9 ideas
| 6950 | You can be rational with undetected or minor inconsistencies [Harman] |
| Full Idea: Rationality doesn't require consistency, because you can be rational despite undetected inconsistencies in beliefs, and it isn't always rational to respond to a discovery of inconsistency by dropping everything in favour of eliminating that inconsistency. | |
| From: Gilbert Harman (Rationality [1995], 1.2) | |
| A reaction: This strikes me as being correct, and is (I am beginning to realise) a vital contribution made to our understanding by pragmatism. European thinking has been too keen on logic as the model of good reasoning. |
| 6954 | A coherent conceptual scheme contains best explanations of most of your beliefs [Harman] |
| Full Idea: A set of unrelated beliefs seems less coherent than a tightly organized conceptual scheme that contains explanatory principles that make sense of most of your beliefs; this is why inference to the best explanation is an attractive pattern of inference. | |
| From: Gilbert Harman (Rationality [1995], 1.5.2) | |
| A reaction: I find this a very appealing proposal. The central aim of rational thought seems to me to be best explanation, and I increasingly think that most of my beliefs rest on their apparent coherence, rather than their foundations. |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
| From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: [Brouwer 1952:510-11] |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
| From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
| A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
| 14665 | We can call the quality of Plato 'Platonity', and say it is a quality which only he possesses [Boethius] |
| Full Idea: Let the incommunicable property of Plato be called 'Platonity'. For we can call this quality 'Platonity' by a fabricated word, in the way in which we call the quality of man 'humanity'. Therefore this Platonity is one man's alone - Plato's. | |
| From: Boethius (Librium de interpretatione editio secunda [c.516], PL64 462d), quoted by Alvin Plantinga - Actualism and Possible Worlds 5 | |
| A reaction: Plantinga uses this idea to reinstate the old notion of a haecceity, to bestow unshakable identity on things. My interest in the quotation is that the most shocking confusions about properties arose long before the invention of set theory. |
| 6955 | Enumerative induction is inference to the best explanation [Harman] |
| Full Idea: We might think of enumerative induction as inference to the best explanation, taking the generalization to explain its instances. | |
| From: Gilbert Harman (Rationality [1995], 1.5.2) | |
| A reaction: This is a helpful connection. The best explanation of these swans being white is that all swans are white; it ceased to be the best explanation when black swans turned up. In the ultimate case, a law of nature is the explanation. |
| 6952 | Induction is 'defeasible', since additional information can invalidate it [Harman] |
| Full Idea: It is sometimes said that inductive reasoning is 'defeasible', meaning that considerations that support a given conclusion can be defeated by additional information. | |
| From: Gilbert Harman (Rationality [1995], 1.4.5) | |
| A reaction: True. The point is that being defeasible does not prevent such thinking from being rational. The rational part of it is to acknowledge that your conclusion is defeasible. |
| 6953 | All reasoning is inductive, and deduction only concerns implication [Harman] |
| Full Idea: Deductive logic is concerned with deductive implication, not deductive reasoning; all reasoning is inductive | |
| From: Gilbert Harman (Rationality [1995], 1.4.5) | |
| A reaction: This may be an attempt to stipulate how the word 'reasoning' should be used in future. It is, though, a bold and interesting claim, given the reputation of induction (since Hume) of being a totally irrational process. |
| 6951 | Ordinary rationality is conservative, starting from where your beliefs currently are [Harman] |
| Full Idea: Ordinary rationality is generally conservative, in the sense that you start from where you are, with your present beliefs and intentions. | |
| From: Gilbert Harman (Rationality [1995], 1.3) | |
| A reaction: This stands opposed to the Cartesian or philosophers' rationality, which requires that (where possible) everything be proved from scratch. Harman seems right, that the normal onus of proof is on changing beliefs, rather proving you should retain them. |