Cross posted at my Fr33Agents blog and Mercenary Scribblings
http://fr33agents.ning.com/profiles/blogs/noncontradiction-logic-and
http://liberalvichy.blogspot.com/2010/04/non-contradiction-logic-and-ontology.html
The ontological law of non-contradiction (a thing is either the case or it is not the case) and identity (a thing is itself) must necessarily hold because if these were not metaphysically true nothing would be the case or not the case. If the ontological LNC were not true, the logical law of non-contradiction (p -p) would not be possible. Not that this is not circular: it is simply the case that if the OLNC were not the case, the LLNC could not exist.

Here I quote Wittgenstein:

Quote:

The steps which are not brought into question are logical inferences. But the reason why they are not brought into question is not that they ‘certainly correspond to the truth’ – or something of the sort, – no, it is just this that is called ‘thinking’, ‘speaking’, ‘inferring’, ‘arguing’. (RFM I. 156.)

and further he says:

Quote:

“Then according to you everybody could continue the series as he likes; and so infer anyhow!” In that case we shan’t call it “continuing the series” and also presumably not “inference.” And thinking and inferring (like counting) is of course bounded for us, not by an arbitrary definition, but by natural limits corresponding to the body of what can be called the role of thinking and inferring in our life. [T]he laws of inference do not compel him to say or write such and such like rails compelling a locomotive. And if you say that, while he may indeed say it, still he can’t think it, then I am only saying that that means, not: try as he may he can’t think it, but: it is for us an essential part of ‘thinking’ that – in talking, writing, etc. – he makes this sort of transition. (RFM I. 116.)

Those who argue that logic is 'intuitive' or 'circular' completely miss the substance of this point (and substance may be literal here, since it is an ontological argument). There is no knowledge outside of reason and no reality outside of non-contradictory properties. Attempts to deny this in, for example, analytic logic, simply fail because without the OLNC their arguments fail to exist, and since the contrary of the OLNC also invalidates the LLNC, their arguments are in fact not arguments. One can not dispute that we can have certain knowledge of ultimate reality such as the OLNC, because anything that failed to meet the OLNC would not be reality.

See also Non-Contradiction as an Ontological Principle: An Interpretation of Aristotle’s Metaphysics IV.3-4 by Matthew Meyer
http://www.princeton.edu/%7Eclassics/conferences/2008/ancientphil/documents/MeyerNon-Contradiction_000.pdf

read this book from a former prof of mine