Logic

In an earlier post I outlined a Socratic approach, for which I would have to conduct a synthesis of all the different fields of philosophy, and, by extension, thought. The assumption is that written into each field is a certain emphasis such as to render them incompatible. This is not the place to defend such an assertion â€' though some amplification may be supplied to my earlier post at a later date. For now, all I want to do is move, by degrees, towards a clearer view of which fields make the most prescient claims to our attention.

The first field I tackle is logic. I will shear my writing of unnecessary incantations to mathematics. All I want to do is to divine its bottom-most assumptions. May God help me.

Though the ontological basis of logic is a vexed question, and though Kripke and Strawson (amongst others) would beg to differ, I will make Russell's Theory of Descriptions the paradigm. It was one which, at any rate, is shared by Quine and Wittgenstein: Russell simply took it to its logical conclusion. He held to a very straightforward account of how it is that names are meaningful â€' ie, he maintained that the meaning of a name is identical to the object to which it refers. For Russell, to know the meaning of a name is to be acquainted with the object to which the name refers. Added to this is the assumption that reality is composed of simple particulars. Analysis ends, Russell holds, when we arrive not at physical atoms but logical atoms (what Wittgenstein called elementary propositions). Names, then, are meaningful just as a result of referring to the simple particulars which are the ultimate constituents of reality. Predicates represent the qualities or properties of particulars and relational expression allow us to represent the relations between particulars. Thus, reality consists of facts: concatenations of simple particulars. Language consists of propositions, which attempt to describe facts. Propositions either fail or succeed in according with the facts â€' ie, propositions are bivalent (true or false). Furthermore, he argues, descriptions (which is his word for ordinary propsositions) cannot have meaning in virtue of picking out objects â€' simply because there need not actually be anything that factually corresponds to such a description. Therefore, it is always possible to deny the existence of something described quite meaningfully, and to thus avoid the problem of Plato's Beard (look it up): and he does so by making existence a property. This is a profoundly Aristotelian turn. It is his way of salvaging Frege's scheme. We can attribute a fictional thing real properties, but not existence â€' for then it is false. Take the proposition: “The present King of France is bald.” The sentence is certainly meaningful. The grammatical subject of the sentence certainly entails the existence of the thing described. But presently, there is no King of France. Therefore, the sentence is false. Hence, the “present King of France” cannot contribute to the meaning of the sentence as a logically proper name.

The contrast between names and descriptions is not to be taken lightly. His theory of descriptions is really designed to make thought and reality converge, as it were; and he does so by saying that ordinary sense-experience can be broken down irreducibly, that properties can be combined in any way so long as they correlate with something which exists. He needed to say this because it is unclear how it would be possible to have any account of meaning without knowledge of the simple particulars I spoke of earlier. And Russell, like Wittgenstein, freely admitted that he could not give any examples of atomic propositions. It was simply uncongenial to them to imagine that nothing lay beyond the discursive empirical realm. More to follow.

So when tackling logic in a discursive empirical realm, do you just completely dismiss the unobservable realms such as pure imaginative thought and dream imagery and how does this thinking fit in with new words that appear in language that in the past had no meaning or concepts such as time.