Logic ought to guide our thinking. It is better, more rational, more intelligent to think logically than to think illogically. Illogical thought leads to bad judgment and error. In any case, if logic had no role to play as a guide to thought, why should we bother with it?The somewhat naïve opinions of the previous paragraph are subject to attack from many sides. It may be objected that an activity does not count as thinking at all unless it is at (...) least minimally logical, so logic is constitutive of thought rather than a guide to it. Or it may be objected that whereas logic describes a system of timeless relations between propositions, thinking is a dynamic process involving revisions, and so could not use a merely static guide. Or again the objection may be that there is no such thing as logic, only a whole variety of different logics, not all of which could possibly be good guides. (shrink)

Two more or less standard methods exist for the systematic, logical construction of classical mathematics, the so-called theory of types, due in the main to Russell, and the Zermelo axiomatic set theory. In systems based upon either of these, the connective of membership, “ε”, plays a fundamental role. Usually although not always it figures as a primitive or undefined symbol.Following the familiar simplification of Russell's theory, let us mean by alogical typein the strict sense any one of the following: (i) (...) the totality consisting exclusively of individuals, (ii) the totality consisting exclusively of classes whose members are exclusively individuals, (iii) the totality consisting exclusively of classes whose members are exclusively classes whose members in turn are exclusively individuals, and so on. Any entity from (ii) is said to beone type higherthan any entity from (i), any entity from (iii), one type higher than any entity from (ii), and so on. In systems based upon this simplified theory of types, the only significant atomic formulae involving “ε” are those asserting the membership of an entity in an entity one type higher. Thus any expression of the form “(x∈y)” is meaningless except where “y” denotes an entity of just one type higher than the type of the entity denoted by “x” It is by means of general type restrictions of this kind that the Russell and other paradoxes are avoided. (shrink)

In Russell's Problems of Philosophy (PP), acquaintance is the basis of thought and also the basis of empirical knowledge. Thought is based on acquaintance, in that a thinker has to be acquainted with the basic constituents of his thoughts. Empirical knowledge is based on acquaintance, in that acquaintance is involved in perception, and perception is the ultimate source of all empirical knowledge.

ARCHAEOLOGYTHE Classical Spartans were noted for their austerity, which seemed already ancient to writers of the fifth century B.C. The early poetry and art of their country show a considerable aesthetic sense. This apparent contradiction has caused some students to conclude that the strict Lycurgan regimen was not introduced till the middle or even the end of the sixth century and that before that date Sparta had culturally been developing in much the same way as other important Greek states. The (...) argument is unsound. (shrink)

In attempting to date the Shield several complementary methods are possible. Roughly these may be classed as literary, historical and archaeological. The literary method indicates that the Shield comes late in the Hesiodic corpus: in particular the use of the F is careful. The historical method suggests a preciser upper limit. Wilamowitz believed that the point of lines 393–401, which give the season in which the combat between Herakles and Kyknos took place, can only be that a commemorative festival was (...) held—at the temple of Apollo at Pagasae, since the scene is laid in Apollo's sanctuary. Mazon continues that the reputation of the temple dates from the end of the Sacred War and the establishment at Pherae of a dynasty with close connections with Delphi : he therefore sets the terminus post quern at about 590. This argument is attractive and possible. Several scholars have attempted to secure a lower limit from the last sentence in Hypothesis A: κα⋯ Στησ⋯χορος δ⋯ φησιν ' Hσ7iota;⋯δου εἶναι τ⋯ πο⋯ημα. But as Wilamowitz observes, we do not know whether the poem in which this mention came was a genuine work of Stesichoros. Certainly it need not make the Shield much earlier than the Stesichorean poem, since our ‘Hesiod’ wrote his epyllion for incorporation in the Ehoiai which was attributed to the genuine Hesiod, and an insertion into such a work could have been very quickly accepted. Mazon's lower limit of 560 is then on insecure grounds. Thirdly there is the possibility that analysis of the decoration of Herakles' shield might give useful comparisons to the conclusions of archaeologists on the chronology of Greek art. It is this method that I shall attempt. (shrink)

My commentators point to respects in which the picture provided in Reference without Referents is incomplete. The picture provided no account of how sentences constructed from intensional verbs can be true when one of the referring expressions fails to refer. And it gave an incomplete, and possibly misleading, account of how to understand certain serious uses of fictional names, as in "Anna Karenina is more intelligent than Emma Bovary" and "Anna Karenina does not exist". In the present response, I indicate (...) how I would now wish to make good these deficiencies. The truth of sentences constructed from intensional verbs can be explained in terms of the truth of sentences that are unproblematic for RWR, for example, sentences dominated by operators expressing propositional attitudes. Reflection on the way in which we can temporarily accept commitments we do not in fact share leads to a more nuanced account of serious uses of fictional names, some of which manifest precisely such a temporary acceptance. /// Mis comentadores señalan aspectos en los que la propuesta de Reference without Referents es incompleta: no ofrecía una explicación de cómo oraciones construidas con verbos intensionales pueden ser verdaderas cuando una de las expresiones referenciales no refiere; y dio una explicación incompleta, y quizás engañosa, de cómo entender ciertos usos serios de nombres de ficción como en "Anna Karenina es más inteligente que Emma Bovary" y "Anna Karenina no existe". En esta respuesta indico cómo quiero ahora subsanar estas deficiencias. La verdad de las oraciones construidas con verbos intensionales puede explicarse en términos de la verdad de oraciones que no son problemáticas para la explicación de Reference without Referents, por ejemplo, oraciones dominadas por operadores que expresan actitudes proposicionales. Una reflexión sobre cómo podemos aceptar temporalmente compromisos que de hecho no compartimos conduce a una explicación más matizada de los usos serios de los nombres de ficción, algunos de los cuales manifiestan precisamente esa aceptación temporal. (shrink)

Wittgenstein's Tractatus contains a wide range of profound insights into the nature of logic and language – insights which will survive the particular theories of the Tractatus and seem to me to mark definitive and unassailable landmarks in our understanding of some of the deepest questions of philosophy. And yet alongside these insights there is a theory of the nature of the relation between language and reality which appears both to be impossible to work out in detail in a way (...) which is completely satisfactory, and to be bizarre and incredible. I am referring to the so-called logical atomism of the Tractatus. The main outlines of this theory at least are clear and familiar: there are elementary propositions which gain their sense from being models of possible states of affairs; such propositions are configurations of names of simple objects, signifying that those simples are analogously configured; every proposition has its sense through being analysable as a truth-functional compound of elementary propositions, thus deriving its sense from the sense of the elementary propositions when this view is taken in conjunction with the idea that the sense of a proposition is completely specified by specifying its truth-conditions. In this way the Tractatus incorporates in its working out a philosophical system analogous to the classical philosophical systems of Leibniz or Spinoza which are regarded by many people, in a sense rightly, as the prehistoric monsters of philosophy which are not to be studied as living organisms, but studied as the curiosities of human thought. And we may here agree that in the end we must simply reject a philosophy which incorporates such features as its postulation of simple eternal objects, or of a possibility of an analysis of a proposition which was presented as a pre-condition for the propositions that we ordinarily utter to make sense, and yet the specific form of which we are unaware of, and so on. (shrink)