71 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
| 4697 | There has been a distinct 'Social Turn' in recent philosophy, like the earlier 'Linguistic Turn' [O'Grady] |
| Full Idea: The Social Turn is as defining a characteristic of contemporary philosophy as the Linguistic Turn has been of the earlier twentieth century period. | |
| From: Paul O'Grady (Relativism [2002], Ch.1) | |
| A reaction: A helpful observation. It ties in with externalism about concepts (Twin Earth), impossibility of Private Language, and externalism about knowledge. |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| Full Idea: The real monuments of philosophy are its problems. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Presumably he means '....rather than its solutions'. No other subject would be very happy with that sort of claim. Compare Idea 8243. A complaint against analytic philosophy is that it has achieved no consensus at all. |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| Full Idea: By now, no education in abstract pursuits is adequate without some familiarity with sets. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: A heart-sinking observation for those who aspire to study metaphysics and modality. The question is, what will count as 'some' familiarity? Are only professional logicians now allowed to be proper philosophers? |
| 4731 | Good reasoning will avoid contradiction, enhance coherence, not ignore evidence, and maximise evidence [O'Grady] |
| Full Idea: The four basic principles of rationality are 1) avoid contradiction, 2) enhance coherence, 3) avoid ignoring evidence, and 4) maximise evidence. | |
| From: Paul O'Grady (Relativism [2002], Ch.5) | |
| A reaction: I like this, and can't think of any additions. 'Coherence' is the vaguest of the conditions. Maximising evidence is still the driving force of science, even if it does sound quaintly positivist. |
| 4735 | Just as maps must simplify their subject matter, so thought has to be reductionist about reality [O'Grady] |
| Full Idea: A map that is identical in all respects with that which is mapped is just useless. So reductionism is not just a good thing - it is essential to thought. | |
| From: Paul O'Grady (Relativism [2002], Ch.6) | |
| A reaction: A useful warning, when thinking about truth. It is folly to want your thoughts to exactly correspond to reality. I want to understand the world, but not if it requires being the world. |
| 4701 | To say a relative truth is inexpressible in other frameworks is 'weak', while saying it is false is 'strong' [O'Grady] |
| Full Idea: Weak alethic relativism holds that while a statement may be true in one framework, it is inexpressible in another. Strong alethic relativism is where a sentence is true relative to one framework, but false relative to another. | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: The weak version will be Kuhn's 'incommensurability' of scientific theories, while the strong version will be full Protagorean relativism, saying all beliefs are true. |
| 4703 | The epistemic theory of truth presents it as 'that which is licensed by our best theory of reality' [O'Grady] |
| Full Idea: The epistemic theory of truth presents it as 'that which is licensed by our best theory of reality'. | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: Dangerous nonsense. This leaves truth shifting as our theories change, it leads to different truths in different cultures, and no palpable falsehood in ignorant cultures. Don't give it house-room. |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| Full Idea: It is an ancient and honourable view that truth is correspondence to fact; Tarski showed us how to do without facts here. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This is a very interesting spin on Tarski, who certainly seems to endorse the correspondence theory, even while apparently inventing a new 'semantic' theory of truth. It is controversial how far Tarski's theory really is a 'correspondence' theory. |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| Full Idea: We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This is the hardest part of Tarski's theory of truth to grasp. |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| Full Idea: In any first-order language, there are infinitely many T-sentences. Since definitions should be finite, the agglomeration of all the T-sentences is not a definition of truth. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This may be a warning shot aimed at Davidson's extensive use of Tarski's formal account in his own views on meaning in natural language. |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| Full Idea: A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: That is, a proof can be enshrined in an arrow. |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| Full Idea: When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier. |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| Full Idea: It is set theory, and more specifically the theory of relations, that articulates order. | |
| From: William D. Hart (The Evolution of Logic [2010]) | |
| A reaction: It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers. |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| Full Idea: The theory of types is a thing of the past. There is now nothing to choose between ZFC and NBG (Neumann-Bernays-Gödel). NF (Quine's) is a more specialized taste, but is a place to look if you want the universe. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| Full Idea: ∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: Getting these two clear may be the most important distinction needed to understand how set theory works. |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| Full Idea: Without the empty set, disjoint sets would have no intersection, and we could not form a∩b without checking that a and b meet. This is an example of the utility of the empty set. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: A novice might plausibly ask why there should be an intersection for every pair of sets, if they have nothing in common except for containing this little puff of nothingness. But then what do novices know? |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| Full Idea: In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'. |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| Full Idea: The usual statement of Foundation is that any nonempty set has a member disjoint from it. This phrasing is ordinal-free and closer to the primitives of ZFC. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| Full Idea: When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The socks example in from Russell 1919:126. |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| Full Idea: It follows from the Axiom of Choice that every set can be well-ordered. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: For 'well-ordered' see Idea 13460. Every set can be ordered with a least member. |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| Full Idea: It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist. |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| Full Idea: 'Comprehension' is the assumption that every predicate has an extension. Naïve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions. |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| Full Idea: That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers). | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains. |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| Full Idea: We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| Full Idea: A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition. |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| Full Idea: One of the glories of Von Neumann's theory of numbers is to define α < β to mean that α ∈ β. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| Full Idea: A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point. |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| Full Idea: Some have claimed that sets should be rethought in terms of still more basic things, categories. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: [He cites F.William Lawvere 1966] It appears to the the context of foundations for mathematics that he has in mind. |
| 4705 | Logical relativism appears if we allow more than one legitimate logical system [O'Grady] |
| Full Idea: Logical relativism emerges if one defends the existence of two or more rival systems that one may legitimately choose between, or move back and forth between. | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: All my instincts rebel against this possibility. All of Aristotle's and Kant's philosophy would be rendered meaningless. Obviously you can create artificial logics (like games), but I believe there is a truth logic. (Pathetic, isn't it?) |
| 4700 | A third value for truth might be "indeterminate", or a point on a scale between 'true' and 'false' [O'Grady] |
| Full Idea: Suggestions for a third value for truth are "indeterminate", or a scale running from "true", through "mostly true", "mainly true", "half true", "mainly false", "mostly false", to "false", or maybe even "0.56 true". | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: Anything on a sliding scale sounds wrong, as it seems to be paracitic on an underlying fixed idea of 'true'. "Indeterminate", though, seems just right for the truth of predictions ('sea-fight tomorrow'). |
| 4704 | Wittgenstein reduced Russell's five primitive logical symbols to a mere one [O'Grady] |
| Full Idea: While Russell and Whitehead used five primitive logical symbols in their system, Wittgenstein suggested in his 'Tractatus' that this be reduced to one. | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: This certainly captures why Russell was so impressed by him. In retrospect what looked like progress presumably now looks like the beginning of the collapse of the enterprise. |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain? |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| Full Idea: Models are ways the world might be from a first-order point of view. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity. |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea. |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| Full Idea: We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| Full Idea: Since we can map the transfinite ordinals one-one into the infinite cardinals, there are at least as many infinite cardinals as transfinite ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| Full Idea: The axiom of infinity with separation yields a least limit ordinal, which is called ω. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| Full Idea: It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| Full Idea: The real numbers were not isolated from geometry until the arithmetization of analysis during the nineteenth century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| Full Idea: Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof. | |
| From: William D. Hart (The Evolution of Logic [2010], 5) | |
| A reaction: If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence. |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| Full Idea: There is a familiar comparison between Euclid (unique parallel) and 'spherical' geometry (no parallel) and 'saddle' geometry (several parallels). | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| Full Idea: Jespersen calls a noun a mass word when it has no plural, does not take numerical adjectives, and does not take 'fewer'. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: Jespersen was a great linguistics expert. |
| 4711 | Anti-realists say our theories (such as wave-particle duality) give reality incompatible properties [O'Grady] |
| Full Idea: The anti-realist says we have theories about the world that are incompatible with each other, and irreducible to each other. They often cite wave-particle duality, which postulate incompatible properties to reality. | |
| From: Paul O'Grady (Relativism [2002], Ch.3) | |
| A reaction: Most physicists, of course, hate this duality, precisely because they can't conceive how the two properties could be real. I say realism comes first, and the theories must try to accommodate that assumption. |
| 4698 | What counts as a fact partly depends on the availability of human concepts to describe them [O'Grady] |
| Full Idea: What counts as a fact partly depends on human input, such as the availability of concepts to describe such facts. | |
| From: Paul O'Grady (Relativism [2002], Ch.1) | |
| A reaction: The point must be taken. I am happy to generalise about 'The Facts', meaning 'whatever is the case', but the individuation of specific facts is bound to hit the current problem. |
| 4715 | We may say that objects have intrinsic identity conditions, but still allow multiple accounts of them [O'Grady] |
| Full Idea: Those defending the claim that objects exist with identity conditions not imposed by us, do not have to say that there is just one account of those objects possible. | |
| From: Paul O'Grady (Relativism [2002], Ch.3) | |
| A reaction: This seems right, but the test question is whether the mind of God contains a single unified theory/account. Are multiple accounts the result of human inadequacy? Yes, I surmise. |
| 4719 | Maybe developments in logic and geometry have shown that the a priori may be relative [O'Grady] |
| Full Idea: A weaker form of relativism holds that developments in logic, in maths and in geometry have shown how a relativised notion of the a priori is possible. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: This is non-Euclidean geometry, and multiple formalisations of logic. Personally I don't believe it. You can expand these subjects, and pursue whimsical speculations, but I have faith in their stable natural core. Neo-Platonism. |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| Full Idea: The conception of Frege is that self-evidence is an intrinsic property of the basic truths, rules, and thoughts expressed by definitions. | |
| From: William D. Hart (The Evolution of Logic [2010], p.350) | |
| A reaction: The problem is always that what appears to be self-evident may turn out to be wrong. Presumably the effort of arriving at a definition ought to clarify and support the self-evident ingredient. |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| Full Idea: In the case of the parallels postulate, Euclid's fifth axiom (the whole is greater than the part), and comprehension, saying was believing for a while, but what was said was false. This should make a shrewd philosopher sceptical about a priori knowledge. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Euclid's fifth is challenged by infinite numbers, and comprehension is challenged by Russell's paradox. I can't see a defender of the a priori being greatly worried about these cases. No one ever said we would be right - in doing arithmetic, for example. |
| 4720 | Sense-data are only safe from scepticism if they are primitive and unconceptualised [O'Grady] |
| Full Idea: The reason sense-data were immune from doubt was because they were so primitive; they were unstructured and below the level of conceptualisation. Once they were given structure and conceptualised, they were no longer safe from sceptical challenge. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: The question of whether sense-data are conceptualised doesn't have to be all-or-nothing. As concepts creep in, so does scepticism, but so what? Sensible philosophers live with scepticism, like a mad aunt in the attic. |
| 4722 | Modern epistemology centres on debates about foundations, and about external justification [O'Grady] |
| Full Idea: The two dichotomies which set the agenda in contemporary epistemology are the foundationalist-coherentist debate, and the internalist-externalist debate. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: Helpful. Roughly, foundationalists are often externalists (if they are empiricists), and coherentists are often internalists (esp. if they are rationalists). An eccentric combination would make a good PhD. |
| 4724 | Internalists say the reasons for belief must be available to the subject, and externalists deny this [O'Grady] |
| Full Idea: Internalism about justification says that the reasons one has for a belief must be in some sense available to the knowing subject, ..while externalism holds that it is possible for a person to have a justified belief without having access to the reason. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: It strikes me that internalists are talking about the believer being justified, and externalists talk about the belief being justified. I'm with the internalists. If this means cats don't know much, so much the worse for cats. |
| 4723 | Coherence involves support from explanation and evidence, and also probability and confirmation [O'Grady] |
| Full Idea: Coherentist justification is more than absence of contradictions, and will involve issues like explanatory support and evidential support, and perhaps issues about probability and confirmation too. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: Something like this is obviously essential. Is the notion of 'relevance' also needed (e.g. to avoid the raven paradox of induction)? Coherence of justification will combine with correspondence for truth. |
| 4709 | Ontological relativists are anti-realists, who deny that our theories carve nature at the joints [O'Grady] |
| Full Idea: Ontological relativists are anti-realists in the strong sense; they hold as meaningless the view that our theories carve nature at the joints. | |
| From: Paul O'Grady (Relativism [2002], Ch.3) | |
| A reaction: This pinpoints my disagreement with such relativism, as it seems obvious to me that nature has 'joints', and that we would agree with any sensible alien about lots of things. |
| 4725 | Contextualism says that knowledge is relative to its context; 'empty' depends on your interests [O'Grady] |
| Full Idea: Contextualist about knowledge say that "to know" means different things in different context. For example, a warehouse may be empty for a furniture owner, but not for a bacteriologist or a physicist. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: There is obviously some truth in this, but we might say that 'empty' is a secondary quality, or that 'empty for furniture' is not relative. We needn't accept relativism here. |
| 4732 | One may understand a realm of ideas, but be unable to judge their rationality or truth [O'Grady] |
| Full Idea: It is possible to conceive of one understanding the meaning of a realm of ideas, but holding that one cannot judge as to the truth or rationality of the claims made in it. | |
| From: Paul O'Grady (Relativism [2002], Ch.5) | |
| A reaction: I think Davidson gives good grounds for challenging this, by doubt whether one 'conceptual scheme' can know another without grasping its rationality and truth-conditions. |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| Full Idea: A Fregean concept is a function that assigns to each object a truth value. So instead of the colour green, the concept GREEN assigns truth to each green thing, but falsity to anything else. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This would seem to immediately hit the renate/cordate problem, if there was a world in which all and only the green things happened to be square. How could Frege then distinguish the green from the square? Compare Idea 8245. |
| 4710 | Verificationism was attacked by the deniers of the analytic-synthetic distinction, needed for 'facts' [O'Grady] |
| Full Idea: Verificationism came under attack from empiricists who were friendly to the banishment of traditional metaphysics, but unfriendly to the analytic-synthetic distinction, on which the idea of a 'factual statement' depended. | |
| From: Paul O'Grady (Relativism [2002], Ch.3) | |
| A reaction: I don't accept this move because I don't consider the 'facts' to be language-dependent. They are pre-linguistic, they outrun that capacity of our language, and they are available to animals. |
| 4717 | If we abandon the analytic-synthetic distinction, scepticism about meaning may be inevitable [O'Grady] |
| Full Idea: There may be no way to avoid scepticism about meaning if you abandon the analytic-synthetic distinction in the way Quine does. | |
| From: Paul O'Grady (Relativism [2002], Ch.3) | |
| A reaction: My suspicion was always that Quine's proposal began the slippery road to hell. It appears to be pragmatists who are most drawn to Quine's idea. The proposal that all my analytic propositions could be treated as synthetic totally baffles me. |
| 4706 | Early Quine says all beliefs could be otherwise, but later he said we would assume mistranslation [O'Grady] |
| Full Idea: In his earlier work, Quine defended the view that no belief (including logic) is in principle unrevisable, but in his later work (1970) he took the conservative view that we would always impute mistranslation rather than deviancy. | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: I take it he was influenced by Davidson's 'principle of charity'. He says that if someone asserts 'p and not-p', we would assume a misunderstanding of 'and' or 'not'. |
| 4734 | Cryptographers can recognise that something is a language, without translating it [O'Grady] |
| Full Idea: It makes sense to think that one could recognise that something is a language without necessarily being able to translate it; cryptographers do this all the time. | |
| From: Paul O'Grady (Relativism [2002], Ch.5) | |
| A reaction: Maybe, but cryptographers usually have a lot of context to work with. If we met extraterrestrials if might not be so clear. One can only spot patterns, and crystals have those. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 4727 | The chief problem for fideists is other fideists who hold contrary ideas [O'Grady] |
| Full Idea: The chief problem for fideists is other fideists who hold contrary ideas. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: The other problem is trying to find grounds for sticking to the object of one's faith, rather than changing from time to time. |