19 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. |
| 18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
| Full Idea: A model of a language assigns values to non-logical terms. If a sentence is true in every model, its truth doesn't depend on those non-logical terms. Hence the validity of an argument comes from its logical form. Thus models explain logical validity. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: [compressed] Thus you get a rigorous account of logical validity by only allowing the rigorous input of model theory. This is the modern strategy of analytic philosophy. But is 'it's red so it's coloured' logically valid? |
| 18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
| Full Idea: Natural language includes connectives that are not truth-functional. In order for 'p because q' to be true, both p and q have to be true, but knowing the simpler sentences are true doesn't determine whether the larger sentence is true. | |
| From: Vann McGee (Logical Consequence [2014], 2) |
| 18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
| Full Idea: To get any advantage from moving to second-order logic, we need to assign to second-order variables a role different from merely ranging over collections made up of things the first-order variables range over. | |
| From: Vann McGee (Logical Consequence [2014], 7) | |
| A reaction: Thus it is exciting if they range over genuine properties, but not so exciting if you merely characterise those properties as sets of first-order objects. This idea leads into a discussion of plural quantification. |
| 18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
| Full Idea: We can get a less ontologically perilous presentation of the semantics of the predicate calculus by using sets instead of concepts. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: The perilous versions rely on Fregean concepts, and notably Russell's 'concept that does not fall under itself'. The sets, of course, have to be ontologically secure, and so will involve the iterative conception, rather than naive set theory. |
| 18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
| Full Idea: Logically valid sentences are a species of analytic sentence, being true not just in virtue of the meanings of their words, but true in virtue of the meanings of their logical words. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: A helpful link between logical truths and analytic truths, which had not struck me before. |
| 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
| Full Idea: Soundness theorems are seldom very informative, since typically we use informally, in proving the theorem, the very same rules whose soundness we are attempting to establish. | |
| From: Vann McGee (Logical Consequence [2014], 5) | |
| A reaction: [He cites Quine 1935] |
| 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
| Full Idea: One of the culminating achievements of Euclidean geometry was categorical axiomatisations, that describe the geometric structure so completely that any two models of the axioms are isomorphic. The axioms are second-order. | |
| From: Vann McGee (Logical Consequence [2014], 7) | |
| A reaction: [He cites Veblen 1904 and Hilbert 1903] For most mathematicians, categorical axiomatisation is the best you can ever dream of (rather than a single true axiomatisation). |
| 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. |
| 6649 | Chomsky now says concepts are basically innate, as well as syntax [Chomsky, by Lowe] |
| Full Idea: Chomsky now contends that not only the syntax of natural language but also the concepts expressible in it have an innate basis. | |
| From: report of Noam Chomsky (Chomsky on himself [1994]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.7 n25 | |
| A reaction: This seems to follow Fodor, who has been mocked for implying that we have an innate idea of a screwdriver etc. Note that Chomsky says concepts have an innate 'basis'. This fits well with modern (cautious) rationalism, with which I am happy. |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
| Full Idea: If our linguistic conventions entitle us to assert a sentence, they thereby make it true, because of the maxim that 'truth is the norm of assertion'. | |
| From: Vann McGee (Logical Consequence [2014], 8) | |
| A reaction: You could only really deny that maxim if you had no belief at all in truth, but then you can assert anything you like (with full entitlement). Maybe you can assert anything you like as long as it doesn't upset anyone? Etc. |