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| 14273 | Conditional Proof is only valid if we accept the truth-functional reading of 'if' |
| Full Idea: Conditional Proof seems sound: 'From X and Y, it follows that Z. So from X it follows that if Y,Z'. Yet for no reading of 'if' which is stronger that the truth-functional reading is CP valid, at least if we accept ¬(A&¬B);A; therefore B. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.2) | |||
| A reaction: See the section of ideas on Conditionals (filed under 'Modality') for a fuller picture of this issue. Edgington offers it as one of the main arguments in favour of the truth-functional reading of 'if' (though she rejects that reading). |
| 14281 | A thing works like formal probability if all the options sum to 100% |
| Full Idea: One's degrees of belief in the members of an idealised partition should sum to 100%. That is all there is to the claim that degrees of belief should have the structure of probabilities. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.1) |
| 14284 | Conclusion improbability can't exceed summed premise improbability in valid arguments |
| Full Idea: If (and only if) an argument is valid, then in no probability distribution does the improbability of its conclusion exceed the sum of the improbabilities of its premises. We can call this the Probability Preservation Principle. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.2) | |||
| A reaction: [Ernest Adams is credited with this] This means that classical logic is in some way probability-preserving as well as truth-preserving. |
| 14270 | Simple indicatives about past, present or future do seem to form a single semantic kind |
| Full Idea: Straightforward statements about the past, present or future, to which a conditional clause is attached - the traditional class of indicative conditionals - do (in my view) constitute a single semantic kind. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 1) | |||
| A reaction: This contrasts with Idea 14269, where the future indicatives are group instead with the counterfactuals. |
| 14269 | Maybe forward-looking indicatives are best classed with the subjunctives |
| Full Idea: According to some theorists, the forward-looking 'indicatives' (those with a 'will' in the main clause) belong with the 'subjunctives' (those with a 'would' in the main clause), and not with the other 'indicatives'. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 1) | |||
| A reaction: [She cites Gibbard, Dudman and 1988 Bennett; Jackson defends the indicative/subjunctive division, and recent Bennett defends it too] It is plausible to say that 'If you will do x' is counterfactual, since it hasn't actually happened. |
| 14275 | Truth-function problems don't show up in mathematics |
| Full Idea: The main defects of the truth-functional account of conditionals don't show up in mathematics. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.3) | |||
| A reaction: These problems are the paradoxes associated with the material conditional ⊃. Too often mathematical logic has been the tail that wagged the dog in modern philosophy. |
| 14274 | Inferring conditionals from disjunctions or negated conjunctions gives support to truth-functionalism |
| Full Idea: If either A or B is true, then you are intuitively justified in believe that If ¬A, B. If you know that ¬(A&B), then you may justifiably infer that if A, ¬B. The truth-functionalist gets both of these cases (disjunction and negated conjunction) correct. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.1) | |||
| A reaction: [compressed version] This summarises two of Edgington's three main arguments in favour of the truth-functional account of conditions (along with the existence of Conditional Proof). It is elementary classical logic which supports truth-functionalism. |
| 14276 | The truth-functional view makes conditionals with unlikely antecedents likely to be true |
| Full Idea: The truth-functional view of conditionals has the unhappy consequence that all conditionals with unlikely antecedents are likely to be true. To think it likely that ¬A is to think it likely that a sufficient condition for the truth of A⊃B obtains. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.3) | |||
| A reaction: This is Edgington's main reason for rejecting the truth-functional account of conditionals. She says it removes our power to discriminate between believable and unbelievable conditionals, which is basic to practical reasoning. |
| 14290 | Doctor:'If patient still alive, change dressing'; Nurse:'Either dead patient, or change dressing'; kills patient! |
| Full Idea: The doctor says "If the patient is still alive in the morning, change the dressing". As a truth-functional command this says "Make it that either the patient is dead in the morning, or change the dressing", so the nurse kills the patient. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 5) | |||
| A reaction: Isn't philosophy wonderful? |
| 14271 | Non-truth-functionalist say 'If A,B' is false if A is T and B is F, but deny that is always true for TT,FT and FF |
| Full Idea: Non-truth-functional accounts agree that 'If A,B' is false when A is true and B is false; and that it is sometimes true for the other three combinations of truth-values; but they deny that the conditional is always true in each of these three cases. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.1) | |||
| A reaction: Truth-functional connectives like 'and' and 'or' don't add any truth-conditions to the values of the propositions, but 'If...then' seems to assert a relationship that goes beyond its component propositions, so non-truth-functionalists are right. |
| 14272 | I say "If you touch that wire you'll get a shock"; you don't touch it. How can that make the conditional true? |
| Full Idea: Non-truth-functionalists agree that when A is false, 'If A,B' may be either true or false. I say "If you touch that wire, you will get an electric shock". You don't touch it. Was my remark true or false? They say it depends on the wire etc. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.1) | |||
| A reaction: This example seems to me to be a pretty conclusive refutation of the truth-functional view. How can the conditional be implied simply by my failure to touch the wire (which is what benighted truth-functionalists seem to believe)? |
| 14282 | On the supposition view, believe if A,B to the extent that A&B is nearly as likely as A |
| Full Idea: Accepting Ramsey's suggestion that 'if' and 'on the supposition that' come to the same thing, we get an equation which says ...you believe if A,B to the extent that you think that A&B is nearly as likely as A. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.1) |
| 14278 | Truth-functionalists support some conditionals which we assert, but should not actually believe |
| Full Idea: There are compounds of conditionals which we confidently assert and accept which, by the lights of the truth-functionalist, we do not have reason to believe true, such as 'If it broke if it was dropped, it was fragile', when it is NOT dropped. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.5) | |||
| A reaction: [The example is from Gibbard 1981] The fact that it wasn't dropped only negates the nested antecedent, not the whole antecedent. I suppose it also wasn't broken, and both negations seem to be required. |
| 14287 | Does 'If A,B' say something different in each context, because of the possibiites there? |
| Full Idea: A pragmatic constraint might say that as different possibilities are live in different conversational settings, a different proposition may be expressed by 'If A,B' in different conversational settings. | |||
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 4.1) | |||
| A reaction: Edgington says that it is only the truth of the proposition, not its content, which changes with context. I'm not so sure. 'If Hitler finds out, we are in trouble' says different things in 1914 and 1944. |