allzermalmer

Truth suffers from too much analysis

Posts Tagged ‘Socrates’

Gnostic and Agnostic Breakdown

Posted by allzermalmer on August 2, 2013

The main interest is of Agnosticism, and this by default can have some implication with Atheism and Theism.

It will be supposed that Agnosticism is about lack of knowledge or not knowing. Gnosticism will be about having knowledge or knowing. It will be supposed that to have knowledge of a claim, then that claim is Justified, True, and it is Believed.

(Gnostic) K=JTB
(Agnostic) ~K= (A1) NJTB v (A2) JNTB v (A3) JTNB v (A4) NJNTNB

There are four ways to agnosticism, but there is only one way to gnosticism.

(A1) Claim isn’t Justified & Claim is True & Claim is Believed.
(A2) Claim is Justified & Claim isn’t True & Claim is Believed.
(A3) Claim is Justified & Claim is True & Claim isn’t Believed.
(A4) Claim isn’t Justified & Claim isn’t True & Claim isn’t Believed.

(Gnostic Socrates) If Socratesl knows the claim p, then Socrates claim is Justified, True, and Believed by the Socrates.

(Agnostic Socrates) If Socrates doesn’t know the claim p, then…
(A1) Socrates claim isn’t Justified, but Socrates believes the claim and it’s True.
(A2) Socrates claim isn’t True, but Socrates claim is Justified and Believed.
(A3) Socrates claim isn’t Believed, but Socrates claim is Justified and it’s True.
(A4) Socrates claim isn’t Justified, isn’t Believed, and isn’t True.

Suppose that p is “there exists a deity”. So ~p stands for “there doesn’t exist a deity”.

(i)Kp= Socrates knows there exists a deity.
(ii) K~p= Socrates knows that there doesn’t exist a deity.

(iii) ~Kp= Socrates doesn’t know that there exists a deity.
(iv) ~K~p= Socrates doesn’t know that there doesn’t exist a deity.

Assume Socrates doesn’t know that the earth is flat. This is because Socrates knows that the earth isn’t flat. Socrates knowing that the earth isn’t flat implies that it is true that the earth isn’t flat. Socrates can’t know false things (but can believe false things), so Socrates doesn’t know that the earth is flat, especially because Socrates knows that the earth isn’t flat.

So it becomes obvious that:

(i) Kp doesn’t forbid ~K~p:: Socrates knows that there exists a deity doesn’t forbid Socrates doesn’t know there doesn’t exist a deity.

(ii) K~p doesn’t forbid ~Kp:: Socrates knows that there doesn’t exist a deity doesn’t forbid Socrates doesn’t know that there exists a deity.

(iii) ~Kp doesn’t forbid (ii) K~p :: Socrates doesn’t know there exists a deity doesn’t forbid Socrates knows there doesn’t exist a deity.

(iv) ~K~p doesn’t forbid (i) Kp :: Socrates doesn’t know there doesn’t exist a deity doesn’t forbid Socrates knows there does exist a deity.

(iii) or (iv) doesn’t imply that Gnostic, but can be Gnostic. (A1)-(A4) show some reasons on why (iii) and (iv) don’t necessarily imply, but don’t forbid, being Gnostic.

When it comes specifically to “there exists a deity”, it would mean that in order to be Agnostic on that claim, Socrates would have to take part of (iii) and (iv).

In order to be Agnostic, then Socrates doesn’t know there exists a deity and Socrates doesn’t know there doesn’t exist a deity.

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Lack of Knowledge implies Knowledge

Posted by allzermalmer on July 28, 2013

Socrates was once opined to have said that all he knows is that he doesn’t know anything, or I know that I don’t know.

There is a formal system known as epistemic logic. It deals with an epistemic operator, K. One of the epistemic logic is known as negative knowledge, in some sense.

Negative Knowledge: ~Kp –> K~Kp or CNKpKNKp

If I don’t know p then I know that I don’t know P. Not knowing p implies knowing that don’t know p.

If I don’t know what it looks like down at the center of the Earth (or Sun), then I know that I don’t know what it looks like down at the center of the Earth (or Sun).

Furthermore, from this Axiom, we may easily show that not knowing something implies knowing something.

All we need is our axiom of negative knowledge, CNKpKNKp, and the law of contraposition. This law, basically, states that we switch the antecedent (i.e. NKp) with the consequent (i.e. KNKp), and we negate both of those propositions when we switch their places.

By the law of contraposition and negative knowledge, we obtain CNKNKpNNKp.
Now we use the law of double negation to the consequent (i.e. NNKp), and we obtain CNKNKpKp.

We obtain that if we don’t know that we don’t something then we know something.

 

 

 

 

 

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Meno’s Paradox

Posted by allzermalmer on April 11, 2013

Meno: But how will you look for something when you don’t in the least know what it is? How on earth are you going to set up something you don’t know as the object of your search? To put it another way, even if you come right up against it, how will you know that what you have found is the thing you didn’t know?

Socrates: I understand what you mean, Meno. Do you see that an eristic argument you’re introducing, that it isn’t possible for one to inquire either into what one knows, or into what one doesn’t know? For one wouldn’t inquire into what one knows- for one knows it, and there’s no need to inquire into such a thing; nor into what one doesn’t know- for one doesn’t know what one is inquiring into.

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