11 ideas
| 9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
| Full Idea: Logic is part of a normative theory of thinking, not a substitute for thinking. | |
| From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.13) | |
| A reaction: There is some sort of logicians' dream, going back to Leibniz, of a reasoning engine, which accepts propositions and outputs inferences. I agree with this idea. People who excel at logic are often, it seems to me, modest at philosophy. |
| 6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
| Full Idea: In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility. | |
| From: A.C. Grayling (Russell [1996], Ch.2) | |
| A reaction: The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom. |
| 9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt] |
| Full Idea: Vagueness in respect of membership is consistency with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of a concept. | |
| From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.5) | |
| A reaction: I find this view of sets much more appealing than the one that identifies a set with its members. The empty set is less of a problem, as well as non-existents. Logicians prefer the extensional view because it is tidy. |
| 19718 | Indefeasibility does not imply infallibility [Grundmann] |
| Full Idea: Infallibility does not follow from indefeasibility. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Significance') | |
| A reaction: If very little evidence exists then this could clearly be the case. It is especially true of historical and archaeological evidence. |
| 6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |
| Full Idea: Two propositions might contradict each other despite appearing self-evident when considered separately. | |
| From: A.C. Grayling (Russell [1996], Ch.2) | |
| A reaction: Russell's proposal (Idea 5416) is important here, that self-evidence comes in degrees. If self-evidence was all-or-nothing, Grayling's point would be a major problem, but it isn't. Bonjour explores the idea more fully (e.g. Idea 3704) |
| 19717 | Can a defeater itself be defeated? [Grundmann] |
| Full Idea: Can the original justification of a belief be regained through a successful defeat of a defeater? | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Defeater-Defs') | |
| A reaction: [Jäger 2005 addresses this] I would have thought the answer is yes. I aspire to coherent justifications, so I don't see justifications as a chain of defeat and counter-defeat, but as collective groups of support and challenge. |
| 19716 | Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann] |
| Full Idea: An unmodified reliabilism does not accommodate defeaters, and surely there can be defeaters against reliably produced beliefs? | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Defeaters') | |
| A reaction: [He cites Bonjour 1980] Reliabilism has plenty of problems anyway, since a generally reliable process can obviously occasionally produce a bad result. 20:20 vision is not perfect vision. Internalist seem to like defeaters. |
| 19715 | You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann] |
| Full Idea: There are 'rebutting' defeaters against the truth of a previously justified belief, 'undercutting' defeaters against the power of the evidence, and 'reason-defeating' defeaters against the truth of the reason for the belief. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'How') | |
| A reaction: That is (I think) that you can defeat the background, the likelihood, or the truth. He cites Pollock 1986, and implies that these are standard distinctions about defeaters. |
| 19713 | Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann] |
| Full Idea: Advocates of the defeasibility theory have tried to exclude true pieces of information that are misleading defeaters. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'What') | |
| A reaction: He gives as an example the genuine news of a claim that the suspect has a twin. |
| 19714 | Knowledge requires that there are no facts which would defeat its justification [Grundmann] |
| Full Idea: The 'defeasibility theory' of knowledge claims that knowledge is only present if there are no facts that - if they were known - would be genuine defeaters of the relevant justification. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'What') | |
| A reaction: Something not right here. A genuine defeater would ensure the proposition was false, so it would simply fail the truth test. So we need a 'defeater' for a truth, which must therefore by definition be misleading. Many qualifications have to be invoked. |
| 19719 | 'Moderate' foundationalism has basic justification which is defeasible [Grundmann] |
| Full Idea: Theories that combine basic justification with the defeasibility of this justification are referred to as 'moderate' foundationalism. | |
| From: Thomas Grundmann (Defeasibility Theory [2011], 'Significance') | |
| A reaction: I could be more sympathetic to this sort of foundationalism. But it begins to sound more like Neurath's boat (see Quine) than like Descartes' metaphor of building foundations. |