50 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. |
| 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'? |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 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. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 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. |
| 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. |
| 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. |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 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. |
| 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. |
| 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. |
| 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. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |
| 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. |