Jonathan Westphal

In the very early Notebooks 1914‐1916, Ludwig Wittgenstein's principal interests were in logic, but his remarks are scattered through with occasional observations or sequences of observations about epistemology, solipsism, life, and other metaphysical subjects. The Tractatus was published in 1921. Here, as in the Notebooks, Wittgenstein is convinced that there must be elementary propositions, propositions that cannot be analyzed, because they are not composed by applying truth functions to other propositions. The metaphysical structure of the Tractatus began to disintegrate, however, when Wittgenstein realized, as he reported in “Some Remarks on Logical Form”, that he could not analyze propositions about colors as statements of degree. Wittgenstein had begun to replace the idea of a logical space with “logical grammar”, a conception that was in turn destined to be replaced by “language‐games”. He wrote, “The colour octahedron is grammar, since it says that you can speak of a reddish blue but not a reddish green, etc”.

A central argument for the view that God's necessary omniscience [( Bgf p )] precludes freewill is unsound, because the necessity of the consequence is not the necessity of the consequent, and nor is Bgf true. God's belief in some particular proposition f about what I will do is not necessary, as I might do something that makes ~ f true. Fischer and Tognazzini claim that this counterargument argument assumes that I must freely do the something that makes f true. But plainly it doesn't. All that it assumes is that I will do the something that makes f true. It makes no difference whether I do that thing unfreely, or "deterministicall". The argument does not assume the existence of a case of freewill in the face of divine foreknowledge, but instead considers the necessity of God's belief in some particular designated proposition f. The argument does not depend, as Fischer and Tognazzini suppose, on whether God's knowledge is a function of the facts (omniscience) or vice versa (infallibility)

On Friday God knew everything, including f, a proposition about what Jones would do on Monday; we can write the time-indexed proposition that on Friday God believed f as Bgf. If Jones does not do the thing that makes f true, then the resulting state of affairs will be ∼f. So on Monday, before a certain time – ‘ t time’ – Jones has it in his power to bring it about that ∼f. It seems to follow that on Monday Jones has it in his power to bring it about that on Friday God believed something false. Yet this is impossible, as Bgp ⊃ p . But if f is false – if Jones makes it so on Monday – then so is Bgf, and God is not infallible. So either Jones cannot not do the thing that makes f true, and he has no freewill, or God is not infallible. The traditional responses to this dilemma are subtle, time-honoured and, as I see it, almost completely unconvincing. According to Linda Zagzebski , there are five of them: the Ockhamist response that God’s Friday belief is a so-called ‘soft’ fact, itself a problematic notion; the confused Molinist claim that on Friday God has something called ‘middle knowledge’ , so that God knows what Jones would do, but does not will it or know what Jones would do if … ); and the more sensible but still perplexing solution of Boethius’s that God’s knowing is not in time, so that the time-indexed proposition Bgf is not true. (How does it help to move the knowing that is said to determine our actions from the past to the timeless? It seems to …

The argument given by Peter van Inwagen for the second premise on his "First Formal Argument" in An Essay on Free Will is invalid. The second premise hinges on the principle that since a proposition p , some statement about the present, is actually true, ~p can't be true. ~p must be false. What is the reason? The principle is that ~p cannot be true at the same time as p . I argue that, among other things, in its attachment to this sort of principle, van Inwagen's argument commits the most familiar of all the modal scope fallacies

We provide a study of Russell’s argument (in _An Inquiry into Meaning and Truth_) against naive realism in which we distinguish five different forms of the argument. We agree with McLendon’s (1956) criticism, that Russell’s premiss that naive realism _leads to physics_ (our emphasis) is ambiguous as between “leads historically or psychologically” and “leads logically”. However, physics does logically lead to naive realism, in the sense that it presupposes it. In that case it is physics that is false. There is also the possibility that physics and naive realism are compatible, and that possibility obtains if phenomenalism is true.

I discuss an argument for Leibniz’s principle of sufficient reason, the argument that he gives from considerations about necessary and sufficient conditions. I consider two versions that Leibniz offers, a longer and a shorter one. I also wish to assess a criticism of the longer version of Leibniz’s argument made by the distinguished Leibniz scholar Robert Merrihew Adams in 1994. Adams claims that Leibniz’s argument for the principle of sufficient reason begs the question. A simple formalization of the argument in propositional logic shows that this is not the case, but reveals two further difficulties. The first difficulty (a) has to do with the apparent failure of the derivation of the principle that the existence of the “aggregate” of the necessary conditions for the existence of a thing implies the existence of the sufficient conditions. The second difficulty (b) is that Leibniz’s second premise plays no obvious role in his derivation. I try to solve these problems, on his behalf.

In ‘Concerning the Absurdity of Life’ Quentin Smith accuses us of contradicting ourselves in our argument against Thomas Nagel. On the one hand we said that Mozart's Piano Concerto No. 23 is not ‘insignificant’ compared with cosmic radiation. On the other we said that the life of a man of integrity or humanity could be lived without a formal claim to Value, so that there was nothing for Nagel's external perspective to negate. But where is the contradiction? We put ‘emotional value’, used of Mozart's concerto, in scare quotes, to show that we disapproved of the phrase, and we also called the emotional value ‘so-called’ with the same intention. What we said about the life of the man of integrity, as we characterized it, was that no formal claim about Value was made for it—note the capital V. ‘Formal’ was meant to make the same point. We meant neither to assert nor to deny that Value was objectively present in the concerto. If we had asserted it, that would have meant that the concerto was no good. If we had denied it, that would have committed us to a styptic view of what it would be for it to be false that it was no good. Also not wanted was to understand how music has a value, for example in education. Smith did not see that we were gunning for just the kind of analysis he gives of integrity and humanity. Hence that capital V in our reference to ‘Value’. It was meant ironically. Is a man's integrity ‘living by his values’, as Smith says, or is ‘humanity’, as we used it, ‘respecting the value of other human beings’? Integrity is surely, as the OED says, more a certain kind of unbrokenness or wholeness, being uncorrupted, even sinless, or innocent. The OED rightly makes no mention of values. Nor does it mention them under ‘humanity’: kindness, benevolence, humaneness, ‘traits or touches of human nature or feeling; points that appeal to man’. It is not true, let alone analytically true, as Smith says, that the notions of integrity and humanity involve value.

There are many problems of universals, at least the four distinguished by Jenny Teichmann. Consider her second one. ‘How can we form a general term when we are faced with easily distinguishable, widely differing examples?’ The term ‘blue’, for example, covers a wide range of—well, what does it cover a wide range of? A wide range of the colour blue? This is nonsense. What it covers is a wide range of blues —shades of blue. But we do not form a general term when faced with or referring to these items. We distinguish them: cerulean, ultramarine, cyan, cobalt, navy blue and so on. ‘Blue’ is not the name of any of these shades of blue. It does not ‘cover’ anything except the colour , of which it is the name. ‘Blue’ is the name of the colour blue. There are no widely differing, easily distinguishable examples of that . The colour blue cannot differ widely or easily be distinguished from the colour blue. Leibniz's law prevents it. It is shades of blue which differ and are easily distinguishable. The moment we try to say, ‘But this differs from that’, the question will be, ‘This and that what? ’ If the answer is, ‘This colour ’ and ‘That colour ’, then a mistake has been made. For there is no differing and distinguishing in this case. Teichmann's problem cannot even be stated. If we say that what differ are this blue and that blue, which is the right thing to say, then we have two count nouns which mean ‘shade of blue’. There is no general term for these different shades. There is no answer to the question, ‘What is the name of all these differing shades?’ Certainly they are all blues, but each has its own name, and it is not ‘blue’. Teichmann's question cannot arise here either. The question, ‘What do blues have in common in virtue of which they are blue?’ is either elliptical or bad logical grammar. Which it is depends on the construal, or misconstrual, of ‘are blue’. The question should be either, ‘…in virtue of which they are blues ’ in the plural— they are not identical with the colour blue—or ‘…in virtue of which they are shades of blue.’ The plural agreement must come somewhere

In ‘Concerning the Absurdity of Life’ Quentin Smith accuses us of contradicting ourselves in our argument against Thomas Nagel. On the one hand we said that Mozart's Piano Concerto No. 23 is not ‘insignificant’ compared with cosmic radiation. On the other we said that the life of a man of integrity or humanity could be lived without a formal claim to Value, so that there was nothing for Nagel's external perspective to negate. But where is the contradiction? We put ‘emotional value’, used of Mozart's concerto, in scare quotes, to show that we disapproved of the phrase, and we also called the emotional value ‘so-called’ with the same intention. What we said about the life of the man of integrity, as we characterized it, was that no formal claim about Value was made for it—note the capital V. ‘Formal’ was meant to make the same point. We meant neither to assert nor to deny that Value was objectively present in the concerto. If we had asserted it, that would have meant that the concerto was no good. If we had denied it, that would have committed us to a styptic view of what it would be for it to be false that it was no good. Also not wanted was to understand how music has a value, for example in education. Smith did not see that we were gunning for just the kind of analysis he gives of integrity and humanity. Hence that capital V in our reference to ‘Value’. It was meant ironically. Is a man's integrity ‘living by his values’, as Smith says, or is ‘humanity’, as we used it, ‘respecting the value of other human beings’? Integrity is surely, as the OED says, more a certain kind of unbrokenness or wholeness, being uncorrupted, even sinless, or innocent. The OED rightly makes no mention of values. Nor does it mention them under ‘humanity’: kindness, benevolence, humaneness, ‘traits or touches of human nature or feeling; points that appeal to man’. It is not true, let alone analytically true, as Smith says, that the notions of integrity and humanity involve value.

Das „Problem der Induktion", dessen Formulierung man gewöhnlich David Hume zuschreibt, hat Leibniz schon am Anfang des 18. Jahrhunderts formuliert und gelöst. Die Methode von Leibniz war sowohl „Hume-isch" als auch rationalistisch. Sie begreift in sich eine Herabsetzung des Empirischen und auch den Gebrauch der „Geheimkräfte", die Hume ausschalten wollte. Ohne solche „Geheimkräfte" gibt es keine Harmonie im klassischen Sinn von Leibniz . Für Leibniz ist eine Hypothese vorzuziehen, die eine Harmonie behauptet oder die maximale Verschiedenheit der Phänomene mit der minimalen Kompliziertheit der zugrundeliegenden Regel zusammenfaßt. Hier sind Beispiele von Gesetzen mit „produktiven Mechanismen" oder „Geheimkräften" gegeben, die der Leibnizschen Erklärung in der Physik und der Mathematik entsprechen. Die Schwerkraft entspricht diesen Gesichtspunkten nicht und ist daher unvernünftig im Leibnizschen Sinne; deshalb werden Induktionen über Schwerkraftsysteme als empirische Regeln betrachtet. Die Leibnizsche Theorie zeigt auch, wie man die wohlbekannten Beispiele von Hume erkennen und vorhersagen kann, nämlich aufgrund des richtigen wissenschaftlichen Verständnisses der Natur der Nahrung und des Feuers. Kants Prinzip der zeitlichen Reihenfolge wird zu seinen Ungunsten mit dem sechsten Grundsatz der Leibnizschen Abhandlung über die Metaphysik verglichen. Wir haben nach Leibniz doch einen vernünftigen Zugang zu der Wirklichkeit, die hinter den Empfindungen liegt, und die Verneinung dessen war es, was das empiristische Problem der Induktion erzeugt hat. Das Problem der Induktion ist ein reductio ad absurdum des Empirismus

Dans la première méditation, Descartes a conclu, en regard des songes, « qu'il n'y a point d'indices concluants, ni de marques assez certaines par où l'on puisse distinguer nettement la veille d'avec la sommeil [...] » . À la fin de la sixième méditation, il a conclu qu'il y a de tels indices, mais qu'on a besoin de la garantie de Dieu pour savoir si ces indices sont réellement des indices de la veille. Cottingham a proposé une objection générale contre tels indices de la veille: On peut rêver cet indice. Selon les raisonnements de Cottingham, il s'agit de l'existence de l'indice. Or, chez Leibniz et Descartes il ne s'agit pas de cela, mais il est question de savoir si l'indice est vraiment un indice de la veille. La prétention que l'indice puisse être présent en songe fait une pétition de principe. Notre examen des indices que Leibniz et Berkeley ont proposés révèle cette pétition