15 ideas
| 19306 | It is a principle of reasoning not to clutter your mind with trivialities [Harman] |
| Full Idea: I am assuming the following principle: Clutter Avoidance - in reasoning, one should not clutter one's mind with trivialities. | |
| From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 2) | |
| A reaction: I like Harman's interest in the psychology of reasoning. In the world of Frege, it is taboo to talk about psychology. |
| 19304 | The rules of reasoning are not the rules of logic [Harman] |
| Full Idea: Rules of deduction are rules of deductive argument; they are not rules of inference or reasoning. | |
| From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 1) | |
| A reaction: And I have often noticed that good philosophing reasoners and good logicians are frequently not the same people. |
| 19307 | If there is a great cost to avoiding inconsistency, we learn to reason our way around it [Harman] |
| Full Idea: We sometimes discover our views are inconsistent and do not know how to revise them in order to avoid inconsistency without great cost. The best response may be to keep the inconsistency and try to avoid inferences that exploit it. | |
| From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 2) | |
| A reaction: Any decent philosopher should face this dilemma regularly. I assume non-philosophers don't compare the different compartments of their beliefs very much. Students of non-monotonic logics are trying to formalise such thinking. |
| 19309 | Logic has little relevance to reasoning, except when logical conclusions are immediate [Harman] |
| Full Idea: Although logic does not seem specially relevant to reasoning, immediate implication and immediate inconsistency do seem important for reasoning. | |
| From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 2) | |
| A reaction: Ordinary thinkers can't possibly track complex logical implications, so we have obviously developed strategies for coping. I assume formal logic is contructed from the basic ingredients of the immediate and obvious implications, such as modus ponens. |
| 19303 | Implication just accumulates conclusions, but inference may also revise our views [Harman] |
| Full Idea: Implication is cumulative, in a way that inference may not be. In argument one accumulates conclusions; things are always added, never subtracted. Reasoned revision, however, can subtract from one's view as well as add. | |
| From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 1) | |
| A reaction: This has caught Harman's attention, I think (?), because he is looking for non-monotonic reasoning (i.e. revisable reasoning) within a classical framework. If revision is responding to evidence, the logic can remain conventional. |
| 9540 | A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell] |
| Full Idea: A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: In the interpreted version of the logic, 1 and 0 would become T (true) and F (false). The procedure seems to be called nowadays a 'valuation'. |
| 9541 | The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell] |
| Full Idea: The Law of Transposition says that (P→Q) → (¬Q→¬P). | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: That is, if the consequent (Q) of a conditional is false, then the antecedent (P) must have been false. |
| 9543 | The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell] |
| Full Idea: An axiomatic system is most naturally consistent iff no thesis is the negation of another thesis. It can be shown that every axiom is valid, that the transformation rules are validity-preserving, and if a wff α is valid, then ¬α is not valid. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: [The labels 'soundness' and 'consistency' seem interchangeable here, with the former nowadays preferred] |
| 9544 | A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell] |
| Full Idea: To say that an axiom system is 'weakly complete' is to say that every valid wff of the system is derivable as a thesis. ..The system is 'strongly complete' if it cannot have any more theses than it has without falling into inconsistency. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: [They go on to say that Propositional Logic is strongly complete, but Modal Logic is not] |
| 19305 | The Gambler's Fallacy (ten blacks, so red is due) overemphasises the early part of a sequence [Harman] |
| Full Idea: The Gambler's Fallacy says if black has come up ten times in a row, red must be highly probable next time. It overlooks how the impact of an initial run of one color can become more and more insignificant as the sequence gets longer. | |
| From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 1) | |
| A reaction: At what point do you decide that the roulette wheel is fixed, rather than that you have fallen for the Gambler's Fallacy? Interestingly, standard induction points to the opposite conclusion. But then you have prior knowledge of the wheel. |
| 19310 | High probability premises need not imply high probability conclusions [Harman] |
| Full Idea: Propositions that are individually highly probable can have an immediate implication that is not. The fact that one can assign a high probability to P and also to 'if P then Q' is not sufficient reason to assign high probability to Q. | |
| From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 3) | |
| A reaction: He cites Kyburg's Lottery Paradox. It is probable that there is a winning ticket, and that this ticket is not it. Thus it is NOT probable that I will win. |
| 19308 | We strongly desire to believe what is true, even though logic does not require it [Harman] |
| Full Idea: Moore's Paradox: one is strongly disposed not to believe both P and that one does not believe that P, while realising that these propositions are perfectly consistent with one another. | |
| From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 2) | |
| A reaction: [Where in Moore?] A very nice example of a powerful principle of reasoning which can never be captured in logic. |
| 19311 | In revision of belief, we need to keep track of justifications for foundations, but not for coherence [Harman] |
| Full Idea: The key issue in belief revision is whether one needs to keep track of one's original justifications for beliefs. What I am calling the 'foundations' theory says yes; what I am calling the 'coherence' theory says no. | |
| From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 4) | |
| A reaction: I favour coherence in all things epistemological, and this idea seems to match real life, where I am very confident of many beliefs of which I have forgotten the justification. Harman says coherentists need the justification only when they doubt a belief. |
| 19312 | Coherence is intelligible connections, especially one element explaining another [Harman] |
| Full Idea: Coherence in a view consists in connections of intelligibility among the elements of the view. Among other things these included explanatory connections, which hold when part of one's view makes it intelligible why some other part should be true. | |
| From: Gilbert Harman (Change in View: Principles of Reasoning [1986], 7) | |
| A reaction: Music to my ears. I call myself an 'explanatory empiricist', and embrace a coherence theory of justification. This is the framework within which philosophy should be practised. Harman is our founder, and Paul Thagard our guru. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |