21 ideas
| 12585 | Most people can't even define a chair [Peacocke] |
| Full Idea: Ordinary speakers are notoriously unsuccessful if asked to offer an explicit definition of the concept 'chair'. | |
| From: Christopher Peacocke (A Study of Concepts [1992], 6.1) |
| 9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
| Full Idea: ZF set theory is a first-order axiomatization. Variables range over sets, there are no second-order variables, and primitive predicates are just 'equals' and 'member of'. The axiom of extensionality says sets with the same members are identical. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 7) | |
| A reaction: If the eleven members of the cricket team are the same as the eleven members of the hockey team, is the cricket team the same as the hockey team? Our cricket team is better than our hockey team, so different predicates apply to them. |
| 9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
| Full Idea: The main alternative to ZF is two-sorted theories, with some variables ranging over classes. Classes have more generous existence assumptions: there is a universal class, containing all sets, and a class containing all ordinals. Classes are not members. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 7.1.1) | |
| A reaction: My intuition is to prefer strict systems when it comes to logical theories. The whole point is precision. Otherwise we could just think about things, and skip all this difficult symbolic stuff. |
| 9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
| Full Idea: It must not be concluded from the rejection of excluded middle that intuitionistic logic operates with three values: true, false, and neither true nor false. It does not make use of true and false, but only with a construction being a proof. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 8.1) | |
| A reaction: This just sounds like verificationism to me, with all its problems. It seems to make speculative statements meaningless, which can't be right. Realism has lots of propositions which are assumed to be true or false, but also unknowable. |
| 9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
| Full Idea: First-order logic is distinguished by generalizations (quantification) only over objects: second-order logic admits generalizations or quantification over properties or kinds of objects, and over relations between them, and functions defined over them. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Second-order logic was introduced by Frege, but is (interestingly) rejected by Quine, because of the ontological commitments involved. I remain unconvinced that quantification entails ontological commitment, so I'm happy. |
| 9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
| Full Idea: There are two ways of characterizing logical truths and correct inference. Proof-theoretic or syntactic characterizations, if the formalization admits of proof or derivation; and model-theoretic or semantic versions, being true in all interpretations. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Dummett calls this distinction 'fundamental'. The second one involves truth, and hence meaning, where the first one just responds to rules. ..But how can you have a notion of correctly following a rule, without a notion of truth? |
| 9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
| Full Idea: It can be argued that the notion of ordinal numbers is more fundamental than that of cardinals. To count objects, we must count them in sequence. ..The theory of ordinals forms the substratum of Cantor's theory of cardinals. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 5) | |
| A reaction: Depends what you mean by 'fundamental'. I would take cardinality to be psychologically prior ('that is a lot of sheep'). You can't order people by height without first acquiring some people with differing heights. I vote for cardinals. |
| 9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
| Full Idea: The number 4 cannot be characterized solely by its position in a system, because it has different positions in the system of natural numbers and that of the positive whole numbers, whereas these systems have the very same structure. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 6.1) | |
| A reaction: Dummett seems to think this is fairly decisive against structuralism. There is also the structure of the real numbers. We will solve this by saying that the wholes are abstracted from the naturals, which are abstracted from the reals. Job done. |
| 12581 | Perceptual concepts causally influence the content of our experiences [Peacocke] |
| Full Idea: Once a thinker has acquired a perceptually individuated concept, his possession of that concept can causally influence what contents his experiences possess. | |
| From: Christopher Peacocke (A Study of Concepts [1992], 3.3) | |
| A reaction: Like having 35 different words for 'snow', I suppose. I'm never convinced by such claims. Having the concepts may well influence what you look at or listen to, but I don't see the deliverances of the senses being changed by the concepts. |
| 12579 | Perception has proto-propositions, between immediate experience and concepts [Peacocke] |
| Full Idea: Perceptual experience has a second layer of nonconceptual representational content, distinct from immediate 'scenarios' and from conceptual contents. These additional contents I call 'protopropositions', containing an individual and a property/relation. | |
| From: Christopher Peacocke (A Study of Concepts [1992], 3.3) | |
| A reaction: When philosophers start writing this sort of thing, I want to turn to neuroscience and psychology. I suppose the philosopher's justification for this sort of speculation is epistemological, but I see no good coming of it. |
| 12586 | Consciousness of a belief isn't a belief that one has it [Peacocke] |
| Full Idea: I dispute the view that consciousness of a belief consists in some kind of belief that one has the belief. | |
| From: Christopher Peacocke (A Study of Concepts [1992], 6.2) | |
| A reaction: Thus if one is trying to grasp the notion of higher-order thought, it doesn't have to be just more of same but one level up. Any sensible view of the brain would suggest that one sort of activity would lead into an entirely different sort. |
| 18568 | Philosophy should merely give necessary and sufficient conditions for concept possession [Peacocke, by Machery] |
| Full Idea: Peacocke's 'Simple Account' says philosophers should determine the necessary and sufficient conditions for possessing a concept, and psychologists should explain how the human mind meets these conditions. | |
| From: report of Christopher Peacocke (A Study of Concepts [1992]) by Edouard Machery - Doing Without Concepts 2 | |
| A reaction: One can't restrict philosophy so easily. Psychologists could do that job themselves, and dump philosophy. Philosophy is interested in the role of concepts in meaning, experience and judgement. If psychologists can contribute to philosophy, fine. |
| 18571 | Peacocke's account of possession of a concept depends on one view of counterfactuals [Peacocke, by Machery] |
| Full Idea: Peacocke's method for discovering the possession conditions of concepts is committed to a specific account of counterfactual judgements - the Simulation Model (judgements we'd make if the antecedent were actual). | |
| From: report of Christopher Peacocke (A Study of Concepts [1992]) by Edouard Machery - Doing Without Concepts 2.3.4 | |
| A reaction: Machery concludes that the Simulation Model is incorrect. This appears to be Edgington's theory of conditionals, though Machery doesn't mention her. |
| 18572 | Peacocke's account separates psychology from philosophy, and is very sketchy [Machery on Peacocke] |
| Full Idea: Peacocke's Simple Account fails to connect the psychology and philosophy of concepts, it subordinates psychology to specific field of philosophy, it is committed to analytic/synthetic, and (most important) its method is very sketchy. | |
| From: comment on Christopher Peacocke (A Study of Concepts [1992]) by Edouard Machery - Doing Without Concepts 2.3.5 | |
| A reaction: Machery says Peacocke proposes a research programme, and he is not surprised that no one has every followed. Machery is a well-known champion of 'experimental philosophy', makes philosophy respond to the psychology. |
| 12577 | Possessing a concept is being able to make judgements which use it [Peacocke] |
| Full Idea: Possession of any concept requires the capacity to make judgements whose content contain it. | |
| From: Christopher Peacocke (A Study of Concepts [1992], 2.1) | |
| A reaction: Idea 12575 suggested that concept possession was an ability just to think about the concept. Why add that one must actually be able to make a judgement? Presumably to get truth in there somewhere. I may only speculate and fantasise, rather than judge. |
| 12578 | A concept is just what it is to possess that concept [Peacocke] |
| Full Idea: There can be no more to a concept than is determined by a correct account of what it is to possess that concept. | |
| From: Christopher Peacocke (A Study of Concepts [1992], 3.2) | |
| A reaction: He calls this the Principle of Dependence. An odd idea, if you compare 'there is no more to a book than its possession conditions'. If the principle is right, I struggle with the proposal that a philosopher might demonstrate such a principle. |
| 12587 | Employing a concept isn't decided by introspection, but by making judgements using it [Peacocke] |
| Full Idea: On the account I have been developing, what makes it the case that someone is employing one concept rather than another is not constituted by his impression of whether he is, but by complex facts about explanations of his judgements. | |
| From: Christopher Peacocke (A Study of Concepts [1992], 7.2) | |
| A reaction: I presume this brings truth into the picture, and hence establishes a link between the concept and the external world, rather than merely with other concepts. There seems to be a shadowy behaviourism lurking in the background. |
| 12584 | An analysis of concepts must link them to something unconceptualized [Peacocke] |
| Full Idea: At some point a good account of conceptual mastery must tie the mastery to abilities and relations that do not require conceptualization by the thinker. | |
| From: Christopher Peacocke (A Study of Concepts [1992], 5.3) | |
| A reaction: This obviously implies a physicalist commitment. Peacocke seeks, as so many do these days in philosophy of maths, to combine this commitment with some sort of Fregean "platonism without tears" (p.101). I don't buy it. |
| 9335 | Concepts are constituted by their role in a group of propositions to which we are committed [Peacocke, by Greco] |
| Full Idea: Peacocke argues that it may be a condition of possessing a certain concept that one be fundamentally committed to certain propositions which contain it. A concept is constituted by playing a specific role in the cognitive economy of its possessor. | |
| From: report of Christopher Peacocke (A Study of Concepts [1992]) by John Greco - Justification is not Internal §9 | |
| A reaction: Peacocke is talking about thought and propositions rather than language. Good for him. I always have problems with this sort of view: how can something play a role if it doesn't already have intrinsic properties to make the role possible? |
| 9336 | A concept's reference is what makes true the beliefs of its possession conditions [Peacocke, by Horwich] |
| Full Idea: Peacocke has a distinctive view of reference: The reference of a concept is that which will make true the primitively compelling beliefs that provide its possession conditions. | |
| From: report of Christopher Peacocke (A Study of Concepts [1992]) by Paul Horwich - Stipulation, Meaning and Apriority §9 | |
| A reaction: The first thought is that there might occasionally be more than one referent which would do the job. It seems to be a very internal view of reference, where I take reference to be much more contextual and social. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |