77 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. |
| 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? |
| 1708 | In "Callias is just/not just/unjust", which of these are contraries? [Aristotle] |
| Full Idea: Take, for example, "Callias is just", "Callias is not just", and "Callias is unjust"; which of these are contraries? | |
| From: Aristotle (On Interpretation [c.330 BCE], 23a31) |
| 1703 | It is necessary that either a sea-fight occurs tomorrow or it doesn't, though neither option is in itself necessary [Aristotle] |
| Full Idea: It is not necessary for a sea-battle to take place tomorrow, nor for one not to take place tomorrow - though it is necessary for one to take place OR not take place tomorrow. | |
| From: Aristotle (On Interpretation [c.330 BCE], 19a30) |
| 1704 | Statements are true according to how things actually are [Aristotle] |
| Full Idea: Statements are true according to how things actually are. | |
| From: Aristotle (On Interpretation [c.330 BCE], 19a33) |
| 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. |
| 22272 | Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates' [Potter on Aristotle] |
| Full Idea: When Aristotle moved from basic name+verb (in 'De Interpretatione') to noun+noun logic...names had to be treated as special cases, so that 'Socrates' is treated as short for 'everything that is Socrates'. | |
| From: comment on Aristotle (On Interpretation [c.330 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Supp' | |
| A reaction: Just the sort of rewriting that Russell introduced for definite descriptions. 'Twas ever the logicians' fate to shoehorn ordinary speech into awkward containers. |
| 9405 | Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values [Aristotle] |
| Full Idea: Square of Opposition: horizontals - 'contraries' can't both be true, and 'subcontraries' can't both be false; verticals - 'subalternatives' have downwards-only implication; diagonals - 'contradictories' have opposite truth values. | |
| From: Aristotle (On Interpretation [c.330 BCE], Ch.12-13) | |
| A reaction: This is still used in modern discussion (e.g. by Stalnaker against Kripke), and there is a modal version of it (Fitting and Mendelsohn p.7). Corners read: 'All F are G', 'No F are G', 'Some F are G' and 'Some F are not G'. |
| 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. |
| 9728 | Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 1: 'It is necessary that P' and 'It is not possible that not P' are the contraries (not both true) of 'It is necessary that not P' and 'It is not possible that P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12a) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 9729 | Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 2: 'It is not necessary that not P' and 'It is possible that P' are the subcontraries (not both false) of 'It is not necessary that P' and 'It is possible that not P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12b) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 9730 | Modal Square 3: □P and ¬◊¬P are 'contradictories' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 3: 'It is necessary that P' and 'It is not possible that not P' are the contradictories (different truth values) of 'It is not necessary that P' and 'It is possible that not P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12c) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 9731 | Modal Square 4: □¬P and ¬◊P are 'contradictories' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 4: 'It is necessary that not P' and 'It is not possible that P' are the contradictories (different truth values) of 'It is not necessary that not P' and 'It is possible that P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12d) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 9732 | Modal Square 5: □P and ¬◊¬P are 'subalternatives' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 5: 'It is necessary that P' and 'It is not possible that not P' are the subalternatives (first implies second) of 'It is not necessary that not P' and 'It is possible that P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12e) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 9733 | Modal Square 6: □¬P and ¬◊P are 'subalternatives' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 6: 'It is necessary that not P' and 'It is not possible that P' are the subalternatives (first implies second) of 'It is not necessary that P' and 'It is possible that not P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12f) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 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. |
| 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. |
| 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) |
| 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. |
| 21593 | In talking of future sea-fights, Aristotle rejects bivalence [Aristotle, by Williamson] |
| Full Idea: Unlike Aristotle, Stoics did not reject Bivalence for future contingencies; it is true or false that there will be a sea-fight tomorrow. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], 19a31) by Timothy Williamson - Vagueness 1.2 | |
| A reaction: I'd never quite registered this simple account of the sea-fight. As Williamson emphasises, one should not lightly reject the principle of bivalence. Has Aristotle entered a slippery slope? Stoics disagreed with Aristotle. |
| 1701 | A prayer is a sentence which is neither true nor false [Aristotle] |
| Full Idea: A prayer is a sentence which is neither true nor false. | |
| From: Aristotle (On Interpretation [c.330 BCE], 17a01) |
| 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? |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 1706 | Non-existent things aren't made to exist by thought, because their non-existence is part of the thought [Aristotle] |
| Full Idea: It is not true to say that what is not, since it is thought about, is something that is; for what is thought about it is not that it is, but that it is not. | |
| From: Aristotle (On Interpretation [c.330 BCE], 21a31) | |
| A reaction: At least there has been one philosopher who was quite clear about the distinction between a thought and what the thought is about (its content). Often forgotten! |
| 1707 | Maybe necessity and non-necessity are the first principles of ontology [Aristotle] |
| Full Idea: Perhaps the necessary and non-necessary are first principles of everything's either being or not being. | |
| From: Aristotle (On Interpretation [c.330 BCE], 23a18) |
| 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. |
| 12132 | Indiscernibility is a necessary and sufficient condition for identity [Brody] |
| Full Idea: Enduring objects should be taken as fundamental in an ontology, and for all such objects indiscernibility is both a necessary and sufficient condition for identity. | |
| From: Baruch Brody (Identity and Essence [1980], 3) | |
| A reaction: Brody offers a substantial defence, but I don't find it plausible. Apart from Black's well known twin spheres example (Idea 10195), discernibility is relative to the powers of the observer. Two similar people in the mist aren't thereby identical. |
| 15834 | Brody bases sortal essentialism on properties required throughout something's existence [Brody, by Mackie,P] |
| Full Idea: Brody bases sortal essentialism on the notion of a property that an individual must possess throughout its existence if it possesses it at any time in its existence. | |
| From: report of Baruch Brody (Identity and Essence [1980]) by Penelope Mackie - How Things Might Have Been 7.1 | |
| A reaction: Brody tends to treat categories as properties, which I dislike. How do you assess 'must' here? A person may possess a mole throughout life without it being essential. |
| 12140 | Modern emphasis is on properties had essentially; traditional emphasis is on sort-defining properties [Brody] |
| Full Idea: The modern emphasis has been on the connection between essential properties and the properties that an object must have essentially. But traditionally there is also the connection between essential properties and the sort of thing that it is. | |
| From: Baruch Brody (Identity and Essence [1980], 5.6) | |
| A reaction: These are the modal essence and the definitional essence. My view is that he has missed out a crucial third (Aristotelian) view, which is that essences are explanatory. This third view can subsume the other two. |
| 11895 | A sortal essence is a property which once possessed always possessed [Brody, by Mackie,P] |
| Full Idea: Brody bases sortal essentialism on the notion of a property that an individual must possess throughout its existence if it possesses it at any time in its existence. ...'Once an F, always an F'. ...Being a parrot is not a temporary occupation. | |
| From: report of Baruch Brody (Identity and Essence [1980]) by Penelope Mackie - How Things Might Have Been 7.1 | |
| A reaction: Hm. Would being less than fifty metres tall qualify as a sortal essence, for a giraffe or a uranium rod? If there is one thing an essential property should be, it is important. How do we assess importance? By explanatory power! Watch this space. |
| 12141 | Maybe essential properties are those which determine a natural kind? [Brody] |
| Full Idea: We can advance the thesis that all essential properties either determine a natural kind or are part of an essential property that does determine a natural kind. | |
| From: Baruch Brody (Identity and Essence [1980]) | |
| A reaction: A useful clear statement of the view. I am opposed to it, because I take it to be of the essence of Socrates that he is philosophical, but humans are not essentially philosophical, and philosophers are unlikely to be a natural kind. |
| 12137 | De re essentialism standardly says all possible objects identical with a have a's essential properties [Brody] |
| Full Idea: To say that an object a has a property P essentially is to say that it has P, and in all of certain worlds (all possible, all in which something identical with it exists, ...) the object identical with it has P. This is the standard de re interpretation. | |
| From: Baruch Brody (Identity and Essence [1980], 5.4) | |
| A reaction: This view always has to be qualified by excluding trivially necessary properties, but that exclusion shows clearly that the notion of essential is more concerned with non-triviality than it is with necessity. |
| 12142 | Essentially, a has P, always had P, must have had P, and has never had a future without P [Brody] |
| Full Idea: 'a has property P essentially' means 'a has P, a always had P, there is no possible past in which P exists without P, and there is no moment of time at which a has had P and at which there is a possible future in which a exists without P' | |
| From: Baruch Brody (Identity and Essence [1980], 6) | |
| A reaction: This is Brody's own final account of essentialism. This is a carefully qualified form of the view that essential properties are, on the whole, the necessary properties, which view I take to be fundamentally mistaken. |
| 12143 | An object having a property essentially is equivalent to its having it necessarily [Brody] |
| Full Idea: An object having a property essentially is equivalent to its having it necessarily. | |
| From: Baruch Brody (Identity and Essence [1980], 6.1) | |
| A reaction: This strikes me as blatantly false. Personally I am toying with the very unorthodox view that essential properties are not at all necessary, and that something can retain its identity while changing its essential character. A philosopher with Alzheimers. |
| 12144 | Essentialism is justified if the essential properties of things explain their other properties [Brody] |
| Full Idea: The reasonableness of the essentialist hypothesis will be proportional to the extent that we can, as a result, use a's possession of P to explain a's other properties, ...and there is an inability to explain otherwise why a has P. | |
| From: Baruch Brody (Identity and Essence [1980], 6.3) | |
| A reaction: Brody as a rather liberal notion of properties. I would hope that we can do rather more than explain a's non-essential properties. If the non-essential properties were entailed by the essential ones, would they not then also be essential? |
| 12139 | Mereological essentialism says that every part that ensures the existence is essential [Brody] |
| Full Idea: Mereological essentialism (whose leading advocate is Chisholm) says that for every x and y, if x is ever part of y, then y is necessarily such that x is part of y at any time that y exists. | |
| From: Baruch Brody (Identity and Essence [1980], 5.6) | |
| A reaction: This sounds implausible, especially given the transitivity of parthood. Not only are the planks that constitute Theseus's Ship now essential to it, but all the parts of the planks, every last chip, are as well. |
| 12135 | Interrupted objects have two first moments of existence, which could be two beginnings [Brody] |
| Full Idea: If 'beginning of existence' meant 'first moment of existence after a period of nonexistence', then objects with interrupted existence have two beginnings of existence. | |
| From: Baruch Brody (Identity and Essence [1980], 4.1) | |
| A reaction: One might still maintain that the first beginning was essential to the object, since that is the event that defined it - and that would clarify the reason why we are supposed to think the origins are essential. I say the origin explains it. |
| 12130 | a and b share all properties; so they share being-identical-with-a; so a = b [Brody] |
| Full Idea: Suppose that a and b have all of their properties in common. a certainly has the property of-being-identical-with-a. So, by supposition, does b. Then a = b. | |
| From: Baruch Brody (Identity and Essence [1980], 1.2) | |
| A reaction: Brody defends this argument, and seems to think that it proves the identity of indiscernibles. As far as I can see it totally begs the question, since we can only assume that both have the property of being-identical-with-a if we have assumed a = b. |
| 12138 | Identity across possible worlds is prior to rigid designation [Brody] |
| Full Idea: Identity across possible worlds is prior to rigid designation. | |
| From: Baruch Brody (Identity and Essence [1980], 5.4) | |
| A reaction: An interesting view. We might stipulate that any possible Aristotle is 'our Aristotle', but you would still need criteria for deciding which possible Aristotle's would qualify. Long-frozen Aristotles, stupid Aristotles, alien Aristotle's, deformed... |
| 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. |
| 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. |
| 2337 | For Aristotle meaning and reference are linked to concepts [Aristotle, by Putnam] |
| Full Idea: In 'De Interpretatione' Aristotle laid out an enduring theory of reference and meaning, in which we understand a word or any other sign by associating that word with a concept. This concept determines what the word refers to. | |
| From: report of Aristotle (On Interpretation [c.330 BCE]) by Hilary Putnam - Representation and Reality 2 p.19 | |
| A reaction: Sounds right to me, despite all this Wittgensteinian stuff about beetles in boxes. When you meet a new technical term in philosophy, you must struggle to fully grasp the concept it proposes. |
| 13763 | Spoken sounds vary between people, but are signs of affections of soul, which are the same for all [Aristotle] |
| Full Idea: Spoken sounds are symbols of affections in the soul, ...and just as written marks are not the same for all men, neither are spoken sounds. But what these are in the first place signs of - affections of the soul - are the same for all. | |
| From: Aristotle (On Interpretation [c.330 BCE], 16a03-08) | |
| A reaction: Loux identifies this passage as the source of the 'conceptualist' view of propositions, which I immediately identify with. The view that these propositions are 'the same for all' is plausible for normal objects, but dubious for complex abstractions. |
| 1705 | It doesn't have to be the case that in opposed views one is true and the other false [Aristotle] |
| Full Idea: It is not necessary that of every affirmation and opposite negation one should be true and the other false. For what holds for things that are does not hold for things that are not but may possibly be or not be. | |
| From: Aristotle (On Interpretation [c.330 BCE], 19a39) | |
| A reaction: Thus even if Bivalence holds, and the only truth-values are T and F, it doesn't follow that Excluded Middle holds, which says that every proposition must have one of those two values. |
| 1702 | Things may be necessary once they occur, but not be unconditionally necessary [Aristotle] |
| Full Idea: To say that everything that is, is of necessity, when it is, is not the same as saying unconditionally that it is of necessity. | |
| From: Aristotle (On Interpretation [c.330 BCE], 19a25) |