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

[general ideas about conditionals]

11 ideas
Modal logic began with translation difficulties for 'If...then' [Lewis,CI, by Girle]
     Full Idea: C.I.Lewis began his groundbreaking work in modal logic because he was concerned about the unreliability of the material conditional as a translation of 'If ... then' conditionals.
     From: report of C.I. Lewis (Symbolic Logic (with Langford) [1932]) by Rod Girle - Modal Logics and Philosophy 12.3
     A reaction: Compare 'if this is square then it has four corners' with 'if it rains then our afternoon is ruined'. Different modalities seem to be involved. We even find that 'a square has four corners' will be materially implied if it rains!
In nearby worlds where A is true, 'if A,B' is true or false if B is true or false [Stalnaker]
     Full Idea: Consider a possible world in which A is true and otherwise differs minimally from the actual world. 'If A, then B' is true (false) just in case B is true (false) in that possible world.
     From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1
     A reaction: This is the first proposal to give a possible worlds semantics for conditional statements. Edgington observes that worlds which are nearby for me may not be nearby for you.
A conditional probability does not measure the probability of the truth of any proposition [Lewis, by Edgington]
     Full Idea: Lewis was first to prove this remarkable result: there is no proposition A*B such that, in all probability distributions, p(A*B) = pA(B) [second A a subscript]. A conditional probability does not measure the probability of the truth of any proposition.
     From: report of David Lewis (Probabilities of Conditionals [1976]) by Dorothy Edgington - Conditionals (Stanf) 3.1
     A reaction: The equation says the probability of the combination of A and B is not always the same as the probability of B given A. Bennett refers to this as 'The Equation' in the theory of conditionals. Edgington says a conditional is a supposition and a judgement.
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)
It is a mistake to think that conditionals are statements about how the world is [Edgington]
     Full Idea: The mistake philosophers have made, in trying to understand the conditional, is to assume that its function is to make a statement about how the world is (or how other possible worlds are related to it), true or false, as the case may be.
     From: Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 1)
     A reaction: 'If pigs could fly we would never catch them' may not be about the world, but 'if you press this switch the light comes on' seems to be. Actually even the first one is about the world. I've an inkling that Edgington is wrong about this. Powers!
Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess]
     Full Idea: Three main theories of the truth of indicative conditionals are Materialism (the conditions are the same as for the material conditional), Idealism (identifying assertability with truth-value), and Nihilism (no truth, just assertability).
     From: John P. Burgess (Philosophical Logic [2009], 4.3)
It is doubtful whether the negation of a conditional has any clear meaning [Burgess]
     Full Idea: It is contentious whether conditionals have negations, and whether 'it is not the case that if A,B' has any clear meaning.
     From: John P. Burgess (Philosophical Logic [2009], 4.9)
     A reaction: This seems to be connected to Lewis's proof that a probability conditional cannot be reduced to a single proposition. If a conditional only applies to A-worlds, it is not surprising that its meaning gets lost when it leaves that world.
Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) [Williamson]
     Full Idea: The strict conditional implies the counterfactual conditional: □(A⊃B) ⊃ (A□→B) - suppose that A would not have held without B holding too; then if A had held, B would also have held.
     From: Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 1)
     A reaction: [He then adds a reading of his formula in terms of possible worlds] This sounds rather close to modus ponens. If A implies B, and A is actually the case, what have you got? B!
The standard view of conditionals is that they are truth-functional [Read]
     Full Idea: The standard view of conditionals is that they are truth-functional, that is, that their truth-values are determined by the truth-values of their constituents.
     From: Stephen Read (Thinking About Logic [1995], Ch.3)
The point of conditionals is to show that one will accept modus ponens [Read]
     Full Idea: The point of conditionals is to show that one will accept modus ponens.
     From: Stephen Read (Thinking About Logic [1995], Ch.3)
     A reaction: [He attributes this idea to Frank Jackson] This makes the point, against Grice, that the implication of conditionals is not conversational but a matter of logical convention. See Idea 21396 for a very different view.
Some people even claim that conditionals do not express propositions [Read]
     Full Idea: Some people even claim that conditionals do not express propositions.
     From: Stephen Read (Thinking About Logic [1995], Ch.7)
     A reaction: See Idea 14283, where this appears to have been 'proved' by Lewis, and is not just a view held by some people.