Nicholas Denyer

Sun and Line: The Role of the Good

“I understand that less than I understand the Good of Plato,” says a slave in comedy. The slaves understanding of the Good would not have been much helped by attending Platos own public lecture on the subject: the majority of the audience “came in the expectation of acquiring some of those things that conventionally count as human goods, such as health, wealth, strength, and in general some wonderful happiness; but when the discussion turned out to be on the mathematical sciences - numbers, geometry, astronomy - and the conclusion to be that good is one, this struck them as utterly paradoxical; whereupon some came to despise the business, and others started to make complaints.” Nevertheless, in one respect at least, it is actually quite easy to grasp what Plato has to say about the Good. If for the moment we confine our attention to Forms of artifacts, it is easy to understand and accept the Republic s claim that the Good has the privileged position of being what accounts for the existence and intelligibility of Forms, much as the Sun has the privileged position of being what accounts for the growth and visibility of plants (508b-e, 509b). For the claim will then be that everything about an ideal artifact is teleologically explicable. The ideal wheel is circular, and it has its axle in its center. These things are so because that is the best way for a wheel to be: a buckled wheel, or for that matter a circular wheel with its axle off-center, would give a bumpy ride. And the Good accounts in this way for every aspect of the ideal wheel: if, for example, we ask about the color of the ideal wheel, then the only answer is that it has no particular color; and that is because there is no one color that is the best one for a wheel to have.

Catholic and Apostolic

Whatever else Christianity may be, the agapeistic way of life, a personal relationship with Jesus, or whatever, it is also a matter of holding certain things to be true. Of recent times that has been denied by some whose job it is to think about these things. For there are theologians who, though apparently convinced by logical positivism that the traditional formulations of Christian belief do not express truths, wish nevertheless to retain the name of Christian. Positivism however in any case never had much more than fashion to recommend it; and it was already ceasing to be fashionable among philosophers as it started to be fashionable among theologians. To conjoin furthermore an acceptance of positivism with a wish to be called Christian strikes me at least as mere perversity.

Is Anything Absolutely Wrong

Like anything else, human actions can be described in many ways. For example, this morning I put some meat out on a dish, and served the cat’s breakfast; and as it happens, both these descriptions are true of just a single action of mine, for the cat’s breakfast was the only meat I put out this morning. In this essay, I will discuss how the various descriptions that an action might satisfy are related to the action’s being wrong or otherwise. In particular, I will explore the idea that certain descriptions (e.g. ‘dismembering a baby’) are such that any action satisfying any of those descriptions is for that reason wrong, whatever other descriptions (e.g. ‘saving a life’) it may also satisfy. This idea is called absolutism. It was once the conventional wisdom.1

Plato's Theory of Stuffs

Those who examine Platos theory of forms have from Aristotle onwards tended to interpret it as a theory of universals. Enough in the dialogues appears to support such an interpretation for it not to be entirely wrongheaded. Nevertheless, the conception of forms as universals or as the meanings of general terms produces a baffled incredulity when we consider some of the things that Plato has to say about them. It would be outlandish enough anyway to be told that a universal is an object; it becomes positively outrageous when we are informed furthermore that the object which is the universal being a so-and-so is itself a very superior so-and-so, existing separate from and independent of the particulars it characterizes and causing them to have the nature that they do. Could Plato have seriously thought and meant things so foolish? I doubt it, for there is a more charitable, less Aristotelian, way to interpret what Plato says about forms. This is the way suggested by Eudoxus and those others who apparently drew on Anaxagoras’ theoryof the homoiomeries in the exposition of Plato: a Platonic form is like an Anaxagorean stuff and accounts for the character of a particular ‘as white does, by being mixed with the white thing’ (Aristotle, Metaphysics 991314–19, 1079–8–23). In this paper I wish to build on Eudoxus’ suggestion and show how all the most troubling contentions that Plato makes about forms turn out to be either true or at least quite plausible if we suppose that forms are meant, not as universals, but as chemical elements instead. Platos theory of forms is not a grotesque misunderstanding of universals; it is a sober, intelligent, and largely true account of the elemental stuffs from which the world is made.

Names, Verbs and Sentences

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.

II–Nicholas Denyer

In De Caelo 1: 11-12 Aristotle argued that whatever is and always will be true is necessarily true. His argument works, once we grant him the highly plausible principle that if something is true, then it can be false if and only if it can come to be false. For example, assume it true that the sun is and always will be hot. No proposition of this form can ever will be hot. No proposition of this form can ever come to be false. Hence this proposition cannot be false. Hence it is necessarily true, and so too is anything that follows from it. In particular, it is necessarily true that the sun is hot. Moreover, if the sun not only is and always will be hot, but also always has been, then it follows by similar reasoning that the sun not only cannot now fail to be hot, but also never could have failed. Anything everlastingly true is therefore, in the strictest sense of the term, necessarily true.

Why do Mirrors Reverse Left/Right and not Up/Down?

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 (forwards into the mirror); and we can call the opposite direction boutwards (backwards out). 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.