Justified true belief: knowledge and the myth of propositions

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A_Seagull
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Re: Justified true belief: knowledge and the myth of propositions

Post by A_Seagull » Wed Jul 10, 2019 11:59 pm

RCSaunders wrote:
Wed Jul 10, 2019 8:21 pm
A_Seagull wrote:
Wed Jul 10, 2019 5:17 am
So I will just conclude with this: There are some truths of the world such as 'Then Earth goes around the Sun in an elliptical orbit' and 'e**ip=-1', and these truths can be demonstrated from a few simple assumptions and a fairly complex sequence of inferences; but to claim that some banal statement like your 'either some fictional aeroplane crashes or it doesn't' should fit alongside them as a truth of the world is just pathetic.
I totally agree. Except there is no claim the statement was about a physical fact. It is about the nature of reason itself.

Just as 2 plus 2 equals 4 is not a statement about any actual earthly fact, it is said to be true because two of anything added to two more is four, without specifying any actual things.

Euler's identity is not about any physical fact either. The mathematical elements, e, i, and π are all purely concepetual and have no physical existence. e and π are both irrational which means there is no commensurate (physical) unit of measure in which they can be expressed. i does not exist at all except as a concept.

In logic, the law of excluded middle states that for any proposition, either that proposition is true or its negation is true. It is one of the so called three laws of thought, along with the law of noncontradiction, and the law of identity. The law of excluded middle is the basis of the discussion you objected to.

The law of excluded middle is not based on an assumption, it is based on an axiom, that a thing is what it is and cannot be anything else. An axiom (not the nonsense proposed by modern day philosophers) is true because to deny it is self-contradictory. If you were not who and what you are you would be something and someone else. You could not be that and be you too. An assumption is something simply posited without conclusive evidence or reason. If you are satisfied with assumptions, fine, I am not.

I have no idea why you are uncomfortable with this reasoning, but if you are, then just ignore what I've written, and believe what you wish, but understand I will do the same.
Axioms are only 'true' within the system that they define. If they don't define a system then they are no more than an opinion. An axiomatic system also needs to define the elements to which it applies.

If you want you can set up an axiomatic system with the 'laws' of logic as axioms. But then what does such a system produce? If it doesn't produce some useful theorems then the system can be labelled as 'useless'.

Mathematics is a good example of an axiomatic system. It produces useful and interesting theorems. However before it can be shown to be 'useful' there needs to be a mapping between one or more of its elements and the world of ides (or if you believe in naïve reality between the elements of mathematics and objects in the real world.) In this respect the mathematical elements of 'i' and '2' are equally abstract, it is just that '2' has a simpler mapping to the real world than 'i'. (That said 'i' is useful for both electronics and quantum mechanics).

To ignore this mapping process and claim that there is a direct and unambiguous link between elements of a logical system and the real world and that axioms such as the 'laws' of logic have a direct correspondence to the real world is naïve.

To claim that axioms are objectively true because there are no obvious counter examples is like claiming that 'all sheep are white' and then waiting for someone to find a black sheep.

If the 'law' of excluded middle was really logical it would not just be either A or not-A, but also incorporate the possibilities of both A and not-A and the possibility of neither A nor not-A.

An example for where such a 'law' does not apply in the real world is in the famous 2-slit experiment. It is less than useful to claim that the buckyball (a molecule of some 50 atoms or more) either passes or does not pass through slit A.

Skepdick
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Re: Justified true belief: knowledge and the myth of propositions

Post by Skepdick » Thu Jul 11, 2019 12:52 pm

surreptitious57 wrote:
Wed Jul 10, 2019 10:12 pm
One could say Earth goes around the Sun in an elliptical orbit is an empirical statement
It's not empirical to you. It's only conceptual to you.
surreptitious57 wrote:
Wed Jul 10, 2019 10:12 pm
Furthermore Earth has been orbiting the Sun for four and a half billion years so its actual trajectory can very easily be determined
Isn't that precisely what the ellipse represents. All of Earth's POSSIBLE positions around the Sun?
surreptitious57 wrote:
Wed Jul 10, 2019 10:12 pm
The equation may pertain to the general not the specific but the precise distance between Earth and the Sun can still be determined at any time
The probability distribution pertains to the general not to the specific, but the precise relation between an airplane and the ground can be determined at any time.

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RCSaunders
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Re: Justified true belief: knowledge and the myth of propositions

Post by RCSaunders » Thu Jul 11, 2019 3:20 pm

A_Seagull wrote:
Wed Jul 10, 2019 11:59 pm
Axioms are only 'true' within the system that they define. If they don't define a system then they are no more than an opinion. An axiomatic system also needs to define the elements to which it applies.
I have no idea why you want to continue discussing what we cannot agree on, because we are starting from completely different premises.

You believe an axiom is an assumption, because you believe what your teachers have taught you. If you did not you could not say something like, "Mathematics is a good example of an axiomatic system. It produces useful and interesting theorems. However before it can be shown to be 'useful' there needs to be a mapping ...." You may be unaware of it but mathematics, especially simple arithmetic, has been successfully understood and used for thousands of years without any notion of some axiomatic system.

As I said, you may be satisfied with, "assumptions," as axioms, I am not. I am only satisfied the observable evidence and the fact that any contradiction means there is a mistake in one's reasoning. If you choose to call assumptions axioms, that is fine, you are free to define the words you use in any way you choose. You may not insist that others accept or use your definitions.

Since "axiom" means "assumption" to you, I'll use another word for what I mean by axiom. I'll use the term absolute and limit it to "logical absolute" to distinguish it from other connotations of the word. An absolute, in the logical sense, means, "that which cannot be denied because its denial is self-contradictory." The word only pertains to the epistemological.
A_Seagull wrote:
Wed Jul 10, 2019 11:59 pm
To claim that axioms are objectively true because there are no obvious counter examples is like claiming that 'all sheep are white' and then waiting for someone to find a black sheep.
That is exactly what real a axiom (logical absolute) is not. Axioms do not pertain to the ontological (material existence), they only pertain to the epistemological (knowledge). They are not about what is known, but about the nature of knowledge itself, and only about that.
A_Seagull wrote:
Wed Jul 10, 2019 11:59 pm
If the 'law' of excluded middle was really logical it would not just be either A or not-A, but also incorporate the possibilities of both A and not-A and the possibility of neither A nor not-A.
The law of excluded middle only pertains to propositions, not physical entities or material existents. It simply means if the proposition, "the cat is in the closet," is true, the proposition, "the cat is not in the closet," must be false, because, the proposition, "the cat is not in the closet," means exactly the same thing as, "that the cat is in the closet is not true." The problem is the word, "true." It would be better to use the word, "valid," to mean if there were an actual cat and an actual closet, if either proposition was true, the other is false, in the same way we say 2 plus 3 equals 5 is true, but really only true if there really are 2 things and 3 things that can be added. 2 plus 3 equals 5 is valid, but only true if what they are 2 of and 3 of can be added together. 2 cups of water and 3 cups of alcohols equals less than 5 cups of liquid when added together.

You have confused the ontological and epistemological, or rather have been taught that confusion and accepted it by faith.

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A_Seagull
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Re: Justified true belief: knowledge and the myth of propositions

Post by A_Seagull » Thu Jul 11, 2019 10:21 pm

RCSaunders wrote:
Thu Jul 11, 2019 3:20 pm
You believe an axiom is an assumption, because you believe what your teachers have taught you.
You have confused the ontological and epistemological, or rather have been taught that confusion and accepted it by faith.
You are talking complete nonsense.. so forget it.

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