Combining Texts

All the ideas for 'Conditionals', 'The Logical Syntax of Language' and 'A General Principle to Explain Laws of Nature'

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8 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy

19395	Philosophy is sanctified, because it flows from God [Leibniz]
	Full Idea: Philosophy is sanctified by having its streams flow from the fountain of God's attributes.
	From: Gottfried Leibniz (A General Principle to Explain Laws of Nature [1687], p.69)

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

13342	Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap]
	Full Idea: Carnap proposed to define consequence as 'sentence X follows from the sentences K iff the sentences K and the negation of X are contradictory', but 1) this is intuitively impossible, and 2) consequence would be changed by substituting objects.
	From: comment on Rudolph Carnap (The Logical Syntax of Language [1934], p.88-) by Alfred Tarski - The Concept of Logical Consequence p.414
	A reaction: This seems to be the first step in the ongoing explicit discussion of the nature of logical consequence, which is now seen by many as the central concept of logic. Tarski brings his new tool of 'satisfaction' to bear.

5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention

13251	Each person is free to build their own logic, just by specifying a syntax [Carnap]
	Full Idea: In logic, there are no morals. Everyone is at liberty to build his own logic, i.e. his own form of language. All that is required is that he must state his methods clearly, and give syntactical rules instead of philosophical arguments.
	From: Rudolph Carnap (The Logical Syntax of Language [1934], §17), quoted by JC Beall / G Restall - Logical Pluralism 7.3
	A reaction: This is understandable, but strikes me as close to daft relativism. If I specify a silly logic, I presume its silliness will be obvious. By what criteria? I say the world dictates the true logic, but this is a minority view.

9. Objects / F. Identity among Objects / 1. Concept of Identity

19394	Inequality can be brought infinitely close to equality [Leibniz]
	Full Idea: Equality may be considered as an infinitely small inequality, and we may make inequality approach equality as much as we wish.
	From: Gottfried Leibniz (A General Principle to Explain Laws of Nature [1687], p.67)
	A reaction: An interesting response to David Lewis's brusque dismissal of the problem of identity, as all-or-nothing...end of story.

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.