2. Formalism (I); Session Dec. 5, 2014

2.1 Ordinary language is vague. And since we use language to communicate thought, communicated thought is often vague and muddled as well.

2.2 Donald Davidson is perhaps right that speaking a language is not a trait we can lose while retaining the power of thought & judgment.

[see, e.g., Davidson, Inquiries into Truth & Interpretation, OUP 1984, 185]

2.3 That’s controversial, though. Steven Pinker, e.g., believes in ‘Mentalese,’ the language of thought, independent of spoken words.

2.3.1 Pinker is a prolific popular writer, his books are easy reads. He’s not so much an academic philosopher, though.

[See, e.g., Simon Blackburn’s review of Pinker’s The Blank Slate in the New Scientist of September 7, 2002. Simon Blackburn, by the way, has a nice & entertaining website at Cambridge]

2.3.2 On Mentalese, check Pinker’s The Language Instinct, 1994, ch. 3 & The Stuff of Thought, 2007, and judge for yourself. But maybe also consult, as an instructive contrast, Wilfrid Sellar’s ‘Myth of Jones,’ in his Empiricism & the Philosophy of Mind of 1956, esp. §§ 56 ff.

2.4 Either way, it can’t perhaps hurt if we do something about language’s vagueness. That’s one purpose of logic.

2.5 Its tool, as it were: Formalization. It was Aristotle, who discovered the formal nature of logical derivation:

2.6 Certain statements can be derived from others on the basis of their formal structure alone, independently of their specific content.

2.7 Thus the distinction between Form & Content. The idea is that inquiring into formal structure may also enlighten our everyday communication.

2.8 Yet we must use vague ordinary language to create the precise formal language of logic. That’s not as silly as it sounds.

2.9. Even Gottlob Frege, founder of modern mathematical logic, to whom we shall return, didn’t build up his symbolic language from scratch.

2.9.1 Rather it’s been a reconstruction of natural language. And Frege hoped that it may in turn also help to cure its vagaries of vagueness.

[see Frege, ‘Der Gedanke’ (1918); Engl in: MIND 65 (1956), 289-311]

2.9.2 Please read Frege’s ‘Der Gedanke.’ It’s easy; no math in it at all. We shall discuss it in January or February.

2.9.3 There are other translations (one by P. Geach); we shall discuss that too. But the one in 2.9.1 is available online.

2.9.4 See also Preface of Frege’s ‘Begriffsschrift’ (1879), where he is confident that his ‘ideography’ can clarify philosopher idioms:

2.9.5 The description of this definitely worthwhile task is also not too difficult & gives a good first impression of Frege’s Platonism.

2.9.6 It’s only 4 pages. Translation in Jean van Heijenoort (ed.), From Frege to Gödel, HUP 1971, 5-8. They have it in your local library.

[I also found an online scan from the van Heijenoort book here. You may find others].

2.10. We shall return to it after we have discussed the beginnings of logic (from Aristotle to Kant) in the next few sessions.

1. Introduction; Session Dec. 1, 2014

1.1 Logic is a tool, as it were, for deriving conclusions from accepted assumptions.

1.2 Here the first problem shows up: What’s an accepted assumption? Such assumptions can be ‘logical’ themselves, or they can be ‘non-logical.’

1.3 ‘Non-logical’ is not pejorative, as common speech sometimes suggests, but just means extra-logical.

1.4 ‘Extra-logical’ is everything beyond the formal machinery of logic. Physics, e.g., is extra-logical (non-logical) in this sense.

1.5 Physics uses logic. This, however, does not make its truths logical truths.

[A nice description of the relation Logic/Science gives W.v.O. Quine, Mathematical Logic, HUP 1981, 7]

1.6 Logical truth is only that which is derived by formal logical means, that is, by certain accepted ‘rules of inference.’

1.7 It is assumed (cf. 1.1) that these formal rules, to which we come later in detail, lead to logically true conclusions.

1.8 No logic, however, can derive from a sequence of completely false factual, e.g. physical, premises a formally true conclusion.

1.9 So for a true scientific conclusion we need both factually true premises and a consistent sequence of formal logical inferences.

1.10 Application: A critical test of any scientific theory is its accuracy in predicting phenomena before they are observed.

1.11 Any such prediction must involve the application of the formal rules of logical inference.