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Friday, October 07, 2016

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Who is that handsome devil?

“Are the laws of logic laws of thought? Yes, of course. What else would they be?” Lukasiewicz: ‘It is not true … that logic is the science of the laws of thought. It is not the object of logic to investigate how we are thinking or how we ought to think’.

“Kant, Husserl, and Frege all rejected psychologism in logic.” Kant, Logic §22 ‘As to quality, judgments (Urteile) are either affirmative (bejahende), negative (verneinende) or infinite (unendliche). In the affirmative judgment, the subject is thought (gedacht) under the sphere (Sphäre) of the predicate’.

Before Russell, traditional logic spoke of ‘judgments’, whereas modern logic talks about propositions or more likely sentences (propositions are creatures of darkness for some). Kant speaks of the subject being ‘thought’ under the sphere of the predicate. Seems like psychologism to me.

Aristotle’s On Interpretation, by contrast, talks about psychology being ‘an investigation distinct from that which lies before us’. He speaks rather of linguistic items like 'noun' and 'verb', 'denial' 'affirmation', 'proposition' and 'sentence.' A sentence is a noun plus a verb. A proposition is a special type of sentence capable of truth or falsity. An affirmation (κατάφασισ) is a declaration (ἀπόφανσις) of something of something, negation (ἀπόφασις) is a declaration of something ‘from’ (ἀπὸ) something. No psychology or thought there.

It is from ἀπόφασις that we get ‘apophatic’ theology, no?

He is indeed a handsome devil, and he has a beautiful daughter.

We discussed Lukasiewicz two and a half years ago: http://maverickphilosopher.typepad.com/maverick_philosopher/2014/04/lukasiewicz-on-logical-form.html

Kant rejects psychologism in the section *Begriff der Logik* in the Intro to his Logic.

I argue that the laws of logic cannot be empirical generalizations here: http://maverickphilosopher.typepad.com/maverick_philosopher/2012/06/are-the-laws-of-logic-empirical-generalizations.html

But you didn't engage the main point. Whatever logic exactly is, it is different from DF.

>>But you didn't engage the main point. Whatever logic exactly is, it is different from DF.

Too difficult for now.

Still struggling with what you actually mean.

1. Is your point is about quantification? Are you claiming that when we assert (p) [p or not-p], the range of the quantifier ‘lasso’ can reach outside the DF into another world where ordinary truths about propositions do not apply? The problem is that I don’t see how to distinguish it from the claim that LEM does not apply to all propositions. What is all this stuff about ‘discursive framework’ meant to be about?

2. Or is it that anything we express using quantifiers e.g. ‘(p) [p or not-p]’ is by its very nature within the DF. So it is true that the LEM always applies, but the statement ‘the LEM always applies’ is by its very nature within the DF? This is very Wittgensteinian. There are as it were certain truths which we cannot express because their expression would require using a framework which does not allow us to express them.

So the problem is that you are trapped between expressing something which is false, and expressing something that you can’t express at all.

I am surprised that you are not getting it at all. I have another post in the works that may help.

Hello Bill,
It’s often said that the physics of the very small cannot be accommodated within the terms of the DF---one runs up against violations of LEM. Yet we do have some mathematics which gives us a grasp of such physics. Now I imagine that we would want to include the whole of mathematics inside the DF. If so, we would seem to have a paradox. On the other hand, what would it mean for our understanding of the reach of the DF if we were to exclude (the relevant) mathematics? This strikes me as a genuine puzzle and I wonder what your take on it is.

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