66 ideas
| 6052 | Definitions identify two concepts, so they presuppose identity [McGinn] |
| Full Idea: Any definition must presuppose the notion of identity precisely because a definition affirms the identity of two concepts. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: McGinn is arguing that identity is fundamental to thought, and this seems persuasive. It may be, though, that while identities are inescapable, definitions are impossible. |
| 6064 | Regresses are only vicious in the context of an explanation [McGinn] |
| Full Idea: Regresses are only vicious in the context of some explanatory aim, not in themselves. | |
| From: Colin McGinn (Logical Properties [2000], Ch.2 n11) | |
| A reaction: A nice point. It is not quite clear how 'pure' reason could ever be vicious, or charming, or sycophantic. The problem about a vicious regress is precisely that it fails to explain anything. Now benign regresses are something else… (see Idea 2523) |
| 6088 | Truth is a method of deducing facts from propositions [McGinn] |
| Full Idea: Truth is essentially a method of deducing facts from propositions. | |
| From: Colin McGinn (Logical Properties [2000], Ch.5) | |
| A reaction: Very persuasive. McGinn is offering a disquotational account of truth, but in a robust form. Of course, deduction normally takes the form of moving infallibly from one truth to another, but that model of deduction won't fit this particular proposal. |
| 6084 | 'Snow does not fall' corresponds to snow does fall [McGinn] |
| Full Idea: We can say that the proposition that snow does not fall from the sky corresponds to the fact that snow does fall from the sky - in the sense that there is a mapping from fact to proposition. | |
| From: Colin McGinn (Logical Properties [2000], Ch.5) | |
| A reaction: A very nice difficulty for the correspondence theory. It becomes essential to say how the two things correspond before it can offer any sort of account of the truth-relation. |
| 6085 | The idea of truth is built into the idea of correspondence [McGinn] |
| Full Idea: The correspondence theory has an air of triviality, and hence undeniability, but this is because it implicitly builds the idea of truth into the notion of correspondence. | |
| From: Colin McGinn (Logical Properties [2000], Ch.5) | |
| A reaction: If this is accepted, it is a really fatal objection to the theory. Russell tried to use the idea of 'congruency' between beliefs and reality, but that may be open to the same objection. McGinn is claiming that truth is essentially indefinable. |
| 6083 | The coherence theory of truth implies idealism, because facts are just coherent beliefs [McGinn] |
| Full Idea: If 'snow falls from the sky' is true iff it coheres with other beliefs, this is a form of idealism; snow could surely fall from sky even if there were no beliefs in the world to cohere with each other. | |
| From: Colin McGinn (Logical Properties [2000], Ch.5) | |
| A reaction: The coherence theory of truth strikes me as yet another blunder involving a confusion of ontology and epistemology. Of course, idealism may be true, but I have yet to hear a good reason why I should abandon commonsense realism. |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| Full Idea: Gödel's proof wrought an abrupt turn in the philosophy of mathematics. We had supposed that truth, in mathematics, consisted in provability. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Willard Quine - Forward to Gödel's Unpublished | |
| A reaction: This explains the crisis in the early 1930s, which Tarski's theory appeared to solve. |
| 6086 | Truth is the property of propositions that makes it possible to deduce facts [McGinn] |
| Full Idea: Truth is a property of a proposition from which one can deduce the fact stated by the proposition. | |
| From: Colin McGinn (Logical Properties [2000], Ch.5) | |
| A reaction: This is McGinn's explanation of the disquotational account of truth ('p' is true iff p). The redundancy theorist would reply that you can deduce p from 'p' without mentioning truth, but it remains to ask why this deduction is possible. |
| 6087 | Without the disquotation device for truth, you could never form beliefs from others' testimony [McGinn] |
| Full Idea: Imagine being in a community which had no concept of truth; ..you cannot disquote on p and hence form beliefs about the world as a result of testimony, since you lack the device of disquotation that is the essence of truth. | |
| From: Colin McGinn (Logical Properties [2000], Ch.5) | |
| A reaction: Whether his theory is right or not, the observation that testimony is the really crucial area where we must have a notion of truth is very good. How about 'truth is what turns propositions into beliefs'? |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| Full Idea: Gödel's incompleteness results of 1931 show that all axiom systems precise enough to satisfy Hilbert's conception are necessarily incomplete. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1215 | |
| A reaction: [Hallett italicises 'necessarily'] Hilbert axioms have to be recursive - that is, everything in the system must track back to them. |
| 6051 | In 'x is F and x is G' we must assume the identity of x in the two statements [McGinn] |
| Full Idea: If we say 'for some x, x is F and x is G' we are making tacit appeal to the idea of identity in using 'x' twice here: it has to be the same object that is both F and G. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: This may well be broadened to any utterances whatsoever. The only remaining question is to speculate about whether it is possible to think without identities. The Hopi presumably gave identity to processes rather objects. How does God think? |
| 6055 | Both non-contradiction and excluded middle need identity in their formulation [McGinn] |
| Full Idea: To formulate the law of non-contradiction ('nothing can be both F and non-F') and the law of excluded middle ('everything is either F or it is not-F'), we need the concept of identity (in 'nothing' and 'everything'). | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: Two good examples in McGinn's argument that identity is basic to all thinking. But the argument also works to say that necessity is basic (since both laws claim it) and properties are basic. Let's just declare everything 'basic', and we can all go home. |
| 6059 | Identity is unitary, indefinable, fundamental and a genuine relation [McGinn] |
| Full Idea: I have endorsed four main theses about identity: it is unitary, it is indefinable, it is fundamental, and it is a genuine relation | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: That it is fundamental to our thinking seems certain (but to all possible thought?). That it is a relation looks worth questioning. One might challenge unitary by comparing the identity of numbers, values, electrons and continents. I can't define it. |
| 9175 | We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke] |
| Full Idea: We may fix the reference of 'Cicero' by use of some descriptive phrase, such as 'author of these works'. But once we have this reference fixed, we then use the name 'Cicero' rigidly to designate the man who in fact we have identified by his authorship. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.183) | |
| A reaction: Even supposedly rigid names can shift reference, as Evans's example of 'Madagascar' shows (Idea 9041). Reference is a much more social activity than Kripke is willing to admit. There is a 'tradition' of reference (Dummett) for the name 'Cicero'. |
| 9171 | The function of names is simply to refer [Kripke] |
| Full Idea: The function of names is simply to refer. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.167) | |
| A reaction: This is Kripke reverting to the John Stuart Mill view of names. If I say "you are a right Casanova" I don't simply refer to Casanova. In notorious examples like 'Homer' reference is fine, but the object of reference is a bit elusive. |
| 6067 | Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn] |
| Full Idea: What the existential quantifier does is indicate the quantity of things in question - it says that some are; it is left up to the predicate 'exists' to express existence. | |
| From: Colin McGinn (Logical Properties [2000], Ch.2) | |
| A reaction: This seems right. The whole quantification business seems like a conjuring trick to conceal the embarrassingly indefinable and 'metaphysical' notion of 'existence'. Cf Idea 7697. |
| 6042 | The quantifier is overrated as an analytical tool [McGinn] |
| Full Idea: The quantifier has been overrated as a tool of logical and linguistic analysis. | |
| From: Colin McGinn (Logical Properties [2000], Pref) | |
| A reaction: I find this proposal quite thrilling. Twentieth century analytical philosophy has been in thrall to logic, giving the upper hand in philosophical discussion to the logicians, who are often not very good at philosophy. |
| 6069 | 'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn] |
| Full Idea: We would do much better to call 'some' the 'partial quantifier' (rather than the 'existential quantifier'), on analogy with the universal quantifier - as neither of them logically implies existence. | |
| From: Colin McGinn (Logical Properties [2000], Ch.2) | |
| A reaction: Like McGinn's other suggestions in this chapter, this strikes me as a potentially huge clarification in linguistic analysis. I wait with interest to see whether the philosophical logicians take it up. I bet they don't. |
| 6068 | We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn] |
| Full Idea: We could introduce an 'intentional quantifier' (Ix) which means 'some of the things we talk about..'; we could then say 'some of the things we talk about are F and exist' (Ix, x is F and x exists). | |
| From: Colin McGinn (Logical Properties [2000], Ch.2) | |
| A reaction: This immediately strikes me as a promising contribution to the analytical toolkit. McGinn is supporting his view that existence is a predicate, and so belongs inside the proposition, not outside. |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| Full Idea: The inherent limitations of the axiomatic method were first brought to light by the incompleteness theorems. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Koellner - On the Question of Absolute Undecidability 1.1 |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| Full Idea: Second Incompleteness Theorem: roughly, nice theories that include enough basic arithmetic can't prove their own consistency. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 1.5 | |
| A reaction: On the face of it, this sounds less surprising than the First Theorem. Philosophers have often noticed that it seems unlikely that you could use reason to prove reason, as when Descartes just relies on 'clear and distinct ideas'. |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| Full Idea: Gödel showed PA cannot be proved consistent from with PA. But 'reflection principles' can be added, which are axioms partially expressing the soundness of PA, by asserting what is provable. A Global Reflection Principle asserts full soundness. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Halbach,V/Leigh,G.E. - Axiomatic Theories of Truth (2013 ver) 1.2 | |
| A reaction: The authors point out that this needs a truth predicate within the language, so disquotational truth won't do, and there is a motivation for an axiomatic theory of truth. |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| Full Idea: Where Gödel's First Theorem sabotages logicist ambitions, the Second Theorem sabotages Hilbert's Programme. | |
| From: comment on Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 36 | |
| A reaction: Neo-logicism (Crispin Wright etc.) has a strategy for evading the First Theorem. |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| Full Idea: My undecidable arithmetical sentence ...is not at all absolutely undecidable; rather, one can always pass to 'higher' systems in which the sentence in question is decidable. | |
| From: Kurt Gödel (On Formally Undecidable Propositions [1931]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.1 | |
| A reaction: [a 1931 MS] He says the reals are 'higher' than the naturals, and the axioms of set theory are higher still. The addition of a truth predicate is part of what makes the sentence become decidable. |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| Full Idea: Gödel's far-reaching work on the nature of logic and formal systems reveals that there can be no single consistent theory from which all mathematical truths can be derived. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.8 |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| Full Idea: Gödel's theorem states that either arithmetic is incomplete, or it is inconsistent. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Georges Rey - Contemporary Philosophy of Mind 8.7 |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| Full Idea: First Incompleteness Theorem: any properly axiomatised and consistent theory of basic arithmetic must remain incomplete, whatever our efforts to complete it by throwing further axioms into the mix. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 1.2 | |
| A reaction: This is because it is always possible to formulate a well-formed sentence which is not provable within the theory. |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| Full Idea: The vast continent of arithmetical truth cannot be brought into systematic order by laying down a fixed set of axioms and rules of inference from which every true mathematical statement can be formally derived. For some this was a shocking revelation. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by E Nagel / JR Newman - Gödel's Proof VII.C | |
| A reaction: Good news for philosophy, I'd say. The truth cannot be worked out by mechanical procedures, so it needs the subtle and intuitive intelligence of your proper philosopher (Parmenides is the role model) to actually understand reality. |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| Full Idea: Gödel's Second Incompleteness Theorem says that true unprovable sentences are clearly semantic consequences of the axioms in the sense that they are necessarily true if the axioms are true. So semantic consequence outruns provability. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Robert Hanna - Rationality and Logic 5.3 |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| Full Idea: First Incompleteness Theorem: If S is a sufficiently powerful formal system, then if S is consistent then S is syntactically incomplete. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Gödel found a single sentence, effectively saying 'I am unprovable in S', which is neither provable nor refutable in S. |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| Full Idea: Second Incompleteness Theorem: If S is a sufficiently powerful formal system, then if S is consistent then S cannot prove its own consistency | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems much less surprising than the First Theorem (though it derives from it). It was always kind of obvious that you couldn't use reason to prove that reason works (see, for example, the Cartesian Circle). |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| Full Idea: The original Gödel construction gives us a sentence that a theory shows is true if and only if it satisfies the condition of being unprovable-in-that-theory. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 20.5 |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| Full Idea: An approximation of Gödel's Theorem imagines a statement 'This system of mathematics can't prove this statement true'. If the system proves the statement, then it can't prove it. If the statement can't prove the statement, clearly it still can't prove it. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 | |
| A reaction: Gödel's contribution to this simple idea seems to be a demonstration that formal arithmetic is capable of expressing such a statement. |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| Full Idea: Gödel defended impredicative definitions on grounds of ontological realism. From that perspective, an impredicative definition is a description of an existing entity with reference to other existing entities. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Stewart Shapiro - Thinking About Mathematics 5.3 | |
| A reaction: This is why constructivists must be absolutely precise about definition, where realists only have to do their best. Compare building a car with painting a landscape. |
| 6070 | Existence is a primary quality, non-existence a secondary quality [McGinn] |
| Full Idea: Existence is like a primary quality; non-existence is like a secondary quality. | |
| From: Colin McGinn (Logical Properties [2000], Ch.2 n29) | |
| A reaction: Since McGinn thinks existence really is a property, and hence, presumably, a predicate, I don't quite see why he uses the word "like". A nicely pithy and thought-provoking remark. |
| 6062 | Existence can't be analysed as instantiating a property, as instantiation requires existence [McGinn] |
| Full Idea: Paraphrasing existence statements into statements about the instantiation of a property does not establish that existence is not a predicate, since the notion of instantiation must be taken to have existence built into it. | |
| From: Colin McGinn (Logical Properties [2000], Ch.2) | |
| A reaction: Thank you, Colin McGinn! This now strikes me as so obvious that it is astonishing that for the whole of the twentieth century no one seems to have said it. For a century philosophers had swept the ontological dirt under the mat. |
| 6065 | We can't analyse the sentence 'something exists' in terms of instantiated properties [McGinn] |
| Full Idea: The problems of the orthodox view are made vivid by analysis of the sentence 'something exists'; this is meaningful and true, but what property are we saying is instantiated here? | |
| From: Colin McGinn (Logical Properties [2000], Ch.2) | |
| A reaction: A very nice point. McGinn claims that existence is a property, a very generalised one. Personally I don't think anyone is even remotely clear what a property is, so the whole discussion is a bit premature. Must properties have causal powers? |
| 6082 | If causal power is the test for reality, that will exclude necessities and possibilities [McGinn] |
| Full Idea: Whether my body weight is necessary or contingent makes no difference at all to my causal powers, so modality is epiphenomenal; if you took causal potential as a test of reality you would have to declare modes unreal. | |
| From: Colin McGinn (Logical Properties [2000], Ch.4) | |
| A reaction: We could try analysing modality into causal terms, as Lewis proposes with quantification across worlds, or as Quine proposes by reduction to natural regularities. I am not sure what it would mean to declare that modes are 'real'. |
| 6075 | Facts are object-plus-extension, or property-plus-set-of-properties, or object-plus-property [McGinn] |
| Full Idea: A fact may be an object and an extension (Quine's view), or a property and a set of properties, or an object and a property; the view I favour is the third one, which seems the most natural. | |
| From: Colin McGinn (Logical Properties [2000], Ch.3) | |
| A reaction: Personally I tend to use the word 'fact' in a realist and non-linguistic way. There must be innumerable inexpressible facts, such as the single pattern made by all the particles of the universe. McGinn seems to be talking of 'atomic facts'. See Idea 6111. |
| 6058 | Identity propositions are not always tautological, and have a key epistemic role [McGinn] |
| Full Idea: Identity propositions are not always analytic or a priori (as Frege long ago taught us) so there is nothing trivial about such propositions; the claim of redundancy ignores the epistemic role that the concept of identity plays. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: He is referring to Frege's Morning Star/Evening Star distinction (Idea 4972). Wittgenstein wanted to eliminate our basic metaphysics by relabelling it as analytic or tautological, but his project failed. Long live metaphysics! |
| 6053 | Identity is as basic as any concept could ever be [McGinn] |
| Full Idea: Identity has a universality and basicness that is hard to overstate; concepts don't get more basic than this - or more indispensable. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: I agree with this. It seems to me to follow that the natural numbers are just as basic, because they are entailed by the separateness of the identities of things. And the whole of mathematics is the science of the patterns within these numbers. |
| 6043 | Type-identity is close similarity in qualities [McGinn] |
| Full Idea: Two things are said to be type-identical when they are similar enough to be declared qualitatively identical. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: A simple point which brings out the fact that type-identity is unlikely to be any sort of true identity (unless there is absolutely no different at all between two electrons, say). |
| 6044 | Qualitative identity is really numerical identity of properties [McGinn] |
| Full Idea: A statement of so-called qualitative identity is really a statement of numerical identity (that is, identity tout court) about the properties of the objects in question - assuming that there are genuine universals. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: We might agree that two cars are type-identical, even though (under the microscope) we decided that none of their properties were absolutely identical. |
| 6046 | Qualitative identity can be analysed into numerical identity of the type involved [McGinn] |
| Full Idea: We can analyse qualitative identity in terms of numerical identity, by saying that x and y are type-identical if there is a single type T that x and y both are, i.e. they both exemplify the same type. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: This just seems to shift the problem onto the words 'are' and 'exemplify'. This takes us back to the problem of things 'partaking' of Plato's Forms. Better to say that qualitative identity isn't identity - it is resemblance (see Idea 6045). |
| 6045 | It is best to drop types of identity, and speak of 'identity' or 'resemblance' [McGinn] |
| Full Idea: It would be better to drop talk of 'numerical' and 'qualitative' identity altogether, speaking instead simply of identity and resemblance. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1 n4) | |
| A reaction: This is the kind of beautifully simple proposal I pay analytical philosophers to come up with. I will attempt in future to talk either of 'identity' (which is strict), or 'resemblance' (which comes in degrees). |
| 6066 | Existence is a property of all objects, but less universal than self-identity, which covers even conceivable objects [McGinn] |
| Full Idea: Existence is a property universal to all objects that exist, somewhat like self-identity, but less universal, because self-identity holds of all conceivable objects, not merely those that happen to exist. | |
| From: Colin McGinn (Logical Properties [2000], Ch.2) | |
| A reaction: This is a splendidly defiant response to the Kantian slogan that 'existence is not a predicate', and I find McGinn persuasive. I can still not find anyone to explain to me exactly what a property is, so I will reserve judgement. |
| 6054 | Sherlock Holmes does not exist, but he is self-identical [McGinn] |
| Full Idea: Sherlock Holmes does not exist, but he is self-identical (he is certainly not indentical to Dr Watson). | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: Most significant. Identity does not entail existence; identity is necessary for existence (I think) but not sufficient. But the notion of existence might be prior to the notion of identity, and the creation of Holmes be parasitic on real existence. |
| 6047 | All identity is necessary, though identity statements can be contingently true [McGinn] |
| Full Idea: All identity is necessary, although there can be contingently true identity statements - those that contain non-rigid designators. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1 n5) | |
| A reaction: A nice case of the need to keep epistemology and ontology separate. An example might be 'The Prime Minister wears a wig', where 'Prime Minister' may not be a rigid designator. 'Winston wears a wig' will be necessary, if true (which it wasn't). |
| 6049 | Leibniz's Law says 'x = y iff for all P, Px iff Py' [McGinn] |
| Full Idea: Leibniz's Law says 'x = y iff for all P, Px iff Py'. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: That is, two things are the same if when we say that one thing (x) has a property (P), then we are saying that the other thing (y) also has the property. A usefully concise statement of the Law. |
| 6048 | Leibniz's Law is so fundamental that it almost defines the concept of identity [McGinn] |
| Full Idea: Leibniz's Law, which a defender of relative identity might opt to reject, is so fundamental to the notion of identity that rejecting it amounts to changing the subject. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1 n8) | |
| A reaction: The Law here is the 'indiscernibility of identicals'. I agree with McGinn, and anyone who loses their grip on this notion of identity strikes me as losing all grip on reality, and threatening their own sanity (well, call it their 'philosophical sanity'). |
| 6050 | Leibniz's Law presupposes the notion of property identity [McGinn] |
| Full Idea: Leibniz's Law presupposes the notion of property identity. | |
| From: Colin McGinn (Logical Properties [2000], Ch.1) | |
| A reaction: A very important observation, because it leads to recognition of the way in which basic concepts and categories of thought interconnect. Which is more metaphysically basic, identity or properties? It is not easy to say… |
| 6080 | Modality is not objects or properties, but the type of binding of objects to properties [McGinn] |
| Full Idea: Modality has a special ontological category: it consists neither in objects (possible worlds theory) nor in properties (predicate modifier view), but items I have called 'modes', ..which can be hard/soft/rigid/pliable binding of objects to properties. | |
| From: Colin McGinn (Logical Properties [2000], Ch.4) | |
| A reaction: As so often, McGinn is very persuasive. Essentially he is proposing that modality is adverbial. He associates the middle view with David Wiggins. |
| 9174 | It is necessary that this table is not made of ice, but we don't know it a priori [Kripke] |
| Full Idea: Although the statement that this table (if it exists at all) was not made of ice, is necessary, it certainly is not something that we know a priori. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.180) | |
| A reaction: One of the key thoughts in modern philosophy. Kit Fine warns against treating it as a new and exciting toy, but it is a new and exciting toy. Scientific essentialism, which I so want to be true, is built on this proposal. |
| 6079 | If 'possible' is explained as quantification across worlds, there must be possible worlds [McGinn] |
| Full Idea: If we replace modal words like 'possible' with quantification across worlds, clearly the notion of 'world' must exclude impossible worlds, otherwise 'possibly p' will be true if 'p' holds in an impossible world. | |
| From: Colin McGinn (Logical Properties [2000], Ch.4) | |
| A reaction: The point here, of course, is that the question is being begged of what 'possible' and 'impossible' actually mean. |
| 9172 | A 'rigid designator' designates the same object in all possible worlds [Kripke] |
| Full Idea: By 'rigid designator' I mean a term that designates the same object in all possible worlds. | |
| From: Saul A. Kripke (Identity and Necessity [1971]) | |
| A reaction: I am persistently troubled by the case of objects which are slightly different in another possible world. Does 'Aristotle' refer to him as young or old? Might the very same man have had a mole on his cheek? |
| 9173 | We cannot say that Nixon might have been a different man from the one he actually was [Kripke] |
| Full Idea: It seems that we cannot say "Nixon might have been a different man from the man he in fact was", unless we mean it metaphorically. He might have been a different sort of person. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.176) | |
| A reaction: The problem is that being a 'different sort of person' could become more and more drastic, till Nixon is unrecognisable. I don't see how I can stipulate that a small and dim mouse is Richard Nixon, even in a possible world with magicians. |
| 9176 | Modal statements about this table never refer to counterparts; that confuses epistemology and metaphysics [Kripke] |
| Full Idea: Statements about the modal properties of this table never refer to counterparts. However, if someone confuses the epistemological problems and the metaphysical problems he will be well on the way to the counterpart theory of Lewis. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.184 n16) | |
| A reaction: I can't make out what we should say about a possible object which is very nearly this table. Kripke needs the table to have a clear and unwavering essence, but tables are not that sort of thing. How would Kripke define 'physical object'? |
| 6081 | Necessity and possibility are big threats to the empiricist view of knowledge [McGinn] |
| Full Idea: It is clear that modality is a prima-facie threat to the usual kind of naturalistic-causal-empiricist theory of knowledge. | |
| From: Colin McGinn (Logical Properties [2000], Ch.4) | |
| A reaction: This is why modern empiricists spend of a lot of energy on trying to analyse counterfactuals and laws of nature. Rationalists are much happier to assert necessities a priori, but then they often don't have much basis for their claims. |
| 6071 | Scepticism about reality is possible because existence isn't part of appearances [McGinn] |
| Full Idea: Scepticism about the external world is possible because you can never build existence into the appearances, so it must always be inferred or assumed. | |
| From: Colin McGinn (Logical Properties [2000], Ch.2) | |
| A reaction: When McGinn's claim that existence is a very universal property begins to produce interesting observations like this, I think we should take it very seriously. |
| 9177 | Identity theorists must deny that pains can be imagined without brain states [Kripke] |
| Full Idea: The identity theorist has to hold that we are under some illusion in thinking that we can imagine that there could have been pains without brain states. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.190) | |
| A reaction: The origin of Robert Kirk's idea that there might be zombies. Kripke is wrong. Of course Kripke and his friends can imagine disembodied pains; the question is whether being able to imagine them makes them possible, which it doesn't. |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| Full Idea: Gödel in his completeness theorem for first-order logic showed that a certain set of syntactically specifiable rules was adequate to capture all first-order valid arguments. No semantics (e.g. reference, truth, validity) was necessary. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Georges Rey - Contemporary Philosophy of Mind 8.2 | |
| A reaction: This implies that a logic machine is possible, but we shouldn't raise our hopes for proper rationality. Validity can be shown for purely algebraic arguments, but rationality requires truth as well as validity, and that needs propositions and semantics. |
| 9178 | Pain, unlike heat, is picked out by an essential property [Kripke] |
| Full Idea: 'Heat' is a rigid designator, which is picked out by the contingent property of being felt in a certain way; pain, on the other hand, is picked out by an essential (indeed necessary and sufficient) property. | |
| From: Saul A. Kripke (Identity and Necessity [1971], p.190 n19) | |
| A reaction: Hm. I could pick out your pain by your contingent whimpering behaviour. I can spot my own potential pain by a combination of bodily damage and pain killing tablets. I suspect him of the same blunder as Descartes on this one. |
| 6077 | Semantics should not be based on set-membership, but on instantiation of properties in objects [McGinn] |
| Full Idea: Semantics should not employ the relationship of set-membership between objects and extensions, but rather the relation of instantiation between objects and properties. | |
| From: Colin McGinn (Logical Properties [2000], Ch.3) | |
| A reaction: At least this means that philosophers won't be required to read fat books on set theory, but they will have to think very carefully about 'instantiation'. A good start is the ideas on 'Partaking' of Platonic Forms in this database (in 'Universals'). |
| 6074 | Clearly predicates have extensions (applicable objects), but are the extensions part of their meaning? [McGinn] |
| Full Idea: We are taught that predicates have extensions - the class of objects of which the predicate is true - which seems hard to deny; but a stronger claim is also made - that extensions are semantically relevant features of predicates. | |
| From: Colin McGinn (Logical Properties [2000], Ch.3) | |
| A reaction: He cites Quine as a spokesman for this view. McGinn is going on to challenge it, by defending universals. It seems to fit in with other externalist theories of concepts and meanings, none of which seems very appealing to me. |
| 6072 | If Satan is the most imperfect conceivable being, he must have non-existence [McGinn] |
| Full Idea: Satan cannot exist because he is the most imperfect conceivable being, and existence is one of the perfections. | |
| From: Colin McGinn (Logical Properties [2000], Ch.2) | |
| A reaction: The logic of this seems right to me. Presumably the theologians would hastily deny this as a definition of Satan; he must have some positive qualities (like power) in order to enact his supreme moral imperfections. NIce, though. |
| 6073 | I think the fault of the Ontological Argument is taking the original idea to be well-defined [McGinn] |
| Full Idea: My own suspicion about the Ontological Argument is that the fault lies in taking notions like 'the most perfect, impressive and powerful being conceivable' to be well-defined. | |
| From: Colin McGinn (Logical Properties [2000], Ch.2) | |
| A reaction: I'm tempted to put it more strongly: the single greatest challenge for the theist with intellectual integrity is to give a clear and coherent definition of God. There must be no internal contradictions, and it must be within the bounds of possibility. |