21 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. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 22142 | In future, only logical limits can be placed on divine omnipotence [Anon (Par), by Boulter] |
| Full Idea: The Condemnation stipulated that all portions of the ancient intellectual heritage that placed non-logical limits on divine omnipotence were no longer to be tolerated. ...Philosophers now had to entertain the wildest ideas with all seriousness. | |
| From: report of Anon (Par) (The Condemnation of 1277 [1277]) by Stephen Boulter - Why Medieval Philosophy Matters 3 | |
| A reaction: Boulter identifies this as 'the ultimate source of Hume's philosophical delirium'. Presumably the angels-on-a-pinhead stuff originated with this. It is crazy to think that the only limit on possible existence is logic. Can God make a planet of uranium? |
| 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. |
| 16716 | It is heresy to require self-evident foundational principles in order to be certain [Anon (Par)] |
| Full Idea: Heresy 151: 'To have certainty regarding any conclusion, it must be founded on self-evident principles'. | |
| From: Anon (Par) (The Condemnation of 1277 [1277], 151), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.3 | |
| A reaction: The correct view is obviously to found certainty on faith and authority. It is one thing to be told that foundationalism is a poor theory, but another to be told it is a heresy, and thus a potential capital crime! |
| 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. |
| 1866 | It is heresy to teach that history repeats every 36,000 years [Anon (Par)] |
| Full Idea: It is heresy to teach that with all the heavenly bodies coming back to the same point after a period of thirty-six thousand years, the same effects as now exist will reappear. | |
| From: Anon (Par) (The Condemnation of 1277 [1277], §92) |
| 1865 | It is heresy to teach that natural impossibilities cannot even be achieved by God [Anon (Par)] |
| Full Idea: It is heresy to teach that what is absolutely impossible according to nature cannot be brought about by God or another agent. | |
| From: Anon (Par) (The Condemnation of 1277 [1277], §17) |
| 1864 | It is heresy to teach that we can know God by his essence in this mortal life [Anon (Par)] |
| Full Idea: It is heresy to teach that we can know God by his essence in this mortal life. | |
| From: Anon (Par) (The Condemnation of 1277 [1277], §9) |