72 ideas
| 13395 | If an analysis shows the features of a concept, it doesn't seem to 'reduce' the concept [Jubien] |
| Full Idea: An analysis of a concept tells us what the concept is by telling us what its constituents are and how they are combined. ..The features of the concept are present in the analysis, making it surprising the 'reductive' analyses are sought. | |
| From: Michael Jubien (Possibility [2009], 4.5) | |
| A reaction: He says that there are nevertheless reductive analyses, such as David Lewis's analysis of modality. We must disentangle conceptual analysis from causal analysis (e.g. in his example of the physicalist reduction of mind). |
| 14684 | A world is 'accessible' to another iff the first is possible according to the second [Salmon,N] |
| Full Idea: A world w' is accessible to a consistent world w if and only if w' is possible in w. Being 'inaccessible to' or 'possible relative to' a consistent world is simply being possible according to that world, nothing more and nothing less. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
| A reaction: More illuminating than just saying that w can 'see' w'. Accessibility is internal to worIds. It gives some connection to why we spend time examining modal logic. There is no more important metaphysical notion than what is possible according to actuality. |
| 14669 | For metaphysics, T may be the only correct system of modal logic [Salmon,N] |
| Full Idea: Insofar as modal logic is concerned exclusively with the logic of metaphysical modality, ..T may well be the one and only (strongest) correct system of (first-order) propositional logic. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) | |
| A reaction: This contrasts sharply with the orthodox view, that S5 (or at the very least S4) is the correct system for metaphysics. |
| 14667 | System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N] |
| Full Idea: Even the conventionally accepted system B, which is weaker than S5 and independent of S4, has not been adequately justified as a fallacy-free system of reasoning about what might have been. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) |
| 14668 | In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N] |
| Full Idea: The characteristic of B has the form φ⊃□◊φ. ...Even if these axioms are necessarily true, it seems logically possible for p to be true while the proposition that p is necessarily possible is at the same time false. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) |
| 14692 | System B implies that possibly-being-realized is an essential property of the world [Salmon,N] |
| Full Idea: Friends of B modal logic commit themselves to the loaded claim that it is logically true that the property of possibly being realized (or being a way things might have been) is an essential property of the world. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], V) | |
| A reaction: I think this 'loaded' formulation captures quite nicely the dispositional view I favour, that the possibilities of the actual world are built into the actual world, and define its nature just as much as the 'categorial' facts do. |
| 14671 | What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N] |
| Full Idea: We can say of a wooden table that it would have been possible for it to have originated from some different matter, even though it is not actually possible. So what is necessary fails to be necessarily necessary, and S4 modal logic is fallacious. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], I) | |
| A reaction: [compressed] |
| 14686 | S5 modal logic ignores accessibility altogether [Salmon,N] |
| Full Idea: When we ignore accessibility altogether, we have finally zeroed in on S5 modal logic. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) |
| 14691 | S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N] |
| Full Idea: Believers in S5 as a correct system of propositional reasoning about what might have been must claim that it is an essential property of any way things might have been that things might have been that way. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], V) | |
| A reaction: Salmon is working in a view where you are probably safe to substitute 'necessary' for 'essential' without loss of meaning. |
| 14693 | The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N] |
| Full Idea: Counterpart-theoretic modal semantics allows for the retention of S5 modal propositional logic, at a considerable cost. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], V n18) | |
| A reaction: See the other ideas in this paper by Salmon for his general attack on S5 as the appropriate system for metaphysical necessity. He favours the very modest System T. |
| 14670 | Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N] |
| Full Idea: Metaphysical modal logic concerns metaphysical (or alethic) necessity and metaphysical (alethic) possibility, or necessity and possibility tout court - as opposed to such other types of modality as physical necessity, epistemic necessity etc. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro n2) |
| 13378 | It is a mistake to think that the logic developed for mathematics can clarify language and philosophy [Jubien] |
| Full Idea: It has often been uncritically assumed that logic that was initially a tool for clarifying mathematics could be seamlessly and uniformly applied in the effort to clarify ordinary language and philosophy, but this has been a real mistake. | |
| From: Michael Jubien (Possibility [2009], Intro) | |
| A reaction: I'm not saying he's right (since you need stupendous expertise to make that call) but my intuitions are that he has a good point, and he is at least addressing a crucial question which most analytical philosophers avert their eyes from. |
| 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. |
| 13402 | We only grasp a name if we know whether to apply it when the bearer changes [Jubien] |
| Full Idea: We cannot be said to have a full grasp of a name unless we have a definite disposition to apply it or to withhold it under whatever conceivable changes the bearer of the name might come to undergo. | |
| From: Michael Jubien (Possibility [2009], 5.3) | |
| A reaction: This is right, and an excellent counterproposal to the logicians' notion that names have to rigidly designate. As a bare minimum, you are not supposed to deny the identity of your parents because they have grown a bit older, or a damaged painting. |
| 13405 | The baptiser picks the bearer of a name, but social use decides the category [Jubien] |
| Full Idea: The person who introduces a proper name gets to pick its bearer, but its category - and consequently the meaning of the name - is determined by social use. | |
| From: Michael Jubien (Possibility [2009], 7) | |
| A reaction: New 'division of labour'. The idea that a name has some sort of meaning seems right and important. If babies were switched after baptism, social use might fix the name to the new baby. The namer could stipulate the category at the baptism. Too neat. |
| 13399 | Examples show that ordinary proper names are not rigid designators [Jubien] |
| Full Idea: There are plenty of examples to show that ordinary proper names simply are not rigid designators. | |
| From: Michael Jubien (Possibility [2009], 5.1) | |
| A reaction: His examples are the planet Venus and the dust of which it is formed, and a statue made of clay. In other words, for some objects, perhaps under certain descriptions (e.g. functional ones), the baptised matter can change. Rigidity is an extra topping. |
| 13398 | We could make a contingent description into a rigid and necessary one by adding 'actual' to it [Jubien] |
| Full Idea: 'The winner of the Derby' satisfies some horse, but only accidentally. But we could 'rigidify' the description by inserting 'actual' into it, giving 'the actual winner of the Derby'. Winning is a contingent property, but actually winning is necessary. | |
| From: Michael Jubien (Possibility [2009], 5.1) | |
| A reaction: I like this unusual proposal because instead of switching into formal logic in order to capture the ideas we are after, he is drawing on the resources of ordinary language, offering philosophers a way of speaking plain English more precisely. |
| 13392 | Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien] |
| Full Idea: There is a readiness of philosophers to 'translate' English, with its seeming multitude of kind-driven quantifiers, into first-order logic, with its single wide-open quantifier. | |
| From: Michael Jubien (Possibility [2009], 4.1) | |
| A reaction: As in example he says that reference to a statue involves a 'statue-quantifier'. Thus we say things about the statue that we would not say about the clay, which would involve a 'clay-quantifier'. |
| 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. |
| 13404 | To exist necessarily is to have an essence whose own essence must be instantiated [Jubien] |
| Full Idea: For a thing to exist necessarily is for it to have an entity-essence whose own entity-essence entails being instantiated. | |
| From: Michael Jubien (Possibility [2009], 6.4) | |
| A reaction: This is the culmination of a lengthy discussion, and is not immediately persuasive. For Jubien the analysis rests on a platonist view of properties, which doesn't help. |
| 13386 | If objects are just conventional, there is no ontological distinction between stuff and things [Jubien] |
| Full Idea: Under the Quinean (conventional) view of objects, there is no ontological distinction between stuff and things. | |
| From: Michael Jubien (Possibility [2009], 1.5) | |
| A reaction: This is the bold nihilistic account of physical objects, which seems to push all of our ontology into language (English?). We could devise divisions into things that were just crazy, and likely to lead to the rapid extinction of creatures who did it. |
| 13403 | The category of Venus is not 'object', or even 'planet', but a particular class of good-sized object [Jubien] |
| Full Idea: The category of Venus is not 'physical object' or 'mereological sum', but narrower. Surprisingly, it is not 'planet', since it might cease to be a planet and still merit the name 'Venus'. It is something like 'well-integrated, good-sized physical object'. | |
| From: Michael Jubien (Possibility [2009], 5.3) | |
| A reaction: Jubien is illustrating Idea 13402. This is a nice demonstration of how one might go about the task of constructing categories - by showing the modal profiles of things to which names have been assigned. Categories are file names. |
| 13375 | The idea that every entity must have identity conditions is an unfortunate misunderstanding [Jubien] |
| Full Idea: The pervasiveness, throughout philosophy, of the assumption that entities of various kinds need identity conditions is one unfortunate aspect of Quine's important philosophical legacy. | |
| From: Michael Jubien (Possibility [2009], Intro) | |
| A reaction: Lowe seems to be an example of a philosopher who habitually demands individuation conditions for everything that is referred to. Presumably the alternative is to take lots of things as primitive, but this seems to be second best. |
| 13393 | Any entity has the unique property of being that specific entity [Jubien] |
| Full Idea: For any entity of any sort, abstract or concrete, I assume there is a property of being that specific entity. For want of a better term, I will call such properties entity-essences. They are 'singulary' - not instantiable by more than one thing at a time. | |
| From: Michael Jubien (Possibility [2009], 4.2) | |
| A reaction: Baffling. Why would someone who has mocked all sorts of bogus philosophical claims based on logic then go on to assert the existence of such weird things as these? I can't make sense of this property being added to a thing's other properties. |
| 13388 | It is incoherent to think that a given entity depends on its kind for its existence [Jubien] |
| Full Idea: It is simply far-fetched - even incoherent - to think that, given an entity, of whatever kind, its being a single entity somehow consists in its satisfying some condition involving the kind to which it belongs (or concepts related to that kind). | |
| From: Michael Jubien (Possibility [2009], 2.3) | |
| A reaction: Well said. I can't see how philosophers have allowed themselves to drift into such a daft view. Kinds blatantly depend on the individuals that constitute them, so how could the identity of the individuals depend on their kind? |
| 13384 | Objects need conventions for their matter, their temporal possibility, and their spatial possibility [Jubien] |
| Full Idea: We need a first convention to determine what matter constitutes objects, then a second to determine whether there are different temporal possibilities for a given object, then a third for different spatial possibilities. | |
| From: Michael Jubien (Possibility [2009], 1.5) | |
| A reaction: This is building up a Quinean account of objects, as mere matter in regions of spacetime, which are then precisely determined by a set of social conventions. |
| 13385 | Basically, the world doesn't have ready-made 'objects'; we carve objects any way we like [Jubien] |
| Full Idea: There is a certain - very mild - sense in which I don't think the physical world comes with ready-made objects. I think instead that we (conventionally) carve it up into objects, and this can be done any way we like. | |
| From: Michael Jubien (Possibility [2009], 1.5) | |
| A reaction: I have no idea how one could begin to refute such a view. Obviously there are divisions (even if only of physical density) in the world, but nothing obliges us to make divisions at those points. We happily accept objects with gaps in them. |
| 13383 | If the statue is loved and the clay hated, that is about the object first qua statue, then qua clay [Jubien] |
| Full Idea: If a sculptor says 'I love the statue but I really hate that piece of clay - it is way too hard to work with' ...the statement is partly is partly about that object qua statue and partly about that object qua piece of clay. | |
| From: Michael Jubien (Possibility [2009], 1.4) | |
| A reaction: His point is that identity is partly determined by the concept or category under which the thing falls. Plausible. Lots of identity muddles seem to come from our conceptual scheme not being quite up to the job when things change. |
| 13400 | If one entity is an object, a statue, and some clay, these come apart in at least three ways [Jubien] |
| Full Idea: A single entity is a physical object, a piece of clay and a statue. We seem to have that the object could be scattered, but not the other two; the object and the clay could be spherical, but not the statue; and only the object could have different matter. | |
| From: Michael Jubien (Possibility [2009], 5.2) | |
| A reaction: His proposal, roughly, is to reduce object-talk to property-talk, and then see the three views of this object as referring to different sets of properties, rather than to a single thing. Promising, except that he goes platonist about properties. |
| 13401 | The idea of coincident objects is a last resort, as it is opposed to commonsense naturalism [Jubien] |
| Full Idea: I find it surprising that some philosophers accept 'coincident objects'. This notion clearly offends against commonsense 'naturalism' about the world, so it should be viewed as a last resort. | |
| From: Michael Jubien (Possibility [2009], 5.2 n9) | |
| A reaction: I'm not quite clear why he invokes 'naturalism', but I pass on his intuition because it seems right to me. |
| 13380 | Parts seem to matter when it is just an object, but not matter when it is a kind of object [Jubien] |
| Full Idea: When thought of just as an object, the parts of a thing seem definitive and their arrangement seems inconsequential. But when thought of as an object of a familiar kind it is reversed: the arrangement is important and the parts are inessential. | |
| From: Michael Jubien (Possibility [2009], 1.4) | |
| A reaction: This is analogous to the Ship of Theseus, where we say that the tour operator and the museum keeper give different accounts of whether it is the same ship. The 'kind' Jubien refers to is most likely to be a functional kind. |
| 13376 | We should not regard essentialism as just nontrivial de re necessity [Jubien] |
| Full Idea: I argue against the widely accepted characterization of the doctrine of 'essentialism' as the acceptance of nontrivial de re necessity | |
| From: Michael Jubien (Possibility [2009], Intro) | |
| A reaction: I agree entirely. The notion of an essence is powerful if clearly distinguished. The test is: can everything being said about essences be just as easily said by referring to necessities? If so, you are talking about the wrong thing. |
| 14678 | Any property is attached to anything in some possible world, so I am a radical anti-essentialist [Salmon,N] |
| Full Idea: By admitting possible worlds of unlimited variation and recombination, I simply abandon true metaphysical essentialism. By my lights, any property is attached to anything in some possible world or other. I am a closet radical anti-essentialist. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], II) | |
| A reaction: Salmon includes impossible worlds within his scheme of understanding. It strikes me that this is metaphysical system which tells us nothing about how things are: it is sort of 'logical idealist'. Later he talks of 'we essentialists'. |
| 13381 | Thinking of them as 'ships' the repaired ship is the original, but as 'objects' the reassembly is the original [Jubien] |
| Full Idea: Thinking about the original ship as a ship, we think we continue to have the 'same ship' as each part is replaced; ...but when we think of them as physical objects, we think the original ship and the outcome of the reassembly are one and the same. | |
| From: Michael Jubien (Possibility [2009], 1.4) | |
| A reaction: It seems to me that you cannot eliminate how we are thinking of the ship as influencing how we should read it. My suggestion is to think of Theseus himself valuing either the repaired or the reassembled version. That's bad for Jubien's account. |
| 13382 | Rearranging the planks as a ship is confusing; we'd say it was the same 'object' with a different arrangement [Jubien] |
| Full Idea: That the planks are rearranged as a ship elevates the sense of mystery, because arrangements matter for ships, but if they had been arranged differently we would have the same intuition - that it still counts as the same object. | |
| From: Michael Jubien (Possibility [2009], 1.4) | |
| A reaction: Implausible. Classic case: can I have my pen back? - smashes it to pieces and hands it over with 'there you are' - that's not my pen! - Jubien says it's the same object! - it isn't my pen, and it isn't the same object either! Where is Shelley's skylark? |
| 13379 | If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien] |
| Full Idea: If a bit of matter has a qualitatively indistinguishable object located at a later time, with a path of spacetime connecting them, how could we determine they are identical? Neither identity nor diversity follows from qualitative indiscernibility. | |
| From: Michael Jubien (Possibility [2009], 1.3) | |
| A reaction: All these principles expounded by Leibniz were assumed to be timeless, but for identity over time the whole notion of things retaining identity despite changing has to be rethought. Essentialism to the rescue. |
| 14680 | Logical possibility contains metaphysical possibility, which contains nomological possibility [Salmon,N] |
| Full Idea: Just as nomological possibility is a special kind of metaphysical possibility, so metaphysical possibility is a special kind of logical possibility. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], III) | |
| A reaction: This is the standard view of how the three types of necessity are nested. He gives a possible counterexample in footnote 7. |
| 14690 | In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N] |
| Full Idea: The S5 theorist's miscontrual of English (in the meaning of 'possibly possible') makes nested modality unseen, but it does not make nested modality vanish. Inaccessible worlds are still worlds. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) |
| 14677 | Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever [Salmon,N] |
| Full Idea: It is held that it is the hallmark of metaphysical necessity is that it is completely unrestricted, the limiting case of restricted necessity, with no restrictions whatever. A proposition is necessary only if it is true in absolutely every world whatever. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], II) | |
| A reaction: This is the standard picture which leads to the claim that S5 modal logic is appropriate for metaphysical necessity, because there are no restrictions on accessibility. Salmon raises objections to this conventional view. |
| 14679 | Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted [Salmon,N] |
| Full Idea: Though there is a way things logically could be according to which I am a credit card account, there is no way things metaphysically might be according to which I am a credit card account. This illustrates the restricted nature of metaphysical modality. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], III) | |
| A reaction: His drift is that metaphyical modality is restricted, but expressing it in S5 modal logic (where all worlds see one another) makes it unrestricted, so S5 logic is wrong for metaphysics. I'm impressed by his arguments. |
| 14688 | Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic [Salmon,N] |
| Full Idea: If one confines one's sights to genuinely possible worlds, disavowing the impossible worlds, then metaphysical modality emerges as the limiting case - the 'unrestricted' modality that takes account of 'every' world - and S5 emerges as its proper logic. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
| A reaction: He observes that this makes metaphysical modality 'restricted' simply because you have restricted what 'all worlds' means. Could there be non-maximal worlds? Are logical and metaphysical modality coextensive? I think I like the S5 view. |
| 14685 | Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted [Salmon,N] |
| Full Idea: A mythology gave us the idea that metaphysical necessity is truth in every world whatsoever, without restriction. But the notion of metaphysical modality comes first, and, like every notion of modality, it is restricted. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) |
| 14681 | Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N] |
| Full Idea: With its freedom from the constraint of metaphysical possibility, logical necessity may be construed as accommodating all the axioms and rules of S5. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], III) | |
| A reaction: He goes on to raise problems for this simple thought. The big question: what are the limits of what is actually possible? Compare: what are the limits of what is imaginable? what are the limits of what is meaningfully sayable? |
| 13394 | Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien] |
| Full Idea: Typically philosophers say that for P to entail Q is for the proposition that all P's are Q's to be necessary. I think this analysis is backwards, and that necessity rests on entailment, not vice versa. | |
| From: Michael Jubien (Possibility [2009], 4.4) | |
| A reaction: His example is that being a horse and being an animal are such that one entails the other. In other words, necessities arise out of property relations (which for Jubien are necessary because the properties are platonically timeless). Wrong. |
| 14676 | Nomological necessity is expressed with intransitive relations in modal semantics [Salmon,N] |
| Full Idea: Intransitive relations are introduced into modal semantics for the purposes of interpreting various 'real' or restricted types of modalities, such as nomological necessity. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], II) | |
| A reaction: The point here is that the (so-called) 'laws of nature' are held to change from world to world, so necessity in one could peter out in some more remote world, rather than being carried over everywhere. A very Humean view of such things. |
| 13391 | Modality concerns relations among platonic properties [Jubien] |
| Full Idea: I think modality has to do with relations involving the abstract part of the world, specifically with relations among (Platonic) properties. | |
| From: Michael Jubien (Possibility [2009], 3.2) | |
| A reaction: [Sider calls Jubien's the 'governance' view, since abstract relations govern the concrete] I take Jubien here (having done a beautiful demolition job on the possible worlds account of modality) to go spectacularly wrong. Modality starts in the concrete. |
| 13374 | To analyse modality, we must give accounts of objects, properties and relations [Jubien] |
| Full Idea: The ultimate analysis of possibility and necessity depends on two important ontological decisions: the choice of an analysis of the intuitive concept of a physical object, and the other is the positing of properties and relations. | |
| From: Michael Jubien (Possibility [2009], Intro) | |
| A reaction: In the same passage he adopts Quine's view of objects, leading to mereological essentialism, and a Platonic view of properties, based on Lewis's argument for taking some things at face value. One might start with processes and events instead. |
| 14689 | Necessity and possibility are not just necessity and possibility according to the actual world [Salmon,N] |
| Full Idea: The real meanings of the simple modal terms 'necessary' and 'possible' are not the same as the concepts of actual necessity and actual possibility, necessity and possibility according to the actual world. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
| A reaction: If you were an 'actualist' (who denies everything except the actual world) then you are unlikely to agree with this. In unrestricted possible worlds, being true in one world makes it possible in all worlds. So actual necessity is possible everywhere. |
| 14674 | Impossible worlds are also ways for things to be [Salmon,N] |
| Full Idea: Total ways things cannot be are also 'worlds', or maximal ways for things to be. They are impossible worlds. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], I) | |
| A reaction: This unorthodox view doesn't sound too plausible to me. To think of a circular square as a 'way things could be' sounds pretty empty, and mere playing with words. The number 7 could be the Emperor of China? |
| 14682 | Denial of impossible worlds involves two different confusions [Salmon,N] |
| Full Idea: Every argument I am aware of against impossible worlds confuses ways for things to be with ways things might have been, or worse, confuses ways things cannot be with ways for things to be that cannot exist - or worse yet, commits both errors. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], III) | |
| A reaction: He is claiming that 'ways for things to be' allows impossible worlds, whereas 'ways things might have been' appears not to. (I think! Read the paragraph yourself!) |
| 14687 | Without impossible worlds, how things might have been is the only way for things to be [Salmon,N] |
| Full Idea: If one ignores impossible worlds, then ways things might have been are the only ways for things to be that are left. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
| A reaction: Impossible worlds are included in 'ways for things to be', but excluded from 'ways things might have been'. I struggle with a circle being square as a 'way for circles to be'. I suppose being the greatest philosopher is a way for me to be. |
| 14683 | Possible worlds rely on what might have been, so they can' be used to define or analyse modality [Salmon,N] |
| Full Idea: On my conception, the notions of metaphysical necessity and possibility are not defined or analyzed in terms of the apparatus of possible worlds. The order of analysis is just the reverse: possible worlds rely on the notion of what might have been. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
| A reaction: This view seems to be becoming the new orthodoxy, and I certainly agree with it. I have no idea how you can begin to talk about possible worlds if you don't already have some idea of what 'possible' means. |
| 13389 | The love of possible worlds is part of the dream that technical logic solves philosophical problems [Jubien] |
| Full Idea: I believe the contemporary infatuation with possible worlds in philosophy stems in part from a tendency to think that technical logic offers silver-bullet solutions to philosophical problems. | |
| From: Michael Jubien (Possibility [2009], 3.2) | |
| A reaction: I would say that the main reason for the infatuation is just novelty. As a technical device it was only invented in the 1960s, so we are in a honeymoon period, as we would be with any new gadget. I can't imagine possible worlds figuring much in 100 years. |
| 13390 | Possible worlds don't explain necessity, because they are a bunch of parallel contingencies [Jubien] |
| Full Idea: The fundamental problem is that in world theory, what passes for necessity is in effect just a bunch of parallel 'contingencies'. | |
| From: Michael Jubien (Possibility [2009], 3.2) | |
| A reaction: Jubien's general complaint is that there is no connection between the possible worlds and the actual world, so they are irrelevant, but this is a nicely different point - that lots of contingent worlds can't add up to necessity. Nice. |
| 14672 | Possible worlds are maximal abstract ways that things might have been [Salmon,N] |
| Full Idea: I conceive of possible worlds as certain sorts of maximal abstract entities according to which certain things (facts, states of affairs) obtain and certain other things do not obtain. They are total ways things might have been. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], I) |
| 14675 | Possible worlds just have to be 'maximal', but they don't have to be consistent [Salmon,N] |
| Full Idea: As far as I can tell, worlds need not be logically consistent. The only restriction on worlds is that they must be (in some sense) 'maximal' ways for things to be. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], I) | |
| A reaction: The normal idea of a maximal model is that it must contain either p or ¬p, and not both, so I don't think I understand this thought, but I pass it on. |
| 14673 | You can't define worlds as sets of propositions, and then define propositions using worlds [Salmon,N] |
| Full Idea: It is not a good idea to think of possible worlds as sets of propositions, and at the same time to think of propositions as sets of possible worlds. | |
| From: Nathan Salmon (The Logic of What Might Have Been [1989], I n3) | |
| A reaction: Salmon favours thinking of worlds as sets of propositions, and hence rejects the account of propositions as sets of worlds. He favours the 'Russellian' view of propositions, which seem to me to be the same as 'facts'. |
| 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. |
| 13396 | Analysing mental concepts points to 'inclusionism' - that mental phenomena are part of the physical [Jubien] |
| Full Idea: We have (physicalist) 'inclusionism' when the mental is included in the physical, and mental phenomena are to be found among physical phenomena. Only inclusionism is compatible with a genuine physicalist analysis of mental concepts. | |
| From: Michael Jubien (Possibility [2009], 4.5) | |
| A reaction: This isn't the thesis of conceptual dualism (which I like), but an interesting accompaniment for it. Jubien is offering this as an alternative to 'reductive' analysis, translating all the mental concepts into physical language. He extends 'physical'. |
| 13377 | First-order logic tilts in favour of the direct reference theory, in its use of constants for objects [Jubien] |
| Full Idea: First-order logic tilts in favor of the direct reference account of proper names by using individual constants to play the intuitive role of names, and by 'interpreting' the constants simply as the individuals that are assigned to them for truth-values. | |
| From: Michael Jubien (Possibility [2009], Intro) | |
| A reaction: This is the kind of challenge to orthodoxy that is much needed at the moment. We have an orthodoxy which is almost a new 'scholasticism', that logic will clarify our metaphysics. Trying to enhance the logic for the job may be a dead end. |