59 ideas
| 12027 | There must be a plausible epistemological theory alongside any metaphysical theory [Forbes,G] |
| Full Idea: No metaphysical account which renders it impossible to give a plausible epistemological theory is to be countenanced. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 9.1) | |
| A reaction: It is hard to object to this principle, though we certainly don't want to go verificationist, and thus rule out speculations about metaphysics which are beyond any possible knowledge. Some have tried to prove that something must exist (e.g. Jacquette). |
| 12005 | The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G] |
| Full Idea: We use the symbol 'ι' (Greek 'iota') to form definite descriptions, reading (ιx)F(x) as 'the x which is such that F(x)', or simply as 'the F'. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 4.1) | |
| A reaction: Compare the lambda operator in modal logic, which picks out predicates from similar formulae. |
| 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
| Full Idea: The best known axiomatization of PL is Whitehead/Russell. There are four axioms: (p∨p)→p, q→(p∨q), (p→q)→(q∨p), and (q→r)→((p∨q)→(p∨r)), plus Substitution and Modus Ponens rules. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by GE Hughes/M Cresswell - An Introduction to Modal Logic Ch.1 |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| Full Idea: The axiom of Reducibility ...is crucial in the reduction of classes to logic, ...and seems to be a quite legitimate logical notion for Russell. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 6.4 | |
| A reaction: This is an unusual defence of the axiom, which is usually presumed to have been kicked into the long grass by Quine. If one could reduce classes to logic, that would destroy the opposition to logicism in a single neat coup. |
| 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell adduces two reasons against the extensional view of classes, namely the existence of the null class (which cannot very well be a collection), and the unit classes (which would have to be identical with their single elements). | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Structure and Ontology p.459 | |
| A reaction: Gödel believes in the reality of classes. I have great sympathy with Russell, when people start to claim that sets are not just conveniences to help us think about things, but actual abstract entities. Is the singleton of my pencil is on this table? |
| 18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
| Full Idea: Classes, so far as we introduce them, are merely symbolic or linguistic conveniences, not genuine objects. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.72), quoted by Penelope Maddy - Naturalism in Mathematics III.2 |
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| Full Idea: Russell call 'if...then' implication, when the material conditional is a much better account; C.I.Lewis (in founding modern modal logic) preserved Russell's confusion by creating 'strict implication', and called that implication. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Willard Quine - Reply to Professor Marcus p.177 | |
| A reaction: [A compession of Quine's paragraph]. All of this assumes that logicians can give an accurate account of what if...then means, when ordinary usage is broad and vague. Strict implication seems to drain all the normal meaning out of 'if...then'. |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| Full Idea: In Mr Russell's idea of implication, if twenty random sentences from a newspaper were put in a hat, and two of them drawn at random, one will certainly imply the other, and it is an even bet the implication will be mutual. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by C.I. Lewis - A Pragmatic Conception of the A Priori p.366 | |
| A reaction: This sort of lament leads modern logicians to suggest 'relevance' as an important criterion. It certainly seems odd that so-called 'classical logic' should contain a principle so at variance with everyday reasoning. |
| 21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
| Full Idea: Russell did not view logic as an uninterpreted calculus awaiting interpretations [the modern view]. Rather, logic is a single 'interpreted' body of a priori truths, of propositions rather than sentence forms - but maximally general and topic neutral. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 1 | |
| A reaction: This is the view which Wittgenstein challenged, saying logic is just conventional. Linsky claims that Russell's logicism is much more plausible, once you understand his view of logic. |
| 12010 | Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G] |
| Full Idea: The typical semantic account of validity for propositional connectives like 'and' presupposes that meaning is given by truth-tables. On the natural deduction view, the meaning of 'and' is given by its introduction and elimination rules. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 4.4) |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| Full Idea: In 'Principia' a young science was enriched with a new abstract theory of relations, ..and not only Cantor's set theory but also ordinary arithmetic and the theory of measurement are treated from this abstract relational standpoint. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 | |
| A reaction: I presume this is accounting for relations in terms of ordered sets. |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| Full Idea: For Russell the real number 2 is the class of rationals less than 2 (i.e. 2/1). ...Notice that on this definition, real numbers are classes of rational numbers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| Full Idea: Although Russell takes numbers to be certain classes, his 'no-class' theory then eliminates all mention of classes in favour of the 'propositional functions' that define them; and in the case of the numbers these just are the numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by David Bostock - Philosophy of Mathematics 9.B.4 |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| Full Idea: Russell and Whitehead took arithmetic to be higher-order logic, ..and came close to identifying numbers with numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.148 | |
| A reaction: The point here is 'higher-order'. |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| Full Idea: Unlike Frege, Russell and Whitehead were not realists about mathematical objects, and whereas Frege thought that only arithmetic and analysis are branches of logic, they think the vast majority of mathematics (including geometry) is essentially logical. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: If, in essence, Descartes reduced geometry to algebra (by inventing co-ordinates), then geometry ought to be included. It is characteristic of Russell's hubris to want to embrace everything. |
| 10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
| Full Idea: What is missing, above all, in 'Principia', is a precise statement of the syntax of the formalism. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 |
| 10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
| Full Idea: Russell and Whitehead's ramified theory of types worked not with sets, but with propositional functions (similar to Frege's concepts), with a more restrictive assignment of variables, insisting that bound, as well as free, variables be of lower type. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.3 | |
| A reaction: I don't fully understand this (and no one seems much interested any more), but I think variables are a key notion, and there is something interesting going on here. I am intrigued by ordinary language which behaves like variables. |
| 8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
| Full Idea: The Russell/Whitehead type theory reduces mathematics to a consistent founding discipline, but is criticised for not really being logic. They could not prove the existence of infinite sets, and introduced a non-logical 'axiom of reducibility'. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.6 | |
| A reaction: To have reduced most of mathematics to a founding discipline sounds like quite an achievement, and its failure to be based in pure logic doesn't sound too bad. However, it seems to reduce some maths to just other maths. |
| 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
| Full Idea: In the system of 'Principia Mathematica', it is not only the axioms of infinity and reducibility which go beyond pure logic, but also the initial conception of a universal domain of individuals and of a domain of predicates. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.267) by Paul Bernays - On Platonism in Mathematics p.267 | |
| A reaction: This sort of criticism seems to be the real collapse of the logicist programme, rather than Russell's paradox, or Gödel's Incompleteness Theorems. It just became impossible to stick strictly to logic in the reduction of arithmetic. |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| Full Idea: Russell and Whitehead are particularly careful to avoid paradox, and consider the paradoxes to indicate that we create mathematical reality. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: This strikes me as quite a good argument. It is certainly counterintuitive that reality, and abstractions from reality, would contain contradictions. The realist view would be that we have paradoxes because we have misdescribed the facts. |
| 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell insisted on the vicious circle principle, and thus rejected impredicative definitions, which resulted in an unwieldy ramified type theory, with the ad hoc axiom of reducibility. Ramsey's simpler theory was impredicative and avoided the axiom. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 | |
| A reaction: Nowadays the theory of types seems to have been given up, possibly because it has no real attraction if it lacks the strict character which Russell aspired to. |
| 12023 | Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G] |
| Full Idea: It is very plausible that the sorites paradoxes arose from the application of a semantic apparatus appropriate only for sharp predicates to languages containing vague predicates (rather than from deficiency of meaning, or from incoherence). | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 7.3) | |
| A reaction: Sounds wrong. Of course, logic has been designed for sharp predicates, and natural languages are awash with vagueness. But the problems of vagueness bothered lawyers long before logicians like Russell began to worry about it. |
| 12017 | In all instances of identity, there must be some facts to ensure the identity [Forbes,G] |
| Full Idea: For each instance of identity or failure of identity, there must be facts in virtue of which that instance obtains. ..Enough has been said to lend this doctrine some plausibility. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 5.5) | |
| A reaction: Penelope Mackie picks this out from Forbes as a key principle. It sounds to be in danger of circularity, unless the 'facts' can be cited without referring to, or implicitly making use of, identities - which seems unlikely. |
| 12024 | If we combined two clocks, it seems that two clocks may have become one clock. [Forbes,G] |
| Full Idea: If we imagine a possible world in which two clocks in a room make one clock from half the parts of each, the judgement 'these two actual clocks could have been a single clock' does not seem wholly false. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 7.4) | |
| A reaction: You would, of course, have sufficient parts left over to make a second clock, so they look like a destroyed clock, so I don't think I find Forbes's intuition on this one very persuasive. |
| 11885 | Only individual essences will ground identities across worlds in other properties [Forbes,G, by Mackie,P] |
| Full Idea: Forbes argues that, unless we posit individual essences, we cannot guarantee that identities across possible worlds will be appropriately grounded in other properties. | |
| From: report of Graeme Forbes (The Metaphysics of Modality [1985]) by Penelope Mackie - How Things Might Have Been 2.4 | |
| A reaction: There is a confrontation between Wiggins, who says identity is primitive, and Forbes, who says identity must be grounded in other properties. I think I side with Forbes. |
| 12014 | An individual essence is a set of essential properties which only that object can have [Forbes,G] |
| Full Idea: An individual essence of an object x is a set of properties I which satisfies the following conditions: i. every property P in I is an essential property of x; ii. it is not possible that some object y distinct from x has every member of I. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 5.1) | |
| A reaction: I am coming to the view that stable natural kinds (like electrons or gold) do not have individual essences, but complex kinds (like tigers or tables) do. The view is based on the idea that explanatory power is what individuates an essence. |
| 12015 | Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G] |
| Full Idea: A non-trivial individual essence is properties other than a) those following from a de dicto truth, b) properties of existence and self-identity (or their cognates), c) properties derived from necessities in some other category. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 5.1) | |
| A reaction: [I have compressed Forbes] Rather than adding all these qualificational clauses to our concept, we could just tighten up on the notion of a property, saying it is something which is causally efficacious, and hence explanatory. |
| 12013 | Essential properties depend on a category, and perhaps also on particular facts [Forbes,G] |
| Full Idea: The essential properties of a thing will typically depend upon what category of thing it is, and perhaps also on some more particular facts about the thing itself. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 5.1) | |
| A reaction: I see no way of dispensing with the second requirement, in the cases of complex entities like animals. If all samples are the same, then of course we can define a sample's essence through its kind, but not if samples differ in any way. |
| 13804 | A property is essential iff the object would not exist if it lacked that property [Forbes,G] |
| Full Idea: A property P is an essential property of an object x iff x could not exist and lack P, that is, as they say, iff x has P at every world at which x exists. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 1) | |
| A reaction: This immediately places the existence of x outside the normal range of its properties, so presumably 'existence is not a predicate', but that dictum may be doubted. As it stands this definition will include trivial and vacuous properties. |
| 13805 | Properties are trivially essential if they are not grounded in a thing's specific nature [Forbes,G] |
| Full Idea: Essential properties may be trivial or nontrivial. It is characteristic of P's being trivially essential to x that x's possession of P is not grounded in the specific nature of x. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 2) | |
| A reaction: This is where my objection to the modal view of essence arises. How is he going to explain 'grounded' and 'specific nature' without supplying an entirely different account of essence? |
| 12012 | Essential properties are those without which an object could not exist [Forbes,G] |
| Full Idea: An essential property of an object x is a property without possessing which x could not exist. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 5.1) | |
| A reaction: This is certainly open to question. See Joan Kung's account of Aristotle on essence. I am necessarily more than eight years old (now), and couldn't exist without that property, but is the property part of my essence? |
| 13808 | A relation is essential to two items if it holds in every world where they exist [Forbes,G] |
| Full Idea: A relation R is essential to x and y (in that order) iff Rxy holds at every world where x and y both exist. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 2) | |
| A reaction: I find this bizarre. Not only does this seem to me to have nothing whatever to do with essence, but also the relation might hold even though it is a purely contingent matter. All rabbits are a reasonable distance from the local star. Essence of rabbit? |
| 13806 | Trivially essential properties are existence, self-identity, and de dicto necessities [Forbes,G] |
| Full Idea: The main groups of trivially essential properties are (a) existence, self-identity, or their consequences in S5; and (b) properties possessed in virtue of some de dicto necessary truth. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 2) | |
| A reaction: He adds 'extraneously essential' properties, which also strike me as being trivial, involving relations. 'Is such that 2+2=4' or 'is such that something exists' might be necessary, but they don't, I would say, have anything to do with essence. |
| 13807 | A property is 'extraneously essential' if it is had only because of the properties of other objects [Forbes,G] |
| Full Idea: P is 'extraneously essential' to x iff it is possessed by x at any world w only in virtue of the possession at w of certain properties by other objects. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 2) | |
| A reaction: I would say that these are the sorts of properties which have nothing to do with being essential, even if they are deemed to be necessary. |
| 12022 | Same parts does not ensure same artefact, if those parts could constitute a different artefact [Forbes,G] |
| Full Idea: Sameness of parts is not sufficient for identity of artefacts at a world, since the very same parts may turn up at different times as the parts of artefacts with different designs and functions. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 7.2) | |
| A reaction: Thus the Ship of Theseus could be dismantled and turned into a barn (as happened with the 'Mayflower'). They could then be reconstituted as the ship, which would then have two beginnings (as Chris Hughes has pointed out). |
| 12025 | Artefacts have fuzzy essences [Forbes,G] |
| Full Idea: Artefacts can be ascribed fuzzy essences. ...We might say that it is essential to an artefact to have 'most' of its parts. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 7.6) | |
| A reaction: I think I prefer to accept the idea that essences are unstable things, in all cases. For all we know, electrons might subtly change their general character, or cease to be uniform, tomorrow. Essences explain, and what needs explaining changes. |
| 13809 | One might be essentialist about the original bronze from which a statue was made [Forbes,G] |
| Full Idea: In the case of artefacts, there is an essentialism about original matter; for instance, it would be said of any particular bronze statue that it could not have been cast from a totally different quantity of bronze. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 3) | |
| A reaction: Forbes isn't endorsing this, and it doesn't sound convincing. He quotes the thought 'I wish I had made this pot from a different piece of clay'. We might corrupt a statue by switching bronze, but I don't think the sculptor could do so. |
| 12020 | An individual might change their sex in a world, but couldn't have differed in sex at origin [Forbes,G] |
| Full Idea: In the time of a single world, the same individual can undergo a change of sex, but it is less clear that an individual of one sex could have been, from the outset, an individual of another. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 6.5) | |
| A reaction: I don't find this support for essentiality of origin very persuasive. I struggle with these ideas. Given my sex yesterday, then presumably I couldn't have had a different sex yesterday. Given that pigs can fly, pigs can fly. What am I missing? |
| 11888 | Identities must hold because of other facts, which must be instrinsic [Forbes,G, by Mackie,P] |
| Full Idea: Forbes has two principles of identity, which we can call the No Bare Identities Principle (identities hold in virtue of other facts), and the No Extrinsic Determination Principle (that only intrinsic facts of a thing establish identity). | |
| From: report of Graeme Forbes (The Metaphysics of Modality [1985], 127-8) by Penelope Mackie - How Things Might Have Been 2.7 | |
| A reaction: The job of the philosopher is to prise apart the real identities of things from the way in which we conceive of identities. I take these principles to apply to real identities, not conceptual identities. |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| Full Idea: Trivially, the Identity of Indiscernibles says that two individuals, Castor and Pollux, cannot have all properties in common. For Castor must have the properties of being identical with Castor and not being identical with Pollux, which Pollux can't share. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913], I p.57) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 2 | |
| A reaction: I suspect that either the property of being identical with itself is quite vacuous, or it is parasytic on primitive identity, or it is the criterion which is actually used to define identity. Either way, I don't find this claim very illuminating. |
| 12003 | De re modal formulae, unlike de dicto, are sensitive to transworld identities [Forbes,G] |
| Full Idea: The difference between de re and de dicto formulae is a difference between formulae which are, and formulae which are not, sensitive to the identities of objects at various worlds. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 3.1) |
| 12028 | De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G] |
| Full Idea: De re necessity does not differ from de dicto necessity in respect of how it arises: it is still a form of conceptual necessity. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 9.4) | |
| A reaction: [Forbes proceeds to argue for this claim] Forbes defends a form of essentialism, but takes the necessity to arise from a posteriori truths because of the a priori involvement of other concepts (rather as Kripke argues). |
| 13810 | The source of de dicto necessity is not concepts, but the actual properties of the thing [Forbes,G] |
| Full Idea: It is widely held that the source of de dicto necessity is in concepts, ..but I deny this... even with simple de dicto necessities, the source of the necessity is to be found in the properties to which the predicates of the de dicto truth refer. | |
| From: Graeme Forbes (In Defense of Absolute Essentialism [1986], 3) | |
| A reaction: It is normal nowadays to say this about de re necessities, but this is more unusual. |
| 12008 | Unlike places and times, we cannot separate possible worlds from what is true at them [Forbes,G] |
| Full Idea: There is no means by which we might distinguish a possible world from what is true at it. ...Whereas our ability to separate a place, or a time, from its occupier is crucial to realism about places and times, as is a distance relation. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 4.2) | |
| A reaction: He is objecting to Lewis's modal realism. I'm not fully convinced. It depends whether we are discussing real ontology or conceptual space. In the latter I see no difference between times and possible worlds. In ontology, a 'time' is weird. |
| 12009 | The problem with possible worlds realism is epistemological; we can't know properties of possible objects [Forbes,G] |
| Full Idea: The main objection to realism about worlds is from epistemology. Knowledge of properties of objects requires experience of these objects, which must be within the range of our sensory faculties, but only concrete actual objects achieve that. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 4.2) | |
| A reaction: This pinpoints my dislike of the whole possible worlds framework, ontologically speaking. I seem to be an actualist. I take possibilities to be inferences to the best explanation from the powers we know of in the actual world. We experience potentiality. |
| 12007 | Possible worlds are points of logical space, rather like other times than our own [Forbes,G] |
| Full Idea: Someone impressed by the parallel between tense and modal operators ...might suggest that just as we can speak of places and times forming their own manifolds or spaces, so we can say that worlds are the points of logical space. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 4.2) | |
| A reaction: I particularly like the notion of worlds being "points of logical space", and am inclined to remove it from this context and embrace it as the correct way to understand possible worlds. We must understand logical or conceptual space. |
| 12011 | Transworld identity concerns the limits of possibility for ordinary things [Forbes,G] |
| Full Idea: An elucidation of transworld identity can be regarded as an elucidation of the boundaries of possibility for ordinary things. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 5.1) | |
| A reaction: I presume that if we don't search for some such criterion, we just have to face the possibility that Aristotle could have been a poached egg in some possible world. To know the bounds of possibility, study the powers of actual objects. |
| 12016 | The problem of transworld identity can be solved by individual essences [Forbes,G] |
| Full Idea: The motivation for investigating individual essences should be obvious, since if every object has such an essence, the problem of elucidating transworld identity can be solved. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 5.1) | |
| A reaction: It is important that, if necessary, the identities be 'individual', and not just generic, by sortal, or natural kind. We want to reason about (and explain) truths at the fine-grained level of the individual, not just at the broad level of generalisation. |
| 12004 | Counterpart theory is not good at handling the logic of identity [Forbes,G] |
| Full Idea: The outstanding technical objection to counterpart-theoretic semantics concerns its handling of the logic of identity. In quantified S5 (the orthodox semantics) a = b → □(a = b) is valid, but 'a' must not attach to two objects. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 3.5) |
| 12021 | Haecceitism attributes to each individual a primitive identity or thisness [Forbes,G] |
| Full Idea: Haecceitism attributes to each individual a primitive identity or thisness, as opposed to the sort of essentialism that gives non-trivial conditions sufficient for transworld identity. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 6.6) | |
| A reaction: 'Haecceitism' is the doctrine that things have primitive identity. A 'haecceity' is a postulated property which actually does the job. The key point of the view is that whatever it is is 'primitive', and not complex, or analysable. I don't believe it. |
| 12029 | We believe in thisnesses, because we reject bizarre possibilities as not being about that individual [Forbes,G] |
| Full Idea: The natural response to an unreasonable hypothesis of possibility for an object x, that in such a state of affairs it would not be x which satisfies the conditions, is evidence that we do possess concepts of thisness for individuals. | |
| From: Graeme Forbes (The Metaphysics of Modality [1985], 9.4) | |
| A reaction: We may have a 'concept' of thisness, but we needn't be committed to the 'existence' of a thisness. There is a fairly universal intuition that cessation of existence of an entity when it starts to change can be a very vague matter. |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| Full Idea: By analyzing the paradoxes to which Cantor's set theory had led, ..Russell brought to light the amazing fact that our logical intuitions (concerning such notions as truth, concept, being, class) are self-contradictory. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.452 | |
| A reaction: The main intuition that failed was, I take it, that every concept has an extension, that is, there are always objects which will or could fall under the concept. |
| 21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
| Full Idea: The multiple relations theory of judgement proposes that assertions about propositions are dependent upon genuine facts involving belief and other attitude relations, subjects of those attitudes, and the constituents of the belief. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
| A reaction: This seems to require a commitment to universals (especially relations) with which we can be directly acquainted. I prefer propositions, but as mental entities, not platonic entities. |
| 23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
| Full Idea: When a judgement occurs, there is a certain complex entity, composed of the mind and the various objects of the judgement. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44) | |
| A reaction: This is Russell's multiple-relation theory of judgement, which replaced his earlier belief in unified propositions (now 'false abstractions'). He seems to have accepted Locke's view, that the act of judgement produces the unity. |
| 23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus | |
| A reaction: Morris says this is Russell's multiple-relations theory of judgement. The theory accompanies the rejection of the concept of the unified proposition. When I hear 'Socrates had a mole on his shoulder' I get the meaning without judging. |
| 23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
| Full Idea: When Russell moved to his multiple relation theory of judgement …he then faced difficulties making sense of the unity of sentences. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.44) by Michael Morris - Guidebook to Wittgenstein's Tractatus 3A | |
| A reaction: Roughly, he seems committed to saying that there is only unity if you think there is unity; there is no unity in a sentence prior to the act of judgement. |
| 18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging, and we no longer have an incomplete symbol. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap | |
| A reaction: Personally I would have thought that you needed to know the meaning properly before you could make the judgement, but then he is Bertrand Russell and I'm not. |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
| Full Idea: A 'proposition', in the sense in which a proposition is supposed to be the object of a judgement, is a false abstraction, because a judgement has several objects, not one. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus 2E | |
| A reaction: This is the rejection of the 'Russellian' theory of propositions, in favour of his multiple-relations theory of judgement. But why don't the related objects add up to a proposition about a state of affairs? |
| 20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
| Full Idea: Hesiod reckons envy among the effects of the good and benevolent Eris, and there was nothing offensive in according envy to the gods. ...Likewise the Greeks were different from us in their evaluation of hope: one felt it to be blind and malicious. | |
| From: report of Hesiod (works [c.700 BCE]) by Friedrich Nietzsche - Dawn (Daybreak) 038 | |
| A reaction: Presumably this would be understandable envy, and unreasonable hope. Ridiculous envy can't possibly be good, and modest and sensible hope can't possibly be bad. I suspect he wants to exaggerate the relativism. |