18 ideas
19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
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. |
18261 | A simplification which is complete constitutes a definition [Kant] |
Full Idea: By dissection I can make the concept distinct only by making the marks it contains clear. That is what analysis does. If this analysis is complete ...and in addition there are not so many marks, then it is precise and so constitutes a definition. | |
From: Immanuel Kant (Wiener Logik [1795], p.455), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
A reaction: I think Aristotle would approve of this. We need to grasp that a philosophical definition is quite different from a lexicographical definition. 'Completeness' may involve quite a lot. |
19067 | A successful proof requires recognition of truth at every step [Dummett] |
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 [Dummett] |
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 [Dummett, by Hanna] |
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] |
22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
Full Idea: In logic the question is not one of contingent but of necessary rules, not how to think, but how we ought to think. | |
From: Immanuel Kant (Wiener Logik [1795], p.16), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Trans' | |
A reaction: Presumably it aspires to the objectivity of a single correct account of how we all ought to think. I'm sympathetic to that, rather than modern cultural relativism about reason. Logic is rooted in nature, not in arbitrary convention. |
19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
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 [Dummett] |
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 [Dummett] |
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 [Dummett] |
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 [Dummett] |
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. |
8830 | A belief can be justified when the person has forgotten the evidence for it [Goldman] |
Full Idea: A characteristic case in which a belief is justified though the cognizer doesn't know that it's justified is where the original evidence for the belief has long since been forgotten. | |
From: Alvin I. Goldman (What is Justified Belief? [1976], II) | |
A reaction: This is a central problem for any very literal version of internalism. The fully rationalist view (to which I incline) will be that the cognizer must make a balanced assessment of whether they once had the evidence. Were my teachers any good? |
18260 | If we knew what we know, we would be astonished [Kant] |
Full Idea: If we only know what we know ...we would be astonished by the treasures contained in our knowledge. | |
From: Immanuel Kant (Wiener Logik [1795], p.843), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
A reaction: Nice remark. He doesn't require immediat recall of knowledge. You can't be required to know that you know something. That doesn't imply externalism, though. I believe in securely founded internal knowledge which is hard to recall. |
8832 | If justified beliefs are well-formed beliefs, then animals and young children have them [Goldman] |
Full Idea: If one shares my view that justified belief is, at least roughly, well-formed belief, surely animals and young children can have justified beliefs. | |
From: Alvin I. Goldman (What is Justified Belief? [1976], III) | |
A reaction: I take this to be a key hallmark of the externalist view of knowledge. Personally I think we should tell the animals that they have got true beliefs, but that they aren't bright enough to aspire to 'knowledge'. Be grateful for what you've got. |
8829 | Justification depends on the reliability of its cause, where reliable processes tend to produce truth [Goldman] |
Full Idea: The justificational status of a belief is a function of the reliability of the processes that cause it, where (provisionally) reliability consists in the tendency of a process to produce beliefs that are true rather than false. | |
From: Alvin I. Goldman (What is Justified Belief? [1976], II) | |
A reaction: Goldman's original first statement of reliabilism, now the favourite version of externalism. The obvious immediate problem is when a normally very reliable process goes wrong. Wise people still get it wrong, or right for the wrong reasons. |
19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
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. |
8831 | Introspection is really retrospection; my pain is justified by a brief causal history [Goldman] |
Full Idea: Introspection should be regarded as a form of retrospection. Thus, a justified belief that I am 'now' in pain gets its justificational status from a relevant, though brief, causal history. | |
From: Alvin I. Goldman (What is Justified Belief? [1976], II) | |
A reaction: He cites Hobbes and Ryle as having held this view. See Idea 6668. I am unclear why the history must be 'causal'. I may not know the cause of the pain. I may not believe an event which causes a proposition, or I may form a false belief from it. |
19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
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. |