Olcott

Rubbish. It's not at all clear what that might even mean. Use of ideas from Ayn Rand will only detract from your credibility.

I'll again leave you to it. — Banno

It is a paraphrase of: https://www.britannica.com/topic/cogito-ergo-sum

Banno
21.2k
↪PL Olcott And?

I suggest you glance at the talk page. — Banno

I agree with you, I merely referenced a very famous quote that seems to disagree with you.
We can at the very least know that existence exists right now.

Within the assumption that our memory is not fake we can also know everything that we are aware of that is proven to be completely true entirely on the basis of its meaning. We know that cats are animals.

While we are looking at a cat we can know that we are looking at a cat (as long as it is not a space alien perfectly disguised as a cat). This remains true even if all of actual reality is a mere figment of our own imagination.

Premise: We don't know anything with 100%, absolute, undeniable certainty.
Conclusion: Therefore, we don't know anything.

Of course, no one would actually suggest such an inept argument... — Banno

https://en.wikipedia.org/wiki/I_know_that_I_know_nothing

I proved above that when
"a proposition which asserts its own unprovability. (Gödel 1931:43-44)"

G := ¬(F ⊢ G) — PL Olcott

That this proposition is self-contradictory:
Proving G in F requires a sequence of inferences steps in F that proves there is no such sequence of inference steps in F.

thus the assessment that its formal system is incomplete is incorrect.

If the mathematical notion of incomplete is incorrect for one input then it
cannot be trusted for other inputs.

Copyright 2023 PL Olcott

So then the question for you is, "Is deduction without truth knowledge justification?" — Philosophim

I am back to something close to my original position confusing a space alien perfectly disguised as a duck for an actual duck is the only possible mistakes allowed with my very reasonably plausible approximation of knowledge.

If you believe that your friend has at least five coins in his pocket and you did not see at least five coins then you do not have sufficient justification for your belief. If you see these coins and they turn out to be perfect counterfeits of actual coins you are still justified in your belief. If they are obvious plastic counterfeits then your belief was never justified.

My goal here is to end up with a universal criterion measure for truth such that True(L, x) becomes computable. I am on this forum for the purpose or researching truthmaker theory so that I can write an academic paper breaking new ground in this field.

JTB one must have justification such that the truth of the belief is a necessary consequence of its justification to the best possible extent that counterfeits of things in the world (relevant to the justification of the belief) are detected and rejected when possible.

Are you saying that truth can be unknown but that knowledge cannot be, in the sense that we cannot be said to know unless we know that we know? — Janus

My example is that a space alien that is perfectly disguised as a duck (including Duck DNA)
would be mistaken for a duck thus provide fake knowledge that is not true.

The things that can be known with justified logical certainty are located in an axiomatic
system knowledge ontology verbal model of the actual world.

In the empirical context we can say that we know that what we observe is the case, and that we know that we know it; we simply observe what is the case. So, there is no need for belief in this context. Believing is what we do when we cannot know. — Janus

I think that believing in the case of JTB means that some mind holds the idea of the assertion.
Knowledge is divided from truth in that truth can be unknown.

What is at stake here is the nature of implication, not the meaning of material implication. We are questioning whether material implication is an adequate account of implication. No one is confused about how material implication works. — Leontiskos

The same author says this later on in the same article.

For example, one might think that some sort of relevance notion of entailment is at stake (for example, Restall 1996); the hope is to develop a conception of entailment that maintains that while ‘Socrates is a philosopher’ en-tails ‘Someone is a philosopher’, it does not entail ‘2 + 2 =4’.

To a large extent, the development of conditional logics over the past century has thus been driven by the quest for a more sophisticated account of the connection between antecedent and consequent in conditionals. — SEP | The Logic of Conditionals

When we require that the consequent be a necessary semantic consequence of its antecedent all of the issues go away. A ⇒ B then becomes A ⊨ B and we quit using the former.

We could do as

So we are only considering implications in which the consequent is true. In all such cases — Banno

suggests yet limit the use of ⇒ to propositional logic.

It's never the case that two and two is not four. So we are only considering implications in which the consequent is true. In all such cases, the implication is also true. — Banno

You see these things exactly the same way that I do.

That you deny the truth of statements that are proved completely true entirely on the basis of the meaning of their words sufficiently proves that you don't want any honest dialogue.
— PL Olcott

Maybe you will have better luck next time. :smile: — chiknsld

It has never been any matter of luck. It has always been a matter of applying
very extreme diligence to intuition until the intuition is translated into seamlessly
correct reasoning.

In The Philosophy Forum almost everyone knows the subject matter very well
and everyone besides you seems to want an honest dialogue. This is at least
ten-fold better than any other online forum about philosophy than I have
ever encountered.

That you deny the truth of statements that are proved completely true entirely on the basis
of the meaning of their words sufficiently proves that you don't want any honest dialogue.

I try to always give the benefit of the doubt. At this point there is no doubt.
I had you pegged correctly in my original reply.

:snicker: — chiknsld

Ah so you are a mere Troll after all.

I need to know what happens when you encounter a simulation of yourself. Are you saying that you would not know the difference between yourself and a simulation of yourself? — chiknsld

This is getting a little too silly. An otherwise perfect simulation of myself would not exist
in exactly the same (x,y,z) coordinates relative to the center of the Earth.

I am sorry but there is no way for you to apply this philosophical theory to something as advanced as simulation theory. If you want to know why, that would probably be a different conversation. I have already pointed you to the proper perspective. Good luck! — chiknsld

None the less my key point is that if two things differ in ways that are not discernable
such as an actual duck and a space alien perfectly disguised as a duck (including duck DNA)
then the mistake of incorrectly believing that the space alien is an actual duck cannot possibly
be avoided.

Your initial reply seems to fail to understand that if there is no discernable
difference between X and Y then there is no difference to be discerned.

You seemed to be saying that when no there is no discernable difference
between X and Y that a difference can never-the-less be still be discerned.

We ourselves are not exactly the same as we were one minute ago.
— PL Olcott

You would have to show how this is relevant. :smile: — chiknsld

The very first time that I ever heard about the Identity of indiscernibles
https://en.wikipedia.org/wiki/Identity_of_indiscernibles#:~:text=The%20identity%20of%20indiscernibles%20is,by%20y%20and%20vice%20versa.

I had it completely figured out. If every single property is exactly the
same then two different things <are> one-and-the-same thing, otherwise
they are not one-and-the-same thing. My qualification addresses any
time travel paradox related to the Identity of indiscernibles.

When the entire set of properties of a thing (including its point in time and space)
are identical to another thing then we can know that they are one-and-the-same thing.
— PL Olcott

Identical points in time and space? This would be illogical, and would also undermine the complexity of your simulation as the fundamental grounds of reality (which were once common) are now dissolved. — chiknsld

We ourselves are not exactly the same as we were one minute ago.

When a thing is exactly the same as a duck from all external appearances including
a blood test of DNA, then you can tell it is actually a space alien when it telepathically
invades your thoughts screaming that it <is> a space alien.
— PL Olcott

You touch on a deep truth, though I am not sure you are aware. :smile:

An infinitely irreducible simulation of reality (as it seems you are proposing) in no way addresses the categorical separation between reality and its simulation. — chiknsld

When the entire set of properties of a thing (including its point in time and space)
are identical to another thing then we can know that they are one-and-the-same thing.

If a thing has hidden properties that would distinguish it from other things then
we cannot correctly determine whether it is this other thing or not. We can guess
yet our guess might possibly be incorrect.

It is (by definition) impossible to tell the difference between a thing and its simulation
when there is no discernable difference.

I have my own ideas but I figured I'd open with the simple question: what is logic? (there is more on this than "what is computation," but a lot of it does not seem to address the big questions) — Count Timothy von Icarus

Logic seems best defined as a set of rules forming the axiomatic basis of correct reasoning.
Tarski Undefinability, Gödel Incompleteness and the Principle of Explosion seem to indicate
issues with current systems of logic.

My unique contribution to this is that the above issues can be easily abolished by simply
requiring all conclusions to be a semantically necessary consequence of all of their premises.
Copyright 2023 PL Olcott

The key change that this requires is to fully integrate model theory into the notion of formal systems.

Truth Seeker
38
↪PL Olcott I agree.
seconds ago — Truth Seeker

That is great. There is no simple upvote so I do it verbally.

↪PL Olcott I haven't exchanged words and arguments with you yet, but I appreciate your kindness. I think appreciation is one of the key features of each person. — javi2541997

Thanks for that.

↪PL Olcott How do I know that something self-evident is true? My perceptions could be real or simulations or hallucinations or dreams or illusions. — Truth Seeker

The set of every self-evident truth is stored in a knowledge ontology verbal
model of the actual world. A cat is an animal even if no cats physically exist.

↪PL Olcott How can a duck's consciousness be replaced by an alien? Is consciousness something separate from the body that can be put in different bodies or is it something emergent as a result of brain activities? — Truth Seeker

This is a hypothetical example thought experiment of the boundaries of the
Identity_of_indiscernibles

https://en.wikipedia.org/wiki/Identity_of_indiscernibles#:~:text=The%20identity%20of%20indiscernibles%20is,by%20y%20and%20vice%20versa.

When a thing is exactly the same as a duck from all external appearances including
a blood test of DNA, then you can tell it is actually a space alien when it telepathically
invades your thoughts screaming that it <is> a space alien.
— PL Olcott

When you believe that there is an alien, disguised as a duck, screaming into your head telepathically, there might be deeper epistemic concerns than Gettier problems. — wonderer1

For this thought experiment it is stipulated that the space alien really
is telepathically communicating with you.

If there is a difference then this might be a discernable difference.
If there is NO difference then entails that THERE IS NO discernable difference.
— PL Olcott

↪PL Olcott if you can claim there is no difference, then someone else can claim they are the same. — chiknsld

https://en.wikipedia.org/wiki/Identity_of_indiscernibles

When a thing is exactly the same as a duck from all external appearances including
a blood test of DNA, then you can tell it is actually a space alien when it telepathically
invades your thoughts screaming that it <is> a space alien.

Something not quite right there. Did you mean (the Goldbach conjecture is) true XOR false? Any proposition is either true or false (principle of bivalence). — Agent Smith

It is unknown whether the Goldbach conjecture is true or false because there is currently no known shortcut to the infinite proof of simply testing every natural number.

↪PL Olcott I agree that a shapeshifting alien could be pretending to be a duck and we would not be able to tell without analysing blood samples, etc. — Truth Seeker

If it even has the same DNA as a Duck because it replaced the Duck's consciousness with its own, then we cannot even tell from blood samples.

deduction doesn't give us anything we don't already know, making knowledge production seem near impossible. — Count Timothy von Icarus

The sum total of all analytical human knowledge is simply a {semantic tautology} a set of self-evident truths.

We create new knowledge in a way that is acceptable to the USPTO (Patent and Trademark office) by combining existing ideas together in a uniquely different way.

In epistemology (theory of knowledge), a self-evident proposition is a proposition that is known to be true by understanding its meaning without proof... https://en.wikipedia.org/wiki/Self-evidence

This means that deduction is simply one or more links into the knowledge tree verbal model of the actual world.

Copyright 2023 PL Olcott
I only put copyright notices on key insights that have taken me many years to achieve.

To my mind, this suggests a sort of gradient of "accuracy," if not truth. — Count Timothy von Icarus

If it walks like a duck, quacks like a duck, lays eggs like a duck
and does everything else just like a duck it could still possibly be
a space alien perfectly disguised as a duck.

Thus when a set of physical sensations matches a duck then it
is very reasonably plausible to conclude that it is most likely a duck.

Within the assumption that it is a duck we can know with 100%
perfectly justified complete certainty that it is an animal.

x := y means x is defined to be another name for y
https://en.wikipedia.org/wiki/List_of_logic_symbols
This seem to be the only way that we get actual self-reference
all of the textbooks merely approximate self-reference with ↔

G := ¬(F ⊢ G) // G asserts its own unprovability in F

Proving G in F requires a sequence of inferences steps in F that proves there is no such sequence of inference steps in F.

Copyright 2023 PL Olcott

...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...
(Gödel 1931:43-44)

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems

If there is no difference between reality and a simulation of reality then no difference
can be discerned...
— PL Olcott

Sounds to me like you are proposing a difference! :grin: — chiknsld

If there is a difference then this might be a discernable difference.
If there is NO difference then entails that THERE IS NO discernable difference.

The Gödel sentence is a spin-off of the liar sentence (This sentence is false). The assumption that we make with the liar sentence is that it's a proposition and therefore that it has a truth value. Reject that assumption and no contradiction results as there are no truth values that come into opposition.

Since, the Gödel sentence is the liar sentence in some sense can't we do the same thing we did to the liar sentence: take away its status as a proposition? — TheMadFool

That is my thoughts exactly, yet so far we have not even done this
to the actual Liar Paradox itself: "This sentence is not true."

When we formalize the exact same structure as the Liar Paradox
in Prolog we see that Prolog rejects it as unsound because it has
a cycle in the directed graph of its evalulation sequence.

?- LP = not(true(LP)).
LP = not(true(LP)).

?- unify_with_occurs_check(LP, not(true(LP))).
false.

We get the exact same thing with your simplified Gödel sentence.
He sums up his own work this same way:

...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...
(Gödel 1931:43-44)

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems

Tarski's indefinability theorem. — Banno

Here is his actual proof of that theorem:
https://liarparadox.org/Tarski_275_276.pdf
You seem to have the same passion for this subject that I do.

"I i think therefore I am" seems like the only justifiable 100% certainty to me. The best you can get after that, I would think, it's 99.9 followed by some amount of 9s percent certainty - there's always some doubt for any other statement I think. — flannel jesus

My paraphrase of that is "existence exists right now".
If all of our memories are fake then we cannot be sure
that we really know how to do first grade arithmetic even
though we have a memory from a few seconds ago of doing
first grade arithmetic.

Banno
21.2k
↪PL Olcott Meh. That looks to be all over the place, truth-makers coming form a different place to modal logic, and I'm not too happy about your claims to copyright, so I'll leave you to it. — Banno

The key innovation of my seven years of full time work is that an analytical expression of formal or natural language is only true when it has a semantic entailment (necessity) connection to other expressions of language that have been stipulated to be true.

This is significant because in such a formal system Gödel incompleteness and Tarski Undefinability are impossible.

Expressions stipulated to be true are related to truth conditional semantics. For simplicity we can call them verified facts or Haskell Curry elementary theorems:

Let T be such a theory. Then the elementary statements which
belong to T we shall call the elementary theorems of T; we also
say that these elementary statements are true for T. Thus, given
T, an elementary theorem is an elementary statement which is
true. https://www.liarparadox.org/Haskell_Curry_45.pdf

My ultimate goal of the above work is that this idea be used to create
a True(L,x) software function in AI systems providing them with the
definitive basis to divide truth from falsity. Tarski incorrectly "proved"
that this is impossible.
https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem#General_form

This is a huge problem with current state of the art LLM AI systems such as ChatGPT
https://en.wikipedia.org/wiki/Hallucination_(artificial_intelligence)
They just make stuff up out of thin air and cite it as verified facts.

If there is no difference between reality and a simulation of reality then no difference
can be discerned. https://en.wikipedia.org/wiki/Maya_(religion) might be discernable.

When knowledge is defined as a justified true belief such that the justification necessitates the truth of the belief then the Gettier problem is no longer possible.
— PL Olcott

What could you mean here by "justification necessitates the truth of the belief"? — Banno

Apparently truthmaker theory answers this question. I just found out that all of my ideas for the last seven years have been anchored in truthmaker theory. I had never heard of truthmaker theory prior to two weeks ago.

My own unique take on this is that for analytical truth an expression of language is proved to be true if it is semantically entailed by expressions of language that are stipulated to be true.

These expressions are stipulated to be true on the basis of the verbal model of the actual world. This is assumed to be stored in a knowledge ontology like the CYC project. https://en.wikipedia.org/wiki/Cyc

After very much discussion in this thread I have narrowed down the meaning of empirical knowledge to be when a set of physical sensations map to one or more elements within this model of the world.

Copyright 2023 PL Olcott