77 ideas
| 15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
| Full Idea: Fand P as 'will' and 'was', G as 'always going to be', H as 'always has been', all tenses reduce to 14 cases: the past series, each implying the next, FH,H,PH,HP,P,GP, and the future series PG,G,FG,GF,F,HF, plus GH=HG implying all, FP=PF which all imply. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.8) | |
| A reaction: I have tried to translate the fourteen into English, but am not quite confident enough to publish them here. I leave it as an exercise for the reader. |
| 15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
| Full Idea: In temporal logic, if the converse Barcan formula holds then nothing goes out of existence, and the direct Barcan formula holds if nothing ever comes into existence. These results highlight the intuitive absurdity of the Barcan formulas. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.9) | |
| A reaction: This is my reaction to the modal cases as well - the absurdity of thinking that no actually nonexistent thing might possibly have existed, or that the actual existents might not have existed. Williamson seems to be the biggest friend of the formulas. |
| 9449 | The plausible Barcan formula implies modality in the actual world [Bird] |
| Full Idea: Modality in the actual world is the import of the Barcan formula, and there are good reasons for accepting the Barcan formula. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 1.2) | |
| A reaction: If you thought logic was irrelevant to metaphysics, this should make you think twice. |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| Full Idea: From one point of view intuitionistic logic is a part of classical logic, missing one axiom, from another classical logic is a part of intuitionistic logic, missing two connectives, intuitionistic v and → | |
| From: John P. Burgess (Philosophical Logic [2009], 6.4) |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| Full Idea: The question of the completeness of the full intuitionistic logic for its intended interpretation is not yet fully resolved. | |
| From: John P. Burgess (Philosophical Logic [2009], 6.9) |
| 15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
| Full Idea: The relevantist logician's → is perhaps expressible by 'if A, then B, for that reason'. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.8) |
| 15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
| Full Idea: Among the more technically oriented a 'logic' no longer means a theory about which forms of argument are valid, but rather means any formalism, regardless of its applications, that resembles original logic enough to be studied by similar methods. | |
| From: John P. Burgess (Philosophical Logic [2009], Pref) | |
| A reaction: There doesn't seem to be any great intellectual obligation to be 'technical'. As far as pure logic is concerned, I am very drawn to the computer approach, since I take that to be the original dream of Aristotle and Leibniz - impersonal precision. |
| 15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
| Full Idea: There are topics of great philosophical interest that classical logic neglects because they are not important to mathematics. …These include distinctions of past, present and future, or of necessary, actual and possible. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.1) |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
| Full Idea: The Cut rule (from A|-B and B|-C, infer A|-C) directly expresses the classical doctrine that entailment is transitive. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| Full Idea: Classical logic neglects counterfactual conditionals for the same reason it neglects temporal and modal distinctions, namely, that they play no serious role in mathematics. | |
| From: John P. Burgess (Philosophical Logic [2009], 4.1) | |
| A reaction: Science obviously needs counterfactuals, and metaphysics needs modality. Maybe so-called 'classical' logic will be renamed 'basic mathematical logic'. Philosophy will become a lot clearer when that happens. |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| Full Idea: Philosophical logic is a branch of logic, a technical subject. …Its centre of gravity today lies in theoretical computer science. | |
| From: John P. Burgess (Philosophical Logic [2009], Pref) | |
| A reaction: He firmly distinguishes it from 'philosophy of logic', but doesn't spell it out. I take it that philosophical logic concerns metaprinciples which compare logical systems, and suggest new lines of research. Philosophy of logic seems more like metaphysics. |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
| Full Idea: When formalising arguments it is convenient to have as many connectives as possible available.; but when proving results about formulas it is convenient to have as few as possible. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: Illuminating. The fact that you can whittle classical logic down to two (or even fewer!) connectives warms the heart of technicians, but makes connection to real life much more difficult. Hence a bunch of extras get added. |
| 15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
| Full Idea: Gricean implicature theory might suggest that a disjunction is never assertable when a disjunct is (though actually the disjunction might be 'pertinent') - but the procedure is indispensable in mathematical practice. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.2) | |
| A reaction: He gives an example of a proof in maths which needs it, and an unusual conversational occasion where it makes sense. |
| 15409 | All occurrences of variables in atomic formulas are free [Burgess] |
| Full Idea: All occurrences of variables in atomic formulas are free. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.7) |
| 15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
| Full Idea: By contrast to rigidly designating proper names, …the denotation of definite descriptions is (in general) not rigid but flexible. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.9) | |
| A reaction: This modern way of putting it greatly clarifies why Russell was interested in the type of reference involved in definite descriptions. Obviously some descriptions (such as 'the only person who could ever have…') might be rigid. |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| Full Idea: There are atomic formulas, and formulas built from the connectives, and that is all. We show that all formulas have some property, first for the atomics, then the others. This proof is 'induction on complexity'; we also use 'recursion on complexity'. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: That is: 'induction on complexity' builds a proof from atomics, via connectives; 'recursion on complexity' breaks down to the atomics, also via the connectives. You prove something by showing it is rooted in simple truths. |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
| Full Idea: It might be wondered how one could have any kind of proof procedure at all if transitivity of entailment is disallowed, but the sequent calculus can get around the difficulty. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) | |
| A reaction: He gives examples where transitivity of entailment (so that you can build endless chains of deductions) might fail. This is the point of the 'cut free' version of sequent calculus, since the cut rule allows transitivity. |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| Full Idea: Instead of demonstrations which are either axioms, or follow from axioms by rules, we can have one ever-growing sequence of formulas of the form 'Axioms |- ______', where the blank is filled by Axioms, then Lemmas, then Theorems, then Corollaries. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) |
| 15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
| Full Idea: The valid formulas of classical sentential logic are called 'tautologically valid', or simply 'tautologies'; with other logics 'tautologies' are formulas that are substitution instances of valid formulas of classical sentential logic. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.5) |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| Full Idea: Validity (truth by virtue of logical form alone) and demonstrability (provability by virtue of logical form alone) have correlative notions of logical possibility, 'satisfiability' and 'consistency', which come apart in some logics. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.3) |
| 15412 | Models leave out meaning, and just focus on truth values [Burgess] |
| Full Idea: Models generally deliberately leave out meaning, retaining only what is important for the determination of truth values. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.2) | |
| A reaction: This is the key point to hang on to, if you are to avoid confusing mathematical models with models of things in the real world. |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| Full Idea: In practice there is no need to consider any but mathematical models, models whose universes consist of mathematical objects, since every model is isomorphic to one of these. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.8) | |
| A reaction: The crucial link is the technique of Gödel Numbering, which can translate any verbal formula into numerical form. He adds that, because of the Löwenheim-Skolem theorem only subsets of the natural numbers need be considered. |
| 15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
| Full Idea: The aim in setting up a model theory is that the technical notion of truth in all models should agree with the intuitive notion of truth in all instances. A model is supposed to represent everything about an instance that matters for its truth. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.2) |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| Full Idea: It is a common view that the liar sentence ('This very sentence is not true') is an instance of a truth-value gap (neither true nor false), but some dialethists cite it as an example of a truth-value glut (both true and false). | |
| From: John P. Burgess (Philosophical Logic [2009], 5.7) | |
| A reaction: The defence of the glut view must be that it is true, then it is false, then it is true... Could it manage both at once? |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
| A reaction: The sequence is 'Cauchy' if N exists. |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
| A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
| A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
| A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
| A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
| A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
| A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
| A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
| 9501 | If all existents are causally active, that excludes abstracta and causally isolated objects [Bird] |
| Full Idea: If one says that 'everything that exists is causally active', that rules out abstracta (notably sets and numbers), and it rules out objects that are causally isolated. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.5) | |
| A reaction: I like the principle. I take abstracta to be brain events, so they are causally active, within highly refined and focused brains, and if your physics is built on the notion of fields then I would think a 'causally isolated' object incoherent. |
| 9500 | If naturalism refers to supervenience, that leaves necessary entities untouched [Bird] |
| Full Idea: If one's naturalistic principles are formulated in terms of supervenience, then necessary entities are left untouched. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.5) | |
| A reaction: I take this to be part of the reason why some people like supervenience - that it leaves a pure 'space of reasons' which is unreachable from the flesh and blood inside a cranium. Personall I like the space of reasons, but I drop the 'pure'. |
| 9502 | There might be just one fundamental natural property [Bird] |
| Full Idea: The thought that there might be just one fundamental natural property is not that strange. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 6.3) | |
| A reaction: A nice variation on the Parmenides idea that only the One exists. Bird's point would refer to a possible unification of modern physics. We see, for example, the forces of electricity and of magnetism turning out to be the same force. |
| 9477 | Categorical properties are not modally fixed, but change across possible worlds [Bird] |
| Full Idea: Categorical properties do not have their dispositional characters modally fixed, but may change their dispositional characters (and their causal and nomic behaviour more generally) across different worlds. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1) | |
| A reaction: This is the key ground for Bird's praiseworth opposition to categorical propertie. I take it to be a nonsense to call the category in which we place something a 'property' of that thing. A confusion of thought with reality. |
| 9490 | The categoricalist idea is that a property is only individuated by being itself [Bird] |
| Full Idea: In the categoricalist view, the essential properties of a natural property are limited to its essentially being itself and not some distinct property. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.1) | |
| A reaction: He associates this view with Lewis (modern regularity view) and Armstrong (nomic necessitation), and launches a splendid attack against it. I have always laughed at the idea that 'being Socrates' was one of the properties of Socrates. |
| 9495 | If we abstractly define a property, that doesn't mean some object could possess it [Bird] |
| Full Idea: The possibility of abstract definition does not show that we have defined a property that we can know, independently of any theory, that it is physically possible for some object to possess. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.3.1) | |
| A reaction: This is a naturalist resisting the idea that there is no more to a property than set-membership. I strongly agree. We need a firm notion of properties as features of the actual world; anything else should be called something like 'categorisations'. |
| 9492 | Categoricalists take properties to be quiddities, with no essential difference between them [Bird] |
| Full Idea: The categoricalist conception of properties takes them to be quiddities, which are primitive identities between fundamental qualities, having no difference with regard to their essence. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.5) | |
| A reaction: Compare 'haecceitism' about indentity of objects, though 'quidditism' sounds even less plausible. Bird attributes this view to Lewis and Armstrong, and makes it sound well daft. |
| 9503 | To name an abundant property is either a Fregean concept, or a simple predicate [Bird] |
| Full Idea: It isn't clear what it is to name an abundant property. One might reify them, as akin to Fregean concepts, or it might be equivalent to a simple predication. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 7.1.2) | |
| A reaction: 'Fregean concepts' would make them functions that purely link things (hence relational?). One suspects that people who actually treat abundant properties as part of their ontology (Lewis) are confusing natural properties with predicates. |
| 14540 | Only real powers are fundamental [Bird, by Mumford/Anjum] |
| Full Idea: Bird says only real powers are fundamental. | |
| From: report of Alexander Bird (Nature's Metaphysics [2007]) by S.Mumford/R.Lill Anjum - Getting Causes from Powers 1.5 | |
| A reaction: They disagree, and want higher-level properties in their ontology. I'm with Bird, except that something must exist to have the powers. Powers are fundamental to all the activity of nature, and are intrinsic to the stuff which constitutes nature. |
| 9450 | If all properties are potencies, and stimuli and manifestation characterise them, there is a regress [Bird] |
| Full Idea: Potencies are characterized in terms of their stimulus and manifestation properties, then if potencies are the only properties then these properties are also potencies, and must be characterized by yet further properties, leading to a vicious regress. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 1.2) | |
| A reaction: This is cited as the most popular objection to the dispositional account of properties. |
| 9498 | The essence of a potency involves relations, e.g. mass, to impressed force and acceleration [Bird] |
| Full Idea: The essence of a potency involves a relation to something else; if inertial mass is a potency then its essence involves a relation to a stimulus property (impressed force) and a manifestation property (acceleration). | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.3.3) | |
| A reaction: It doesn't seem quite right to say that the relations are part of the essence, if they might not occur, but some other relations might happen in their place. An essence is what makes a relation possible (like being good-looking). |
| 9474 | A disposition is finkish if a time delay might mean the manifestation fizzles out [Bird] |
| Full Idea: Finkish dispositions arise because the time delay between stimulus and manifestation provides an opportunity for the disposition to go out of existence and so halt the process that would bring about the manifestation. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.2.3) | |
| A reaction: This is a problem for the conditional analysis of dispositions; there may be a disposition, but it never reaches manifestation. Bird rightly points us towards actual powers rather than dispositions that need manifestation. |
| 9475 | A robust pot attached to a sensitive bomb is not fragile, but if struck it will easily break [Bird] |
| Full Idea: If a robust iron pot is attached to a bomb with a sensitive detonator. If the pot is struck, the bomb will go off, so they counterfactual 'if the pot were struck it would break' is true, but it is not a fragile pot. This is a 'mimic' of the disposition. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.2.5.1) | |
| A reaction: A very nice example, showing that a true disposition would have to be an internal feature (a power) of the pot itself, not a mere disposition to behave. The problem is these pesky empiricists, who want to reduce it all to what is observable. |
| 9499 | Megarian actualists deny unmanifested dispositions [Bird] |
| Full Idea: The Megarian actualist denies that a disposition can exist without being manifested. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 5.4) | |
| A reaction: I agree with Bird that this extreme realism seems wrong. As he puts it (p.109), "unrealized possibilities must be part of the actual world". This commitment is beginning to change my understanding of the world I am looking at. |
| 9486 | Why should a universal's existence depend on instantiation in an existing particular? [Bird] |
| Full Idea: An instantiation condition seems to be a failure of nerve as regards realism about universals. If universals really are entities in their own right, why should their existence depend upon a relationship with existing particulars? | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.2.2) | |
| A reaction: I like this challenge, which seems to leave fans of universals no option but full-blown Platonism, which most of them recognise as being deeply implausible. |
| 9472 | Resemblance itself needs explanation, presumably in terms of something held in common [Bird] |
| Full Idea: The realist view of resemblance nominalism is that it is resemblance that needs explaining. When there is resemblance it is natural to want to explain it, in terms of something held in common. Explanations end somewhere, but not with resemblance. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.1.2) | |
| A reaction: I smell a regress. If a knife and a razor resemble because they share sharpness, you have to see that the sharp phenomenon falls within the category of 'sharpness' before you can make the connection, which is spotting its similarity. |
| 9482 | If the laws necessarily imply p, that doesn't give a new 'nomological' necessity [Bird] |
| Full Idea: It does not add to the kinds of necessity to say that p is 'nomologically necessary' iff (the laws of nature → p) is metaphysically necessary. That trick of construction could be pulled for 'feline necessity' (true in all worlds that contain cats). | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1.2) | |
| A reaction: I love it! Bird seems to think that the only necessity is 'metaphysical' necessity, true in all possible worlds, and he is right. The question arises in modal logic, though, of the accessibility between worlds (which might give degrees of necessity?). |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| Full Idea: There is a problem over 'de re' modality (as contrasted with 'de dicto'), as in ∃x□x. What is meant by '"it is analytic that Px" is satisfied by a', given that analyticity is a notion that in the first instance applies to complete sentences? | |
| From: John P. Burgess (Philosophical Logic [2009], 3.9) | |
| A reaction: This is Burgess's summary of one of Quine's original objections. The issue may be a distinction between whether the sentence is analytic, and what makes it analytic. The necessity of bachelors being unmarried makes that sentence analytic. |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| Full Idea: To the extent that there is any conventional wisdom about the question, it is that S5 is correct for alethic logical modality, and S4 correct for apodictic logical modality. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.8) | |
| A reaction: In classical logic these coincide, so presumably one should use the minimum system to do the job, which is S4 (?). |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| Full Idea: Logical necessity is a genus with two species. For classical logic the truth-related notion of validity and the proof-related notion of demonstrability, coincide - but they are distinct concept. In some logics they come apart, in intension and extension. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.3) | |
| A reaction: They coincide in classical logic because it is sound and complete. This strikes me as the correct approach to logical necessity, tying it to the actual nature of logic, rather than some handwavy notion of just 'true in all possible worlds'. |
| 9481 | Logical necessitation is not a kind of necessity; George Orwell not being Eric Blair is not a real possibility [Bird] |
| Full Idea: I do not regard logical necessitation as a kind of necessity. It is logically possible that George Orwell is not Eric Blair, but in what sense is this any kind of possibility? It arises from having two names, but that confers no genuine possibility. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1.2) | |
| A reaction: How refreshing. All kinds of concepts like this are just accepted by philosophers as obvious, until someone challenges them. The whole undergrowth of modal thinking needs a good flamethrower taken to it. |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| Full Idea: Three main theories of the truth of indicative conditionals are Materialism (the conditions are the same as for the material conditional), Idealism (identifying assertability with truth-value), and Nihilism (no truth, just assertability). | |
| From: John P. Burgess (Philosophical Logic [2009], 4.3) |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| Full Idea: It is contentious whether conditionals have negations, and whether 'it is not the case that if A,B' has any clear meaning. | |
| From: John P. Burgess (Philosophical Logic [2009], 4.9) | |
| A reaction: This seems to be connected to Lewis's proof that a probability conditional cannot be reduced to a single proposition. If a conditional only applies to A-worlds, it is not surprising that its meaning gets lost when it leaves that world. |
| 9505 | Empiricist saw imaginability and possibility as close, but now they seem remote [Bird] |
| Full Idea: Whereas the link between imaginability and possibility was once held, under the influence of empiricism, to be close, it is now widely held to be very remote. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 8) | |
| A reaction: Tim Williamson nicely argues the opposite - that assessment of possibility is an adjunct of our ability to think counterfactually, which is precisely an operation of the imagination. Big error is possible, but how else could we do it? |
| 9491 | Haecceitism says identity is independent of qualities and without essence [Bird] |
| Full Idea: The core of haecceitism is the view that the transworld identity of particulars does not supervene on their qualitative features. ...The simplest expression of it is that particulars lack essential properties. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.1) | |
| A reaction: This seems to be something the 'bare substratum' account of substance (associated with Locke). You are left with the difficulty of how to individuate an instance of the haecceity, as opposed to the bundle of properties attached to it. |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
| A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
| 9487 | We can't reject all explanations because of a regress; inexplicable A can still explain B [Bird] |
| Full Idea: Some regard the potential regress of explanations as a reason to think that the very idea of explanation is illusory. This is a fallacy; it is not a necessary condition on A's explaining B that we have an explanation for A also. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.2.4) | |
| A reaction: True, though to say 'B is explained by A, but A is totally baffling' is not the account we are dreaming of. And the explanation would certainly fail if we could say nothing at all about A, apart from naming it. |
| 9493 | We should explain causation by powers, not powers by causation [Bird] |
| Full Idea: The notion of 'causal power' is not to be analysed in terms of causation; if anything, the relationship is the reverse. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.1 n71) | |
| A reaction: It is a popular view these days to take causation as basic (as opposed to the counterfactual account), but I prefer this view. If anything is basic in nature, it is the dynamic force in the engine room, which is the active powers of substances. |
| 9494 | Singularism about causes is wrong, as the universals involved imply laws [Bird] |
| Full Idea: While singularists about causation might think that a particular has its causal powers independently of law, it is difficult to see how a universal could have or confer causal powers without generating what we would naturally think of as a law. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.2.1 n71) | |
| A reaction: This is a middle road between the purely singularist account (Anscombe) and the fully nomological account. We might say that a caused event will be 'involved in law-like behaviour', without attributing the cause to a law. |
| 9507 | Laws are explanatory relationships of things, which supervene on their essences [Bird] |
| Full Idea: The laws of a domain are the fundamental, general explanatory relationships between kinds, quantities, and qualities of that domain, that supervene upon the essential natures of those things. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 10.1) | |
| A reaction: This is the scientific essentialist view of laws [see entries there, in 'Laws of Nature']. There seems uncertainty between 'kinds' and 'qualities' (with 'quantities' looking like a category mistake). I vote, with Ellis, for natural kinds as the basis. |
| 9488 | Laws are either disposition regularities, or relations between properties [Bird] |
| Full Idea: Instead of viewing laws as regular relationships between dispositional properties and stimulus-manifestation, they can be conceived of as a relation between properties. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.4) | |
| A reaction: Bird offers these as the two main views, with the first coming from scientific essentialism, and the second from Armstrong's account of universals. Personally I favour the first, but Bird suggests that powers give the best support for both views. |
| 9496 | That other diamonds are hard does not explain why this one is [Bird] |
| Full Idea: The fact that some other diamonds are hard does not explain why this diamond is hard. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 4.3.2) | |
| A reaction: A very nice aphorism! It pinpoints the whole error of trying to explain the behaviour of the world by citing laws. Why should this item obey that law? Bird prefers 'powers', and so do I. |
| 9479 | Dispositional essentialism says laws (and laws about laws) are guaranteed regularities [Bird] |
| Full Idea: For the regularity version of dispositional essentialism about laws, laws are those regularities whose truth is guaranteed by the essential dispositional nature of one or more of the constituents. Regularities that supervene on such laws are also laws. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.1.2) | |
| A reaction: Even if you accept necessary behaviour resulting from essential dispositions, you still need to distinguish the important regularities from the accidental ones, so the word 'guarantee' is helpful, even if it raises lots of difficulties. |
| 9473 | Laws cannot offer unified explanations if they don't involve universals [Bird] |
| Full Idea: Laws, or what flow from them, are supposed to provide a unified explanation of the behaviours of particulars. Without universals the explanation of the behaviours of things lacks the required unity. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 2.1.2) | |
| A reaction: Sounds a bit question-begging? Gravity seems fairly unified, whereas the frequency of London buses doesn't. Maybe I could unify bus-behaviour by positing a few new universals? The unity should first be in the phenomena, not in the explanation. |
| 9484 | If the universals for laws must be instantiated, a vanishing particular could destroy a law [Bird] |
| Full Idea: If universals exist only where and when they are instantiated, this make serious trouble for the universals view of laws. It would be most odd if a particular, merely by changing its properties, could cause a law to go out of existence. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.2.2) | |
| A reaction: This sounds conclusive. He notes that this is probably why Armstrong does not adopt this view (though Lowe seems to favour it). Could there be a possible property (and concomitant law) which was never ever instantiated? |
| 9506 | Salt necessarily dissolves in water, because of the law which makes the existence of salt possible [Bird] |
| Full Idea: We cannot have a world where it is true both that salt exists (which requires Coulomb's Law to be true), and that it fails to dissolve in water (which requires Coulomb's Law to be false). So the dissolving is necessary even if the Law is contingent. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 8.2) | |
| A reaction: Excellent. It is just like the bonfire on the Moon (imaginable through ignorance, but impossible). People who assert that the solubility of salt is contingent tend not to know much about chemistry. |
| 23713 | Most laws supervene on fundamental laws, which are explained by basic powers [Bird, by Friend/Kimpton-Nye] |
| Full Idea: According to Bird, non-fundamental laws supervene on fundamental laws, and so are ultimately explained by fundamental powers. | |
| From: report of Alexander Bird (Nature's Metaphysics [2007]) by Friend/Kimpton-Nye - Dispositions and Powers 3.6.1 | |
| A reaction: This looks like the picture I subscribe to. Roughly, fundamental laws are explained by powers, and non-fundamental laws are explained by properties, which are complexes of powers. 'Fundamental' may not be a precise term! |
| 9489 | Essentialism can't use conditionals to explain regularities, because of possible interventions [Bird] |
| Full Idea: The straightforward dispositional essentialist account of laws by subjunctive conditionals is false because dispositions typically suffer from finks and antidotes. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 3.4) | |
| A reaction: [Finks and antidotes intervene before a disposition can take effect] This seems very persuasive to me, and shows why you can't just explain laws as counterfactual or conditional claims. Explanation demands what underlies them. |
| 9504 | The relational view of space-time doesn't cover times and places where things could be [Bird] |
| Full Idea: The obvious problem with the simple relational view of space and time is that it fails to account for the full range of spatio-temporal possibility. There seem to be times and places where objects and events could be, but are not. | |
| From: Alexander Bird (Nature's Metaphysics [2007], 7.3.2) | |
| A reaction: This view seems strongly supported by intuition. I certainly don't accept the views of physicists and cosmologists on the subject, because they seem to approach the whole thing too instrumentally. |