Why logic works

[aleph_0]

Kleene is an example of this syntactic view of logic. Now, I defy you to give me one example of a formal logician who claims that logical symbolism has a necessary connection with human consciousness or that formal deductions have a "metaphysically necessary" character.

I don't know about the latter at all, but I think the former might depend on whom you consider a logician. Alasdair MacIntyre probably thinks that's true, and he probably knows formal logic, though I doubt anybody would call him a formal logician. I would gamble (small) money that Stalnaker or maybe early Kit Fine held that view, and there's no doubt Kit is a formal logician. I only say that because they both accepted supervaluationism, which is largely a logical “fix” for ambiguity and indeterminacy, but it’s a shot. (In fact, on that note, since Stalnaker used supervaluationism to logically account for physical indeterminism, maybe he even counts for one of the "metaphysically necessary" guys! If you interpret his claim [perhaps uncharitably] as a kind of Kripkean discovery of a metaphysically necessary a posteriori truth about indeterminacy, he would fit the bill.)

[Edit: Just tacked on the last end-parenthesis.]

Edited February 3, 2009 by aleph_0

[DavidOdden]

Aleph_0, I don't understand what you think the ontological status of the law of non-contradiction is, and while we're at it I'll ask you what you think the status of the laws of conservation of charge and conservation of angular momentum is. The Objectivist position would be that they are recognitions of specific facts of existence. Do you accept that position as well?

[aleph_0]

I don't know what the laws of conservation of charge and angular momentum are. I gather from a quick look on Wikipedia that they're laws of physics, and it seems right to me to say that they're facts of existence.

[DavidOdden]

I don't know what the laws of conservation of charge and angular momentum are. I gather from a quick look on Wikipedia that they're laws of physics, and it seems right to me to say that they're facts of existence.

Assuming you're of the same opinion about logical laws, then I think a lot of the problem you're having in grasping the Objectivist position is that you aren't distinguishing fact from knowledge of fact. I threw in the physics laws since there I think the difference between "facts of reality" and "knowledge of facts of reality" is more obvious. Man must discover the "laws of logic", which he does because he can perceive reality and form concepts. The main difference between the law of non-contradiction and conservation of angular momentum is that the later might, hypothetically, actually not be a true grasp of the facts of reality.

[aleph_0]

I'm not sure about the logical laws. I've been a ponderin on it. But I do understand the Objectivist position. Thank you for the explanation, though.

[Marc K.]

[...] then there is always the chance that he just hasn't seen the right things and that one day he may stumble upon a thing which is not itself. We rule this out as nonsense because it is de jur and not just de facto that we cannot even conceive of observation without identity.

Try to imagine it. You can't. You have not only negated all of the rules of logic, you have negated the existence of the Universe. I am not exaggerating. You need to think really hard on this one.

If everything doesn't have identity, then nothing has identity. You might say: "no, no, not everything, just this one thing that doesn't have identity" and I would retort: "which thing, you mean this particular thing over here."

Every time you tried to point to something that didn't have identity, there it would be. You couldn't point to anything in particular that wasn't something in particular.

So maybe you really do mean that nothing has identity but we know that is not true just by looking around and the fact that we have knowledge and are able to have this conversation.

I know you don't accept the validity of axiomatic concepts but notice what happens when you don't. You end up smashing your head into a brick wall. I urge you to rethink your position and read chapter one of OPAR. The widest abstractions we can make are the ones which apply to every existent in the Universe.

Everything that exists, exists as something specific.

[aleph_0]

You're actually arguing for the very point I was making. When I said, "If the Law were a posteriori, then there is always the chance that he just hasn't seen the right things and that one day he may stumble upon a thing which is not itself." When I gave the hypothesis, "If the Law were a posteriori, that was assuming your premise. The quote means, in essence, if the Law were a thing we learned then there is some state before which we had not yet learned the Law--and at this time, we might have imagined that the Law were false. But we can't imagine that, just as you pointed out! So you agree with me.

And I never said I reject the concept of axiomatic truths. You should treat yourself to reading what I wrote, instead of speaking with the assumption that you're right and the only reason you have for speaking to me is to inform me about how I'm wrong, rather than engaging in a conversation. I do not accept, from the beginning, that you are right and I am wrong--so when you say, "You really need to think hard on this one," [implicitly assuming that I have not and this is the reason for assuming that I have made an error,] it means nothing to me.

[Thomas M. Miovas Jr.]

The quote means, in essence, if the Law were a thing we learned then there is some state before which we had not yet learned the Law--and at this time, we might have imagined that the Law were false. But we can't imagine that, just as you pointed out! So you agree with me.

I don't like to use Kantian terminology because so much baggage comes with it, but there are no a priori laws; there are no laws that existed before man made observations and integrated those observations into laws.

And there was a time when man did not have knowledge on the level of the laws of nature and of logic and he came to all sorts of irrational conclusions that flew in the face of reality. Look at how man falsely concluded that there were gods controlling the universe, and they did this because they did not grasp that A is A. In the Dark Ages that knowledge of logic was lost and look at how man lived -- in complete terror that God made things what they are, but could change everything at any moment with a thought. This was a primacy of consciousness approach to existence.

Similarly, if you think the laws of logic are a priori and make things you perceive what they are, then you are having a primacy of consciousness approach -- you are stating that your consciousness makes things what they are, when, in fact, they are what they are and you see that with observations.

Again, it is not the law of identity that makes it possible for you to see THIS. You see it because it exists; it does not exist because you conceive it or because you have the law of identity in your head prior to observation.

[DavidOdden]

When I said, "If the Law were a posteriori, then there is always the chance that he just hasn't seen the right things and that one day he may stumble upon a thing which is not itself."

That's related to the Popperian falsifiability error. There is no chance of a truth being false.There's your problem.

[aleph_0]

That's related to the Popperian falsifiability error. There is no chance of a truth being false.There's your problem.

Leaving that for another day, I was referring to epistemic possibility which an Objectivist must certainly accept if he is to deny omniscience.

[Flagg]

I haven't the time to review all posts; sorry if I am repeating anything here.

Just start with the metaphysical beginning point: sense perception - not the logically precedent points, i.e. that existence exists, or even that something's independent of the mind, or even that you're conscious. Heck, I'll just assume that the sense perceptions are indivisible, like a monist.

This is a really loose definition:

Sense perceptions =def. "The big arse glob, intuitively, of what's going on with you right now"

exist =def. to posses identity, i.e. a nonempty set of quality.

axiom =def. that which must be used to deny in any proof of the contrary. Remember, we're not question-begging when assuming the laws of logic to prove the axiomatic foundation of the laws of logic. Two different things there.

A1. Sense perceptions exist.

Proof of Axiomatic Nature: Suppose X is a proof that your sense perception isn't so. But you at least perceive the proof. QED.

Let's just assume that the evidence of your senses is where you start, and it is irreducible. Simple enough, eh?

From this it follows that, for at least one element of "reality" (even a silly solipsistic reality) that A is A. Your sense perception is itself. I.e. we have, for all (i.e. the only assumed) reality-constituent p,

p^T=T

or

pvF=T

That's a connection with the Law of Identity. Similarly Non-Contradiction and Excluded Middle follow as axioms; the connections are similar, as well. The other three Laws of Logic, distributivity, associativity, and commutativity, can be grasped partially with one metaphysical existent p here, but until the axiom of other particulars is established, their particular reach isn't yet grasped.

Considering that separate identities exist within sense perception, and that something exists outside of sense perception (your identifying tool), and that your sense perception delivers an external reality, are also axiomatic, with reality being the precedent King of these axioms. But whatever; the set of existents is nonempty (it has our "p") and one may ask, "well, have you checked in all corners of existence that these things are true?" One doesn't have to do that.

Excluded Middle: p v not(p) = T

De Morgan's on this property yields

not (p v not(p)) = not(T)= not (p) and not (p) = F (by Idempotence)

yielding

not(T) = F

independent of consideration of any particular, meaning it holds for all particulars in the context of direct consideration of correspondence to reality.

These puppies hold everywhere in metaphysics.

Also, as a side note, since time presupposes causation (i.e. specifically motion) which is the Law of Identity in action, then asking "Will the laws of logic metaphysically apply in the future?" means to ask "Will the laws of logic apply to situations where the laws of logic apply?" So much for the "problem" of induction.

[Hodges'sPodges]

I cannot understand the meaning of "∃x(Px & ~Px)". Many claim, and I am somewhat sympathetic, that this is just ungrammatical (even though a well-formed formula).

'well formed' and 'grammatical' are synonyms in this context. Though, if you disagree, then it's hardly worth debating, as instead I would prefer just to be cautious around you that you don't always use terminology as in accord with ordinary usage in the study of the subject of formal logic.

As to Frege, you offered that Frege is an example of someone holding the view mentioned (and opposed) by Odden, "propositions aren't statements about reality, and truth has nothing to do with a consciousness or reality, it is purely a syntactic symbol-transformation method."

The claim that Frege holds such a view is ludicrous. Here are the very first words out of Frege's mouth in his very first work on the subject of logic (his 'Begriffsschrift'):

"In apprehending a scientific truth we pass, as a rule, through various degrees of certitude. Perhaps first conjectured on the basis of an insufficient number of particulars, a general proposition comes to be more and more securely established by being connected with other truths through chains of inferences [...]".

"Accordingly, we divide all truths that require justification into two kinds, those for which the proof can be carried out purely by means of logic and those for which it must be surpported by facts of experience. But that a proprosition is of the first kind is surely compatible with the fact that it could nevertheless not have come to consciousness in a human mind without any activity of the senses."

There Frege mentions truth including specifically those "SUPPORTED BY FACTS OF EXPERIENCE". And also, even that the other kind of truths - those that are proven purely by logic - CANNOT COME TO CONSCIOUSNESS WITHOUT THE SENSES. So, in just one passage from the very first paragraph of Frege's first paper in logic, Frege states that facts of experience, consciousness, and the senses are integral to truth. It is plainly incorrect to say that of Frege that he held "propositions aren't statements about reality, and truth has nothing to do with a consciousness or reality, it is purely a syntactic symbol-transformation method".

Edited May 28, 2009 by Hodges'sPodges

[Hodges'sPodges]

Kleene is an example of this syntactic view of logic.

Whatever you mean by "syntactic view of logic", I would appreciate knowing what specific passages in the writings of Kleene you take as expressing "propositions aren't statements about reality, and truth has nothing to do with a consciousness or reality, it is purely a syntactic symbol-transformation method."

Now, I defy you to give me one example of a formal logician who claims that logical symbolism has a necessary connection with human consciousness or that formal deductions have a "metaphysically necessary" character.

Yours is a hollow challenge since I didn't claim that any logician has or would put his views in such a rubric as "necessary connection with" or "metaphyisically necessary". Please, let's stick with what various logicians have actually written, and please for you to show that (not even just one logician, as even Kleene fails as a single example) but that logicians in general hold a view that "propositions aren't statements about reality, and truth has nothing to do with a consciousness or reality, it is purely a syntactic symbol-transformation method". That is, your claim that includes logicians in general hold that (1) truth and consciousness have NOTHING TO DO WITH consciousness or reality and that (2) truth is a METHOD, specifically a symbol-transformation method. Edited May 28, 2009 by Hodges'sPodges