Logics are formal systems, what is it that you think needs to be accounted for?

since logical absolutes are always true everywhere, and not dependent upon human minds, they must be an abstract nonmaterial object.

I dont see any reason to accept this.

if you see no reason to accept that logical absolutes are always true everywhere then have you really been far even as decided to use even go want to do look more like?

Kant was a nominalist; although his philosophy would have been rendered compacter, more consistent, and stronger if its author had taken up realism, as he certainly would have done if he had read Scotus.
--- C.S. Peirce

I dont see any reason to accept this. How do you explain the completeness of different logics?

I don't know, but they all have laws/principals. So if any of them is true you need some abstract absolute, and if all of them are wrong you have to use the very laws of logic in question to disprove them!

Are there any logics that deny the law of contradiction? So that A and Not A can be the same?

Are there any logics that deny the law of contradiction? So that A and Not A can be the same?

How do nominalists account for the laws of logic?

I'm no expert, but it seems to me the laws of logic are universal; and they are certainly not material.
So if you don't believe in abstract objects how do you account for them?

It seems Kant would help us here but don't know Kant well enough to speak with any authority. The antynomies arose when reason was attempted beyond the phenomenal realm.

The term antynomy acquired a special significance in the philosophy of Immanuel Kant (1724-1804), who used it to describe the equally rational but contradictory results of applying to the universe of pure thought the categories or criteria of reason proper to the universe of sensible perception or experience (phenomena). [from wiki]

So something is going on here regarding the limits of logic. I think Kant is called a nominalist in most circles.


Peirce - Philosophy: Nominalism

For Kant the laws of logic were phenomenal. That is how he accounted for them.

Anyway, I thought the 'phenomenal world' was based on human minds, which again, Logical Absolutes are not the product of human minds, because human minds are different, not absolute.

I'm not too good with abstractions - ughaibu or Deckard - can you give me an example of this logic that does not use the law of contradiction?
I mean, how can you know a statement is true if it can't be false or contradicted !?

Thanks for the replies!

How do nominalists account for the laws of logic?

[CENTER] I'm no expert, but it seems to me the laws of logic are universal; and they are certainly not material.
So if you don't believe in abstract objects how do you account for them?

I'm not too good with abstractions - ughaibu or Deckard - can you give me an example of this logic that does not use the law of contradiction?
I mean, how can you know a statement is true if it can't be false or contradicted !?

smany paraconsistent logics validate the Law of Non-Contradiciton

So it still seems that the law of non-contradiction is still an absolute.

Well, thank you very much everybody.

Pretty much what I got out of Paraconsistency is that just because a statement is contradictory does not mean it is false, per se

Any who, the article still say

So it still seems that the law of non-contradiction is still an absolute.

As far as Hegel....ack! He makes me dizzy!

I mean, what the hell is the antithesis of a cow?!

But, to use a real argument. If a guy says "listen, the bible is false because it contradicts itself and the law of contradiction is universal and absolute"

Would a nominalist then say "Maybe the bible IS false, but not for that reason because laws of logic can't be absolute, they depend on human minds which change, so maybe back then the prophets' laws of logic were such that statements could contradict each other and still be true"

In other words, I would say the statement "2+2=4 AND 2+2 does NOT=4" to be a false statement because it contradicts it self AND it always has and always will contradict itself because the law of non-contradiction is absolute and universal.

But a nominalist would say no, using Hegals laws of logic that statement CAN be true, so the law of non-contradiction isn't absolute.

The point I'm getting at is that IF the law of non-contradiction is absolute and universal then it CAN'T be material and hence nominalism CAN'T be true; I'm wondering how a nominalist would answer this - yr saying they would point to Hegel's laws of logic right?

Am I making any sense? :perplexed:

Then what do you suppose a true contradiction to be? Paraconsistent Logic (Stanford Encyclopedia of Philosophy)
You might also consider constructive mathematics, in which the law of excluded middle doesn't apply.

Please allow me to think out loud about this matter.

I don't know enough to say but I think maybe we take a step back rather than using particular examples. The primary Thesis Antithesis Synthesis is Being, Nothing and Becoming.

Rather than look to particulars we could say that the thesis is the law of contradiction is universal and absolute and the antithesis is that this law does not hold in all cases. Hegel's logic proceeds through the negation of the negation but since Hegel's system is dynamic and evolutionary this negation of the negation does not return to the original thesis. There is some B that is neither A nor not A that sort of grows out of the conflict between A and not A and comes closer to reality than both. Some paradigm shift perhaps that causes one to see both A and not A in a new light. Not right nor left but up or something of that sort. A new dimension is added. In the primary case A = Being which brings with it not A = non-being or nothing...at which point the new dimension is added namely, time in this case and we have B = becoming. Ever expanding and revealing more dimensions of thought.

I am completely out of my depth here but I also want to mention Descartes cogito as a possible starting point of Being. I think therefor I am. There are things that I am not. There are things which I am becoming. It is important to consider the starting point. Can we really begin by stating an abstract law such as A and not A cannot both be true. If we remember Descartes method which arguably kicked off modern philosophy such a law could be proposed by some demon but Descartes meditations strip all of this away and the primary existing A is the I the thinking I ever grounded in subjective experience. The attempt to cut the assertion of A completely away from this subjective experience is to not start at the beginning. And I think Hegel, Kant even Hume and Locke all begin from Descartes cogito as the first true assertion, the first A... "I am" and so "I am not" and so "I am becoming".

There is no Platonic realm of real things to resort to and that is what makes Hegel and Kant nominalists. The real beginning is inside, subjective not outside and objective.

There is something after Becoming...It might be passing away...or memory... I have to look it up in a book somewhere...It's surprisingly hard to find online...but I think there is a specific order through several movements through which the primary Being of Consciousness (which I have equated with Descartes cogito) passes through...as dimensions are added to consciousness. It seems to proceed through an adding of axises. We have the X axis establishes the spectrum from Being to Non-Being then add the Y axis which establsishes Becoming and Passing Away and then a Z axis and so on ad infitum.

But in conclusion I believe it is of primary importance to recognize from what point a given philosopher begins to philosophize that is begins to Reason. For Kant, Hegel and the German nominalist idealist I believe the point is Descartes cogito...the one sure thing.

Others begin with the one sure thing of A and not A cannot both be true.

Descartes even dismissed mathematical truths as uncertain and possibly the work of the evil deceiving demon. So I think for Descartes the statement A and not A cannot both be true is equally dismissible.

SO, if Decarte is saying the Law of noncontradiction is "dismissible" then one can never say whether a statement is true or false.

For example the statement " A and not A cannot both be true is equally dismissible." can never be proven true or false, therefore we cannot believe it to be true.

In other words, yr whole paragraph can never be true. No statement can, including "no statement can ever be true"

So nothing anyone says can be intelligible.

So the statement "Nominalism is true" can never be true...

Does anyone know of any person who has tried to live without the law of noncontradiction?

I remember an old logic teacher once say "everytime you choose to walk through a door instead of a wall, you are affirming the law of non-contradiction" :bigsmile: