It is Frege's third contribution that makes the point of departure for the present paper. Not merely did Frege show how to manipulate symbols more exactly; he also gave a searching account of what these symbols mean. Consider a philosophical problem that arises out of the simplest arithmetic. When we say that 5 = 2 + 3, what do we mean? Do we mean that 5 is identical with 2 + 3? But in some ways 5 and 2 + 3 (...) are obviously different. Or do we mean that 5 and 2 + 3 are equal but not identical, equality being a relation that falls short of complete identity? But in that case, some ordinary ways of speaking in mathematics must be false. Suppose a pupil is asked for the positive square root of 25. The phrasing of the question implies that there is one and only one. No doubt he may answer, '5'. But then it follows that the answer '2 + 3' is not allowable, since ex hypothesi 5 and 2 + 3, though equal, are not identical. Yet ordinarily the answer '2 + 3' would be regarded as strange but not as wrong. (shrink)
Is language a social art by some necessity, or merely in point of fact? Is society indispensable in principle, or merely very useful in practice? Is language a social art in its origin only, or also in its definitive nature?
The interest in Leibniz's early writings was not spurred on by any doctrinaire motive; for instance, there was no temptation, as there has been in the case of some other thinkers, to hypothesize a youthful view which was subsequently rejected in some dramatic way comparable to Aristotle's break with the Academy or to Kant's being awakened from his dogmatic slumber. So if scholars should come to conclude that there is no essential or major difference between Leibniz's earliest and his latest (...) doctrines, the conclusion would not shock us; and neither would the opposite conclusion. We are uncommitted. (shrink)
The expectation is fulfilled, but in an unexpected way. 'The first studies toward this book were addressed to topics in the field of ethics' ; but our author, like Wagner composing 'Der Ring des Nibelungen', found himself becoming preoccupied with prolegomena. To these the present volume is wholly devoted. In order to establish its fundamental thesis that valuation is a form of empirical knowledge, two preparatory discussions are called for. An analysis of empirical knowledge in general is one of these; (...) but there is an inquiry properly prior even to this, an examination of the topic of meaning. The articulation of the book is accordingly tripartite; and Book I Meaning and Analytic Truth, Book II Empirical Knowledge, and Book III Valuation are of roughly equal length. (shrink)
If necessity is a generic notion, then, like any generic notion, it becomes specified not by a criterion as such but by a differentia. The differentia of logical necessity is that the denial of a logically necessary proposition is self-contradictory; one of our best criteria of logical necessity is that after careful consideration we see that the denial of the proposition is self-contradictory.
Such a thesis is counter to prevailing trends among contemporary philosophers. All that is about to be maintained is that facts may be regarded as entities, i.e. that it is legitimate and tenable so to regard them; this is much less than saying that they must be so regarded, and that anyone who declined to make use of the category of facts would be mistaken. Yet even so weak a thesis will be viewed askance by many; those who concede its (...) meaningfulness and logical possibility will still, a large proportion of them, dismiss it on other grounds-particularly on the ground of superfluity. And precisely one of the reasons why we have selected this particular thesis for defense, is as an occasion to examine the weight and force of Ockham's Razor. (shrink)