A study in philosophical logic of the meaning of 'true'. Dr Williams demonstrates the shortcomings of various analyses which interpret 'true' as a predicate or truth as a relational property, and clears up a number of important points about propositions, quantification, definite descriptions and correspondence. This 'deflationary metaphysics' is interwoven with a positive theory of his own, which seeks to develop ideas about the late Arthur Prior. The work is marked throughout by great clarity, precision and thoroughness.

A study in philosophical logic of the meaning of 'true'. Dr Williams demonstrates the shortcomings of various analyses which interpret 'true' as a predicate or truth as a relational property, and clears up a number of important points about propositions, quantification, definite descriptions and correspondence. This 'deflationary metaphysics' is interwoven with a positive theory of his own, which seeks to develop ideas about the late Arthur Prior. The work is marked throughout by great clarity, precision and thoroughness.

The concept of identity has been seen to lead to paradox: we cannot truly and usefully say that a thing is the same either as itself or as something else. This book is a full examination of this paradox in philosophical logic, and of its implications for the philosophy of mathematics, the philosphy of mind, and relativism about identity. The author's account involves detailed discussion of the views of Wittgenstein, Russell, Frege, and Hintikka.

Christology seems to fall fairly clearly into two divisions. The first is concerned with the truth of the two propositions: ‘Christ is God’ and ‘Christ is a man’. The second is concerned with the mutual compatibility of these propositions. The first part of Christology tends to confine itself to what is sometimes called ‘positive theology’: that is to say, it is largely given over to examining the Jons revelationis —let us not prejudge currently burning issues by asking what this is—to (...) see what evidence can be found for the truth of these propositions. Clearly, the methods used will be above all those of New Testament exegesis. The second part of Christology will necessarily consist entirely of that speculative theology which is contrasted with positive theology. Even if the earliest speculation on this topic is to be found in the New Testament itself and thus becomes fair game for the exegetes, any attempt to relate the primary truths, ‘Christ is God’ and ‘Christ is a man’, to eachother is a work of reflection, and in the terminology I am using speculative. (shrink)

At Theaetetus 163d-164b Socrates objects to the thesis that knowledge is perception by pointing out that a man who has seen something can still remember it, and so has knowledge of it; but this is impossible, if knowledge is perception, since he is no longer perceiving it.To this Protagoras is made to reply with two sentences at 166b 1–4: .Cornford translates ‘ For instance, do you think you will find anyone to admit that one's present memory of a past impression (...) is an impression of the same character as one had during the original experience, which is now over? It is nothing of the sort’.Cornford understands this as the suggestion that the memory and the original perception are of different things: ‘ All that the objection in fact established was that “ perception” must be stretched to include awareness of memory images’. So too Lee: ‘Protagoras’ “way out”… appears to be to say that what we now know is not properly X but rather our memory trace of X - some present πά θ ο ς quite distinct from X and very different from that ’. McDowel. (shrink)

In a discussion-note in Mind, Father P. M. Farrell, O.P., gave an account, in what he admitted to be an embarrassingly brief compass, of the Thomist doctrine concerning evil. There is one sentence in this discussion which at first glance appears paradoxical. Father Farrell has been arguing that a universe containing ‘corruptible good’ as well as incorruptible is better than one containing ‘incorruptible good’ only. He continues: ‘If, however, they are to manifest this corruptible good, they must be corruptible and (...) they must sometimes corrupt.’ The final words, despite Father Farrell's italics, strike one as expressing, not a self-evident truth, but a non sequitur. The fact that I am capable of committing murder does not entail that I will at some time commit it. It is not immediately obvious that a similar entailment holds in the case of corruption and corruptibility. (shrink)

ἆρ' ∈ἰ kaì ⋯γ ∈´νητον … πρòς τò ɸθαρτόν, ⋯ϕ' ᾧΘ . Aristotle claims so far to have proved that the eternal is incorruptible and that it is ungenerated. He has still to prove the converse of each of these propositions, namely, that whatever is incorruptible is eternal and that whatever is ungenerated is eternal also. After putting the thesis in question form he gives a further definition of ⋯γ∈´νητος and ἄɸθαρτος in the parenthesis of 282 a 27–30. Unfortunately in (...) both cases he uses the assertoric form of the definiens , although in chapter 11 he had used a modal form in the relevant passages ; but this confusion does not seem to affect the immediate trend of the argument. He then shows that his thesis follows necessarily from the convertibility of ⋯γ∈´νητος and ἄɸθαρτος. The additional premiss that is necessary in order to secure this inference, namely, that that which is both ungenerated and incorruptible is eternal, is clear from the definition of the terms. It is also clear from the convertibility of ɸθαρτóς and γ∈ νητóς, which itself is entailed by the supposed convertibility of their contradictories. This last inference seems too trivial to deserve a mention, but Aristotle devotes 282 b 2–5 to proving it. Then, having demonstrated to his satisfaction that the convertibility of ἄɸθαρτος and ⋯γ∈´νητος necessarily implies the eternity of both the incorruptible and the ungenerated, he adds, for good measure, that if the terms are not convertible the implication is no longer necessary. (shrink)

At Theaetetus 163d-164b Socrates objects to the thesis that knowledge is perception by pointing out that a man who has seen something can still remember it, and so has knowledge of it; but this is impossible, if knowledge is perception, since he is no longer perceiving it.To this Protagoras is made to reply with two sentences at 166b 1–4:.Cornford translates ‘ For instance, do you think you will find anyone to admit that one's present memory of a past impression is (...) an impression of the same character as one had during the original experience, which is now over? It is nothing of the sort’.Cornford understands this as the suggestion that the memory and the original perception are of different things: ‘ All that the objection in fact established was that “ perception” must be stretched to include awareness of memory images’. So too Lee: ‘Protagoras’ “way out”… appears to be to say that what we now know is not properly X but rather our memory trace of X - some present πά θ ο ς quite distinct from X and very different from that ’. McDowel. (shrink)

Wittgenstein held that identity is expressible not by a sign of identity but by identity of sign. but belief contexts construed transparently show that repetition of a name is not sufficient to express identity. what is needed is a relational predicate like "=", but like quine's "ref" which converts a two-place into a one-place predicable. geach showed that "self" expresses an operation of this sort; so "same" and "self" turn out to express the same concept, as does "correspond" in explications (...) of the notion of truth. (shrink)

Kant asserts that we cannot represent to ourselves the non-existence of space. In his discussion of the Ontological Argument he maintains that there is nothing whose non-existence is inconceivable. He thus seems to contradict himself. If the non-existence of space is unthinkable, so is the non-existence of a part of space — a place. Indicating a particular place, we might say "There are no objects there", but it would be nonsense to say "There doesn't exist". We can say, as Aristotle (...) saw, "There is a place where there was water and where there is now air"; but to do so is to bind an adverbial variable with a quantifier, not to attach "exists" to the name of a place. To assert of a place, or of space, that it exists or that it does not exist would be nonsense, and the unthinkable in that sense is not something whose negation is, as Kant thought, a necessary truth. (shrink)