27 ideas
| 17729 | Examining concepts can recover information obtained through the senses [Jenkins] |
| Full Idea: My idea is that conceptual examination might be a way of recovering information previously obtained through the senses. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.8) | |
| A reaction: Now you're talking! This is really interesting conceptual analysis, rather than the sort of stamp-collecting approach to analsis practised by the duller sort of philosopher. But why bother with conceptual examination, when you have senses? |
| 9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
| Full Idea: The tendency to attack forms of expression rather than attempting to appreciate what is actually being said is one of the more unfortunate habits that analytic philosophy inherited from Frege. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], IV) | |
| A reaction: The key to this, I say, is to acknowledge the existence of propositions (in brains). For example, this belief will make teachers more sympathetic to pupils who are struggling to express an idea, and verbal nit-picking becomes totally irrelevant. |
| 17740 | Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins] |
| Full Idea: Instead of considering only a proposition's 'correspondence to the facts', we should also consider the correspondence between parts of the proposition and parts of the world (a 'correspondence-as-congruence' view). | |
| From: Carrie Jenkins (Grounding Concepts [2008], Final - Branching) | |
| A reaction: This is something like Russell's Othello example (1912), except that the parts there, with relations seemed to add up to the whole proposition. For Jenkins, presumably parts might correspond, but the whole proposition fail to. |
| 9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
| Full Idea: The conception that what can be numbered is some object (including flocks of sheep) relative to a partition - a choice of unit - survived even in the late nineteenth century in the form of the rejection of the null set (and difficulties with unit sets). | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], IX) | |
| A reaction: This old view can't be entirely wrong! Frege makes the point that if asked to count a pack of cards, you must decide whether to count cards, or suits, or pips. You may not need a 'unit', but you need a concept. 'Units' name concept-extensions nicely! |
| 9984 | We can have a series with identical members [Tait] |
| Full Idea: Why can't we have a series (as opposed to a linearly ordered set) all of whose members are identical, such as (a, a, a...,a)? | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], VII) | |
| A reaction: The question is whether the items order themselves, which presumably the natural numbers are supposed to do, or whether we impose the order (and length) of the series. What decides how many a's there are? Do we order, or does nature? |
| 13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
| Full Idea: The axiomatic conception of mathematics is the only viable one. ...But they are true because they are axioms, in contrast to the view advanced by Frege (to Hilbert) that to be a candidate for axiomhood a statement must be true. | |
| From: report of William W. Tait (Intro to 'Provenance of Pure Reason' [2005], p.4) by Charles Parsons - Review of Tait 'Provenance of Pure Reason' §2 | |
| A reaction: This looks like the classic twentieth century shift in the attitude to axioms. The Greek idea is that they must be self-evident truths, but the Tait-style view is that they are just the first steps in establishing a logical structure. I prefer the Greeks. |
| 17730 | Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins] |
| Full Idea: We might arrive to the concept of infinity by composing concepts of negation and finiteness. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 5.3) | |
| A reaction: Presumably lots of concepts can be arrived at by negating prior concepts (such as not-wet, not-tall, not-loud, not-straight). So not-infinite is perfectly plausible, and is a far better account than some a priori intuition of pure infinity. Love it. |
| 17719 | Arithmetic concepts are indispensable because they accurately map the world [Jenkins] |
| Full Idea: The indispensability of arithmetical concepts is evidence that they do in fact accurately represent features of the independent world. | |
| From: Carrie Jenkins (Grounding Concepts [2008], Intro) | |
| A reaction: This seems to me to be by far the best account of the matter. So why is the world so arithmetical? Dunno, mate; ask someone else. |
| 17717 | Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins] |
| Full Idea: I propose that arithmetical truths are known through an examination of our own arithmetical concepts; that basic arithmetical concepts map the arithmetical structure of the world; that the map obtains in virtue of our normal sensory apparatus. | |
| From: Carrie Jenkins (Grounding Concepts [2008], Pref) | |
| A reaction: She defends the nice but unusual position that arithmetical knowledge is both a priori and empirical (so that those two notions are not, as usually thought, opposed). I am a big Carrie Jenkins fan. |
| 17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |
| Full Idea: A problem for the neo-Fregeans is that it has not proved easy to establish that Hume's Principle is analytic or definitive in the required sense. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.3) | |
| A reaction: It is also asked how we would know the principle, if it is indeed analytic or definitional (Jenkins p.119). |
| 17727 | We can learn about the world by studying the grounding of our concepts [Jenkins] |
| Full Idea: What concept grounding does for us is ensure that our concepts, like the results of our empirical tests, can be treated as a source of information about the independent world. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.4) | |
| A reaction: Presumably we learn our concepts hand-in-hand with experience, so learning our concepts is itself learning about the world. Later checking of concepts and their relations largely confirms what we already knew? |
| 17720 | There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG] |
| Full Idea: Dependence comes in essential, modal, explanatory, conceptual, metaphysical and constitutive forms. | |
| From: report of Carrie Jenkins (Grounding Concepts [2008], 1.2) by PG - Db (ideas) | |
| A reaction: You'll have to look up Jenkins for the details. |
| 17728 | The concepts we have to use for categorising are ones which map the real world well [Jenkins] |
| Full Idea: Concepts which are indispensably useful for categorising, understanding, explaining, and predicting our sensory input are likely to be ones which map the structure of that input well. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.6) | |
| A reaction: Anti-realists about classification seem to think that we just invent an array of concepts, and then start classifying with them. The truth seems to be that the actual classes of worldly thing have generated our concepts. |
| 17726 | Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins] |
| Full Idea: Examining accurate concepts can help us acquire true beliefs about the world, examining justified concepts can help us acquire justified beliefs about the world, and examining grounded concepts can help us acquire knowledge of it. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.4) | |
| A reaction: This summarises Jenkins's empirical account of concepts, and I love it all to bits. I feel that contemporary philosophy is beginning to produce a coherent naturalistic worldview which can replace religion. Bar the rituals. We can have priests... |
| 17734 | It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins] |
| Full Idea: The mere reliability of intuition is not a satisfactory ground for saying it is a source of knowledge - we need to know why it is reliable to understand whether it can be a source of knowledge. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 6.5) | |
| A reaction: My theory is that intuition is simply believing things for reasons which we have either forgotten, or (more likely) reasons which are too complex or subtle to be articulated. Intuition feels rational, because it is rational. Updated view of mind needed. |
| 17723 | Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins] |
| Full Idea: I propose that knowledge is true belief which can be well explained .....just by citing the proposition believed. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 3.1) | |
| A reaction: I don't find this appealing, and my reservation about Jenkins's book is her reliabilist, externalist epistemology. I would add an internalist coherentist epistemology to her very nice theory. 'I believe there are fairies at the bottom of my garden'? |
| 17718 | Grounded concepts are trustworthy maps of the world [Jenkins] |
| Full Idea: Grounded concepts are like trustworthy on-board maps of the independent world. | |
| From: Carrie Jenkins (Grounding Concepts [2008], Intro) | |
| A reaction: You'll probably need more than one concept for it to qualify as a 'map', but I like this idea a lot. The world, rather than we ourselves, creates our concepts. The opposite of the view of Geach in 'Mental Acts'. |
| 17739 | The physical effect of world on brain explains the concepts we possess [Jenkins] |
| Full Idea: I think the physical effects of the world on the brain explain our possessing the concepts we do. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 8.2) | |
| A reaction: A nice slogan for a thought which strikes me as exactly right. |
| 9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
| Full Idea: If the sense of a proposition about the abstract domain is given in terms of the corresponding proposition about the (relatively) concrete domain, ..and the truth of the former is founded upon the truth of the latter, then this is 'logical abstraction'. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], V) | |
| A reaction: The 'relatively' in parentheses allows us to apply his idea to levels of abstraction, and not just to the simple jump up from the concrete. I think Tait's proposal is excellent, rather than purloining 'abstraction' for an internal concept within logic. |
| 9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
| Full Idea: Although (in Cantor and Dedekind) abstraction does not (as has often been observed) play any role in their proofs, but it does play a role, in that it fixes the grammar, the domain of meaningful propositions, and so determining the objects in the proofs. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], V) | |
| A reaction: [compressed] This is part of a defence of abstractionism in Cantor and Dedekind (see K.Fine also on the subject). To know the members of a set, or size of a domain, you need to know the process or function which created the set. |
| 9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
| Full Idea: A different reading of abstraction is that it concerns, not the individuating properties of the elements relative to one another, but rather the individuating properties of the set itself, for example the concept of what is its extension. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], VIII) | |
| A reaction: If the set was 'objects in the room next door', we would not be able to abstract from the objects, but we might get to the idea of things being contain in things, or the concept of an object, or a room. Wrong. That's because they are objects... Hm. |
| 9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
| Full Idea: Why should abstraction from two equipollent sets lead to the same set of 'pure units'? | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996]) | |
| A reaction: [Tait is criticising Cantor] This expresses rather better than Frege or Dummett the central problem with the abstractionist view of how numbers are derived from matching groups of objects. |
| 9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
| Full Idea: If the power |A| is obtained by abstraction from set A, then if A is equipollent to set B, then |A| = |B|. But this does not imply that A = B. So |A| cannot just be A, taken in abstraction, unless that can identify distinct sets, ..or create new objects. | |
| From: William W. Tait (Frege versus Cantor and Dedekind [1996], V) | |
| A reaction: An elegant piece of argument, which shows rather crucial facts about abstraction. We are then obliged to ask how abstraction can create an object or a set, if the central activity of abstraction is just ignoring certain features. |
| 17731 | Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins] |
| Full Idea: I find an updated verificationism plausible, in which we say something meaningful just in case we employ only concepts whose possession could be justified or disjustified by sensory input. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 5.6) | |
| A reaction: Wow! This is the first time I have ever had the slightest sympathy for verificationism. It saves my favourite problem case - of wild but meaningful speculation, for example about the contents of another universe. A very nice idea. |
| 17732 | Success semantics explains representation in terms of success in action [Jenkins] |
| Full Idea: Success semantics is the attempt to understand mental representation by thinking about the ways in which representing the world can lead to success in action. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 6.3) | |
| A reaction: I take this to be what is also known as 'teleological semantics'. It sounds to me as if this might help to explain success in action, but isn't going to explain the representations that result in the success. |
| 17725 | 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins] |
| Full Idea: 'Analytic' might mean conceptually true, or true in virtue of meaning, or where the predicate is contained in the subject, or for sentences which define something, or where meaning is sufficient for the truth. | |
| From: Carrie Jenkins (Grounding Concepts [2008], 4.3) | |
| A reaction: The second one says meaning grounds the truth, where the last one says meaning entails the truth. |
| 467 | A virtue is a combination of intelligence, strength and luck [Ion] |
| Full Idea: The virtue of each thing is a Triad: intelligence, strength, luck. | |
| From: Ion (fragments/reports [c.435 BCE], B1), quoted by (who?) - where? |