22 ideas
| 19081 | Coherence with a set of propositions suggests we can know the proposition corresponds [Davidson, by Donnellan] |
| Full Idea: Davidson argues that the coherence of a set of propositions with a set of beliefs is a good indication that the proposition corresponds to objective facts and that we can know that propositions correspond. | |
| From: report of Donald Davidson (Coherence Theory of Truth and Knowledge [1983]) by Keith Donnellan - Putting Humpty Dumpty Together Again §2.2 | |
| A reaction: Young calls this an 'epistemological route to coherentism'. Davidson is sometimes cited as a fan of the coherence theory of truth, but this just seems to accept Russell's point that coherence is a good test for truth. |
| 17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
| Full Idea: My knowing what the number '33' denotes cannot consist in my knowing that it denotes the number of decimal numbers between '1' and '33', because I would know that even if it were in hexadecimal (which I don't know well). | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: Obviously you wouldn't understand '33' if you didn't understand what '33 things' meant. |
| 17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
| Full Idea: An appreciation of the connection between sameness of number and equinumerosity that it reports is essential to even the most primitive grasp of the concept of cardinal number. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) |
| 17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
| Full Idea: One need not conceive of the numerals as objects in their own right in order to count. The numerals are not mentioned in counting (as objects to be correlated with baseball players), but are used. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: He observes that when you name the team, you aren't correlating a list of names with the players. I could correlate any old tags with some objects, and you could tell me the cardinality denoted by the last tag. I do ordinals, you do cardinals. |
| 17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
| Full Idea: I am not denying that counting can be done mindlessly, without making judgments of cardinality along the way. ...But the question is whether counting is, as it were, fundamentally a mindless exercise. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: He says no. It seems to me like going on a journey, where you can forget where you are going and where you have got to so far, but those underlying facts are always there. If you just tag things with unknown foreign numbers, you aren't really counting. |
| 17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
| Full Idea: Counting is not mere tagging: it is the successive assignment of cardinal numbers to increasingly large collections of objects. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: That the cardinals are 'successive' seems to mean that they are ordinals as well. If you don't know that 'seven' means a cardinality, as well as 'successor of six', you haven't understood it. Days of the week have successors. Does PA capture cardinality? |
| 17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
| Full Idea: It is far from obvious that knowing what 'just as many' means requires knowing what a one-one correspondence is. The notion of a one-one correspondence is very sophisticated, and it is far from clear that five-year-olds have any grasp of it. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: The point is that children decide 'just as many' by counting each group and arriving at the same numeral, not by matching up. He cites psychological research by Gelman and Galistel. |
| 17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
| Full Idea: 'Just as many' is independent of the ability to count, and we shouldn't characterise equinumerosity through counting. It is also independent of the concept of number. Enough cookies to go round doesn't need how many cookies. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: [compressed] He talks of children having an 'operational' ability which is independent of these more sophisticated concepts. Interesting. You see how early man could relate 'how many' prior to the development of numbers. |
| 17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
| Full Idea: The interest of Frege's Theorem is that it offers us an explanation of the fact that the numbers satisfy the Dedekind-Peano axioms. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says 'explaining' does not make it more fundamental, since all proofs explain why their conclusions hold. |
| 17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
| Full Idea: For a long time my daughter had no understanding of the question of how many numerals or numbers there are between 'one' and 'five'. I think she lacked the concept of numerals as objects which can themselves be counted. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: I can't make any sense of numbers actually being objects, though clearly treating all sorts of things as objects helps thinking (as in 'the victory is all that matters'). |
| 17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
| Full Idea: Equinumerosity is not the same concept as being in one-one correspondence with. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says this is the case, even if they are coextensive, like renate and cordate. You can see that five loaves are equinumerous with five fishes, without doing a one-one matchup. |
| 17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
| Full Idea: One can have a perfectly serviceable concept of cardinality without so much as having the concept of one-one correspondence. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: This is the culmination of a lengthy discussion. It includes citations about the psychology of children's counting. Cardinality needs one group of things, and 1-1 needs two groups. |
| 8806 | The concepts of belief and truth are linked, since beliefs are meant to fit reality [Davidson] |
| Full Idea: Knowing what a belief is brings with it the concept of objective truth, for the notion of a belief is the notion of a state that may or may not jibe with reality. | |
| From: Donald Davidson (Coherence Theory of Truth and Knowledge [1983], p.162) | |
| A reaction: I find any discussion of belief that makes no reference to truth (as in Hume) quite puzzling. I can understand it when a belief is just triggered by a sensation ('this is hot'), but not when a belief arrives after careful comparison of reasons. |
| 8252 | Davidson believes experience is non-conceptual, and outside the space of reasons [Davidson, by McDowell] |
| Full Idea: Davidson thinks that experience can be nothing but an extra-conceptual impact on sensibility. So he concludes that experience must be outside the space of reasons. | |
| From: report of Donald Davidson (Coherence Theory of Truth and Knowledge [1983], I.6) by John McDowell - Mind and World I | |
| A reaction: McDowell's challenge to the view that experience is extra-conceptual seems to be the key debate among modern empiricists. My only intuition in this area is that we should beware of all-or-nothing solutions to such problems. |
| 8255 | Davidson says the world influences us causally; I say it influences us rationally [McDowell on Davidson] |
| Full Idea: Davidson urges that we should hold that the world exerts a merely causal influence on our thinking, but I am trying to describe a way in which the world exerts a rational influence on our thinking. | |
| From: comment on Donald Davidson (Coherence Theory of Truth and Knowledge [1983]) by John McDowell - Mind and World II.5 | |
| A reaction: McDowell seems to be fighting for the existence of 'pure' reason in a way that is hard to defend with a thoroughly materialist view of human brains. If the world is coherent, then maybe it is rational, and so has reasons to offer us? |
| 8804 | Reasons for beliefs are not the same as evidence [Davidson] |
| Full Idea: We must find a reason for supposing most of our beliefs are true that is not a form of evidence. | |
| From: Donald Davidson (Coherence Theory of Truth and Knowledge [1983], p.158) | |
| A reaction: This simple observation strikes me as being a key truth in epistemology. It is the same confusion that creates Jackson's Knowledge Argument (Idea 7377) against physicalism (that experiencing red can be thought to be knowledge). |
| 8802 | Sensations lack the content to be logical; they cause beliefs, but they cannot justify them [Davidson] |
| Full Idea: The relation between a sensation and a belief cannot be logical, since sensations are not beliefs or propositional attitudes. The relation must be causal. Sensations cause some beliefs, but they do not show why the belief is justified. | |
| From: Donald Davidson (Coherence Theory of Truth and Knowledge [1983], p.157) | |
| A reaction: This is, I am beginning to think, the single most important idea in the whole of modern epistemology. Animals have beliefs caused in this way, and because they only have simple beliefs about immediate things, most of their beliefs are true. |
| 8801 | Coherent justification says only beliefs can be reasons for holding other beliefs [Davidson] |
| Full Idea: What distinguishes a coherence theory of justification is simply the claim that nothing can count as a reason for holding a belief except another belief. | |
| From: Donald Davidson (Coherence Theory of Truth and Knowledge [1983], p.156) | |
| A reaction: I think I agree fully with this. Red patches and headaches I count as evidence rather than as reasons. Since a red patch can be hallucinatory, and a headache can be dreamed, they can't possibly embody true propositions without critical evaluation. |
| 8805 | Skepticism is false because our utterances agree, because they are caused by the same objects [Davidson] |
| Full Idea: What stands in the way of global skepticism of the senses is the fact that we must take the objects of a belief to be the causes of that belief. And our utterances mean the same thing because belief in their truth is caused by the same objects. | |
| From: Donald Davidson (Coherence Theory of Truth and Knowledge [1983], p.161) | |
| A reaction: This is hardly a knock-down argument against scepticism, but it builds a nice picture. The second half extends the Private Language Argument (e.g. Idea 4158). But I still have non-existent conversations about non-existent things in my dreams. |
| 18703 | Davidson's Cogito: 'I think, therefore I am generally right' [Davidson, by Button] |
| Full Idea: Davidson's Cogito has the form 'I think, therefore I am generally right'. | |
| From: report of Donald Davidson (Coherence Theory of Truth and Knowledge [1983], 16.6) by Tim Button - The Limits of Reason | |
| A reaction: On the whole I would subscribe to this Cogito (as Button calls it), from an evolutionary perspective. There would just be no point in thought if it wasn't generally right in everyday activity. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |