green numbers give full details | back to texts | unexpand these ideas
| 19066 | Philosophy aims to understand the world, through ordinary experience and science |
| Full Idea: Philosophy is an attempt to understand the world, as it is revealed to us both in our ordinary experience and by the discoveries and theories of science. | |||
| From: Michael Dummett (The Justification of Deduction [1973], p.311) | |||
| A reaction: I don't see a sharp division between 'ordinary' and 'scientific'. I really like this idea, first because it makes 'understanding' central, and second because it wants both revelations. In discussing matter and time, there is too much emphasis on science. |
| 19067 | A successful proof requires recognition of truth at every step |
| Full Idea: For a demonstration to be cogent it is necessary that the passage from step to step involve a recognition of truth at each line. | |||
| From: Michael Dummett (The Justification of Deduction [1973], p.313) | |||
| A reaction: Dummett cited Quine (esp. 1970) as having an almost entirely syntactic view of logic. Rumfitt points out that logic can move validly from one falsehood to another. Even a 'proof' might detour into falsehood, but it would not be a 'canonical' proof! |
| 19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning |
| Full Idea: It is arguable whether two-valued truth tables give correct meanings for certain sentential operators, and even whether they constitute legitimate explanations of any possible sentential operators. | |||
| From: Michael Dummett (The Justification of Deduction [1973], p.294) | |||
| A reaction: See 'Many-valued logic' for examples of non-binary truth tables. Presumably logicians should aspire to make their semantics precise, as well as their syntax. |
| 11066 | Deduction is justified by the semantics of its metalanguage |
| Full Idea: For Dummett the semantics of the metalanguage is the external and objective source of the justification of deduction. | |||
| From: report of Michael Dummett (The Justification of Deduction [1973]) by Robert Hanna - Rationality and Logic 3.4 | |||
| A reaction: This is offered as an answer to the Lewis Carroll problem that justifying deduction seems to need deduction, thus leading to a regress. [There is a reply to Dummett by Susan Haack] |
| 19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples |
| Full Idea: A plausible account is that the syntactic notion of consequence is for positive results, that some form of argument is valid; the semantic notion is required for negative results, that some argument is invalid, because a counterexample can be found. | |||
| From: Michael Dummett (The Justification of Deduction [1973], p.292) | |||
| A reaction: This rings true for the two strategies of demonstration, the first by following the rules in steps, the second by using your imagination (or a tableau) to think up problems. |
| 19063 | Beth trees show semantics for intuitionistic logic, in terms of how truth has been established |
| Full Idea: Beth trees give a semantics for intuitionistic logic, by representing sentence meaning in terms of conditions under which it is recognised to have been established as true. | |||
| From: Michael Dummett (The Justification of Deduction [1973], p.305) |
| 19059 | In standard views you could replace 'true' and 'false' with mere 0 and 1 |
| Full Idea: Nothing is lost, on this view, if in the standard semantic treatment of classical sentential logic, we replace the standard truth-values 'true' and 'false' by the numbers 0 and 1. | |||
| From: Michael Dummett (The Justification of Deduction [1973], p.294) | |||
| A reaction: [A long context will explain 'on this view'] He is discussing the relationship of syntactic and semantic consequence, and goes on to criticise simple binary truth-table accounts of connectives. Semantics on a computer would just be 0 and 1. |
| 19062 | Classical two-valued semantics implies that meaning is grasped through truth-conditions |
| Full Idea: The standard two-valued semantics for classical logic involves a conception under which to grasp the meaning of a sentence is to apprehend the conditions under which it is, or is not, true. | |||
| From: Michael Dummett (The Justification of Deduction [1973], p.305) | |||
| A reaction: The idea is that you only have to grasp the truth tables for sentential logic, and that needs nothing more than knowing whether a sentence is true or false. I'm not sure where the 'conditions' creep in, though. |
| 19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory |
| Full Idea: A proof of soundess or completeness is a test, not so much of the logical theory to which it applies, but of the theory of meaning which underlies the semantics. | |||
| From: Michael Dummett (The Justification of Deduction [1973], p.310) | |||
| A reaction: These two types of proof concern how the syntax and the semantics match up, so this claim sounds plausible, though I tend to think of them as more like roadworthiness tests for logic, checking how well they function. |
| 19061 | An explanation is often a deduction, but that may well beg the question |
| Full Idea: An explanation is often a deductive argument, with the fact needing explaining as its conclusion. ...But the conclusion is usually given in advance, and we may only believe the premisses because they plausibly explain the conclusion. | |||
| From: Michael Dummett (The Justification of Deduction [1973], p.296) | |||
| A reaction: [compressed (Dummett's wordy prose cries out for it!)] I suppose this works better in mathematics, which is central to Dummett's interests. In the real world the puzzle is not usually logically implied by its explanation. |
| 19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible |
| Full Idea: In the sense of giving a model for the content of a sentence, its representative power, holism is not a theory of meaning; it is the denial that a theory of meaning is possible. | |||
| From: Michael Dummett (The Justification of Deduction [1973], p.309) | |||
| A reaction: This will obviously be because sentences just don't have meaning in isolation, so their meaning can't be given in terms of the sentences. |