Nicholas Denyer

Imagine a child′s toy arrow, sticking by its rubber sucker to a mirror′s reflective surface. We can call the direction in which such an arrow would point the finwards direction ; and we can call the opposite direction boutwards . When we look at things in a mirror, their images are apparently just as far finwards of the mirror as the things themselves are boutwards of it. For example, if we look at the tail of our arrow and cast our glance finwards, we see first the tail, then the head, then the mirror, then the reflection of the head, and finally the reflection of the tail. We can therefore say that a mirror reverses things in the finwards/boutwards dimension. Moreover, the straight line connecting each thing to its image passes perpendicularly through the plane of the mirror. Hence there is no plane, apart from that of the mirror itself, such that the apparent location of each thing′s image is just as far to the one side of that plane as the original is to the other. This means that the reversal in the finwards/ boutwards dimension is the only reversal of its kind to take place. In particular, there is no such reversal in any dimension at right angles to finwards/boutwards

Philosophers have met with many problems in discussing the interconnected concepts being, identity, and truth, and have advanced many theories to deal with them. Professor Williams argues that most of these problems and theories result from an inadequate appreciation of the ways in which the words `be', `same', and `true' work. By means of linguistic analysis he shows that being and truth are not properties, and identity is not a relation. He is thus able to demystify a number of metaphysical issues concerning the meaning of the word `I', the relation between the mental and the physical, objects of thought, times and places, and the nature of reality. Williams presents his views clearly, with a minimum of technicality, and with rich and apt examples, so that they will be accessible to readers not versed in symbolic logic.

The Protagoras is one of Plato's most entertaining dialogues. It represents Socrates at a gathering of the most celebrated and highest-earning intellectuals of the day, among them the sophist Protagoras. In flamboyant displays of both rhetoric and dialectic, Socrates and Protagoras try to out-argue one another. Their arguments range widely, from political theory to literary criticism, from education to the nature of cowardice; but in view throughout this literary and philosophical masterpiece are the questions of what part knowledge plays in a successful life, and how we may acquire the knowledge that makes for success. This edition contains the first commentary in English on the Greek text for almost a hundred years. The commentary provides the assistance with linguistic, literary and philosophical detail that will enable students and scholars to savour to the full the pleasures of the Protagoras.

Metaphysicians often declare that there are large ontological differences (properties versus individuals, universals versus particulars) correlated with the linguistic distinction between names and verbs. Gaskin argues against all such declarations on the grounds that we may quantify with equal ease over the referents of both types of expression. However, his argument must be wrong, given the massive differences between first- and second-order qualification. Its only grain of truth is that these differences show up only in the logic of relations, and not also in monadic logic.

There are enormous differences between quantifying name-variables only, quantifying verb-variables only, and quantifying both. These differences are found only in the logic of polyadic predication; and this presumably is why Richard Gaskin thinks that they distinguish names from transitive verbs only, and not from verbs generally. But that thought is mistaken: these differences also distinguish names from intransitive verbs. They thus vindicate the common idea that on the difference between names and verbs we may base grandiose metaphysical distinctions, and undermine Gaskin's idea that both names and verbs may be said to designate objects.

Diodorus' Master Argument was intended to show that whatever is possible either is or will be true. The intended conclusion does not follow from the extant premisses of the Master Argument. The Near Miss argues however, from those premisses alone, that nothing can be more than momentarily an exception to the Master Argument's intended conclusion. Strong arguments support even the most contentious of those premisses . We therefore cannot easily ignore the Near Miss. Moreover, there are various supplementary premisses that would turn the Near Miss into an argument with the full force of the Master Argument itself. Each of Diodorus' ancient rivals, since they accepted such doctrines as eternal recurrence, temporal atomism, and the "extended" present, would grant him at least one of these supplementary premisses. So too would any modern who holds that time is not circular, has no beginning, and does not branch

The innocent are immune. We must never, that is, make the object of any violent attack those who bear no responsibility for doing wrong to others; and only with grave reason and in extreme circumstances should we be prepared to cause them any incidental harm as we press home a violent attack against those who are its legitimate objects. This principle of the immunity of the innocent seems almost self-evidently true. This is not to say that the principle is incapable of further development and articulation, unsusceptible of marginal qualification, or underivable from deeper principles. It does however mean that any moral theory which denies this principle altogether will be something that only a fool or a knave could accept.

The definition here ascribed to Philo is entirely in line with what we know of Philo from else where: Alex. Aphr. in APr. 184.6–10; Simp, in Cat. 195.33–196.5; Boethius, in de Int. 234.10–15. The same is not true of the definition here ascribed to Diodorus. For Diodorus, we are told elsewhere, defined the possible as that which either is or will be so: Cic. Fat. 13, 17; Plu. de Stoic rep. 1055d-e; Alex. Aphr. in APr. 183.42–184.5; Boethius, in de Int. 234.22–4,412.16–7. Something has therefore got garbled