| 14304 | Conditionals are true when the antecedent is true, and the consequent has to be true [Diod.Cronus] |
| Full Idea: The connected (proposition) is true when it begins with true and neither could nor can end with false. | |
| From: Diodorus Cronus (fragments/reports [c.300 BCE]), quoted by Stephen Mumford - Dispositions 03.4 | |
| A reaction: [Mumford got the quote from Bochenski] This differs from the truth-functional account because it says nothing about when the antecedent is false, which fits in also with the 'supposition' view, where A is presumed. This idea adds necessity. |
| 14303 | Truth-functional conditionals have a simple falsification, when A is true and B is false [Peirce] |
| Full Idea: The utility of [truth-functional conditionals] is that it puts us in possession of a rule...[namely] The hypothetical proposition may be ...falsified by a single state of things, but only by one in which A [antecedent] is true and B [consequent] is false. | |
| From: Charles Sanders Peirce (On the Algebra of Logic [1895], p.218), quoted by Stephen Mumford - Dispositions | |
| A reaction: Personally I am rather more interested in verifying conditionals than in falsifying them. I certainly don't accept them until they are falsified, unless they have massive support from surrounding facts. |
| 10993 | Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read] |
| Full Idea: Ramsey's Test for conditionals is that a conditional should be believed if a belief in its antecedent would commit one to believing its consequent. | |
| From: report of Frank P. Ramsey (Law and Causality [1928]) by Stephen Read - Thinking About Logic Ch.3 | |
| A reaction: A rather pragmatic approach to conditionals |
| 13766 | 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey] |
| Full Idea: Ramsey suggested that 'if', 'given that' and 'on the supposition that' come to the same thing, and that the degrees of belief in the antecedent should then conform to probability theory. | |
| From: report of Frank P. Ramsey (Truth and Probability [1926]) by Frank P. Ramsey - Law and Causality B | |
| A reaction: [compressed] |
| 14358 | In the possible worlds account of conditionals, modus ponens and modus tollens are validated [Jackson] |
| Full Idea: In the possible worlds account modus ponens is validated (the closest world, the actual, is a B-world just if B is true), and modus tollens is validated (if B is false, the actual world is not an A-world, so A is false). | |
| From: Frank Jackson (Conditionals [2006], 'Famous') | |
| A reaction: [see Jackson for slightly fuller versions] This looks like a minimal requirement for a decent theory of conditionals, so Jackson explains the attractions of the possible worlds view very persuasively. |
| 14359 | Only assertions have truth-values, and conditionals are not proper assertions [Jackson] |
| Full Idea: In the no-truth theory of conditionals they have justified assertion or acceptability conditions but not truth conditions. ...The motivation is that only assertions have truth values, and conditionals are arguments, not proper assertions. | |
| From: Frank Jackson (Conditionals [2006], 'No-truth') | |
| A reaction: Once I trim this idea down to its basics, it suddenly looks very persuasive. Except that I am inclined to think that conditional truths do state facts about the world - perhaps as facts about how more basic truths are related to each other. |
| 14357 | Possible worlds account, unlike A⊃B, says nothing about when A is false [Jackson] |
| Full Idea: In the possible worlds account of conditionals A⊃B is not sufficient for A→B. If A is false then A⊃B is true, but here nothing is implied about whether the world most like the actual world except that A is true is or is not a B-world. | |
| From: Frank Jackson (Conditionals [2006], 'Possible') | |
| A reaction: The possible worlds account seems to be built on Ramsey's idea of just holding A true and seeing what you get. Being committed to B being automatically true if A is false seems highly counterintuitive. |
| 10994 | Conditionals are true if minimal revision of the antecedent verifies the consequent [Stalnaker, by Read] |
| Full Idea: Stalnaker proposes that a conditional is true if its consequent is true in the minimal revision in which the antecedent is true, that is, in the most similar possible world in which the antecedent is true. | |
| From: report of Robert C. Stalnaker (works [1970]) by Stephen Read - Thinking About Logic Ch.3 | |
| A reaction: A similar account of counterfactuals was taken up by Lewis to give a (rather dubious) account of causation. |
| 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 [Edgington] |
| 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? [Edgington] |
| 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)? |
| 13855 | A conditional does not have truth conditions [Edgington] |
| Full Idea: A conditional does not have truth conditions. | |
| From: Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 1) |
| 13859 | X believes 'if A, B' to the extent that A & B is more likely than A & ¬B [Edgington] |
| Full Idea: X believes that if A, B, to the extent that he judges that A & B is nearly as likely as A, or (roughly equivalently) to the extent that he judges A & B to be more likely than A & ¬B. | |
| From: Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 5) | |
| A reaction: This is a formal statement of her theory of conditionals. |
| 14311 | Dispositions are not equivalent to stronger-than-material conditionals [Mumford] |
| Full Idea: The conclusion that disposition ascriptions are not equivalent to stronger-than-material conditionals is largely to be accepted. | |
| From: Stephen Mumford (Dispositions [1998], 04.7) | |
| A reaction: [he attributes the view to C.B.Martin 1994] It is hard to see how to describe a disposition in anything other than conditional terms. Mumford's 'functional role' probably has to be described conditionally. It is how the conditional cashes out. |
| 14185 | Conditionals are just a shorthand for some proof, leaving out the details [Read] |
| Full Idea: Truth enables us to carry various reports around under certain descriptions ('what Iain said') without all the bothersome detail. Similarly, conditionals enable us to transmit a record of proof without its detail. | |
| From: Stephen Read (Formal and Material Consequence [1994], 'Repres') | |
| A reaction: This is his proposed Redundancy Theory of conditionals. It grows out of the problem with Modus Ponens mentioned in Idea 14184. To say that there is always an implied 'proof' seems a large claim. |
| 8949 | In relevance logic, conditionals help information to flow from antecedent to consequent [Fisher] |
| Full Idea: A good account of relevance logic suggests that a conditional will be true when the flow of information is such that a conditional is the device that helps information to flow from the antecedent to the consequent. | |
| From: Jennifer Fisher (On the Philosophy of Logic [2008], 08.III) | |
| A reaction: Hm. 'If you are going out, you'll need an umbrella'. This passes on information about 'out', but also brings in new information. 'If you are going out, I'm leaving you'. What flows is an interpretation of the antecedent. Tricky. |