Combining Texts

All the ideas for 'Conditionals', 'Preface to 'De Revolutionibus'' and 'Difficulties of Transfinite Numbers and Types'

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7 ideas

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism

21558	'Predicative' norms are those which define a class [Russell]
	Full Idea: Norms (containing one variable) which do not define classes I propose to call 'non-predicative'; those which do define classes I shall call 'predicative'.
	From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141)

21559	We need rules for deciding which norms are predicative (unless none of them are) [Russell]
	Full Idea: We need rules for deciding what norms are predicative and what are not, unless we adopt the view (which has much to recommend it) that no norms are predicative. ...[146] A predative propositional function is one which determines a class.
	From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141)
	A reaction: He is referring to his 'no class' theory, which he favoured at that time.

10. Modality / B. Possibility / 8. Conditionals / a. Conditionals

13768	Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington]
	Full Idea: If your interest in logic is confined to applications to mathematics or other a priori matters, it is fine for validity to preserve certainty, ..but if you use conditionals when arguing about contingent matters, then great caution will be required.
	From: Dorothy Edgington (Conditionals [2001], 17.2.1)

10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional

13770	There are many different conditional mental states, and different conditional speech acts [Edgington]
	Full Idea: As well as conditional beliefs, there are conditional desires, hopes, fears etc. As well as conditional statements, there are conditional commands, questions, offers, promises, bets etc.
	From: Dorothy Edgington (Conditionals [2001], 17.3.4)

10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals

13764	Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
	Full Idea: Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'?
	From: Dorothy Edgington (Conditionals [2001], 17.1)
	A reaction: I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional.

13765	'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
	Full Idea: If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B).
	From: Dorothy Edgington (Conditionals [2001], 17.1)
	A reaction: This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true.

14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations

15282	Facts should be deducible from the theory and initial conditions, and prefer the simpler theory [Osiander, by Harré/Madden]
	Full Idea: The two positivist criteria for a scientific theory are that the facts must be deducible from the theory together with initial conditions, and if there is more than one theory the simplest must be chosen.
	From: report of Andreas Osiander (Preface to 'De Revolutionibus' [1543]) by Harré,R./Madden,E.H. - Causal Powers 7.I
	A reaction: Harré and Madden cite this as a famous early statement of positivism. It seems to combine Hempel and Lewis very concisely. Wrong, of course. It does not, though, appear to mention 'laws'.