The relationship between formal logic and general philosophy is discussed under headings such as A Re-examination of Our Tense-Logical Postulates, Modal Logic in the Style of Frege, and Intentional Logic and Indeterminism.
In a pair of very important papers, namely “Space, Time and Individuals” in the Journal of Philosophy for October 1955 and “The Indestructibility and Immutability of Substances” in Philosophical Studies for April 1956, Professor N. L. Wilson began something which badly needed beginning, namely the construction of a logically rigorous “substance-language” in which we talk about enduring and changing individuals as we do in common speech, as opposed to the “space-time” language favoured by very many mathematical logicians, perhaps most notably (...) by Quine. This enterprise of Wilson's is one with which I could hardly sympathize more heartily than I do; and one wishes for this logically rigorous “substance-language” not only when one is reading Quine but also when one is reading many other people. How fantastic it is, for instance, that Kotarbinski1 should call his metaphysics “Reism” when the very last kind of entity it has room for is things —instead of them it just has the world-lines or life-histories of things; “fourdimensional worms”, as Wilson says. Wilson, moreover, has at least one point of superiority to another rebel against space-time talk, P. F. Strawson; namely he does seriously attempt to meet formalism with formalism—to show that logical rigour is not a monopoly of the other side. At another point, however, Strawson seems to me to see further than Wilson; he is aware that substance-talk cannot be carried on without tenses, whereas Wilson tries to do without them. Wilson, in short, has indeed brought us out of Egypt; but as yet has us still wandering about the Sinai Peninsula; the Promised Land is a little further on than he has taken us. (shrink)
WHAT do we mean by saying that a being, God for example, is omniscient? One way of answering this question is to translate ‘God is omniscient’ into some slightly more formalised language than colloquial English, e.g. one with variables of a number of different types, including variables replaceable by statements, and quantifiers binding thes.
We can best begin from Wilson's "simple little puzzle" about Caesar and Antony: "What would the world be like if Julius Caesar had all the properties of Mark Antony and Mark Antony had all the properties of Julius Caesar?" Wilson's own approach to an answer is indirect--he begins by telling us not what such a world would be like but what it would look like. "Clearly the world would look exactly the same under our supposition." But this assumes that the (...) question "What would such a world look like?" is a proper one; which it surely is not. For his answer to it is meaningless until he specifies to whom this supposed world would look as he says it would. It would look exactly the same to him or to me; but would it have looked the same to Caesar or to Antony? In fact Julius Caesar had the experiences of being called "Julius Caesar," being murdered on the Ides of March, and so on, and these are very different experiences from being called "Mark Antony," dallying on the Nile with Cleopatra, and so on; so I don't see how this alternative course of events could possibly have looked the same to Julius Caesar; or--using a similar line of argument--to Mark Antony. So I cannot agree that, as Wilson goes on to say, "our attempt to describe a distinct possible world has produced just the same old world all over again." I am not, indeed, convinced that even a world which looked to everyone just as the actual one does would necessarily be the same world ; but even putting this doubt aside, since the world mentioned wouldn't look to everyone as the actual world does, it wouldn't be the same even by Wilson's own standards. (shrink)
Sufficient texts show that for aristotle the universal notion expresses the same real thing as the particular, Though in a different way. His grounds for a universal so conceived are twofold. First, In every sensible thing there is a basic formal principle that, Though individual, Brings each instance into formal identity with all the other instances. Secondly, In human intellectual cognition there is an active principle that raises knowledge above the status of photographing or registering or cataloguing, And actualizes what (...) was only potential in the real thing. In knowing sensible things universally, The human intellect is able to grasp the concrete thing as characterized by a formal nature, Thereby knowing it in a way that holds equally for all other instances. Though patently incomplete, This conception of the universal is free from internal contradictions. It provides a framework for fruitful discussion, And remains a challenge. (shrink)
The general question to which Edwards here addresses himself is "whether any event whatsoever, and volition in particular, can come to pass without a cause of its existence," and among other arguments for a negative answer he has a reductio ad absurdum, arguing that if an act of will can occur without a cause, then anything at all, no matter how fantastic, can occur without a cause. There is, he says in effect, an inner contradiction in the notion that uncaused (...) events are bound always to be acts of will. We must note, however, in following his argument through, that his language is not quite that which I have just used, and in particular he does not speak primarily of what "occurs" but rather of what "begins to be." He says. (shrink)