15 ideas
| 9837 | 0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett] |
| Full Idea: Husserl contends that 0 is not a number, on the grounds that 'nought' is a negative answer to the question 'how many?'. | |
| From: report of Edmund Husserl (Philosophy of Arithmetic [1894], p.144) by Michael Dummett - Frege philosophy of mathematics Ch.8 | |
| A reaction: I seem to be in a tiny minority in thinking that Husserl may have a good point. One apple is different from one orange, but no apples are the same as no oranges. That makes 0 a very peculiar number. See Idea 9838. |
| 9576 | Multiplicity in general is just one and one and one, etc. [Husserl] |
| Full Idea: Multiplicity in general is no more than something and something and something, etc.; ..or more briefly, one and one and one, etc. | |
| From: Edmund Husserl (Philosophy of Arithmetic [1894], p.85), quoted by Gottlob Frege - Review of Husserl's 'Phil of Arithmetic' | |
| A reaction: Frege goes on to attack this idea fairly convincingly. It seems obvious that it is hard to say that you have seventeen items, if the only numberical concept in your possession is 'one'. How would you distinguish 17 from 16? What makes the ones 'multiple'? |
| 17444 | Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck] |
| Full Idea: Husserl famously argued that one should not explain number in terms of equinumerosity (or one-one correspondence), but should explain equinumerosity in terms of sameness of number, which should be characterised in terms of counting. | |
| From: report of Edmund Husserl (Philosophy of Arithmetic [1894]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: [Heck admits he hasn't read the Husserl] I'm very sympathetic to Husserl, though nearly all modern thinking favours Frege. Counting connects numbers to their roots in the world. Mathematicians seem oblivious of such things. |
| 8851 | Coherentists say that regress problems are assuming 'linear' justification [Williams,M] |
| Full Idea: From the point of view of the coherentist, Agrippa's Dilemma fails because it presupposes a 'linear' conception of justifying inference. | |
| From: Michael Williams (Without Immediate Justification [2005], §2) | |
| A reaction: [He cites Bonjour 1985 for this view] Since a belief may have several justifications, and one belief could justify a host of others, there certainly isn't a simple line of justifications. I agree with the coherentist picture here. |
| 3597 | Foundations need not precede other beliefs [Wittgenstein] |
| Full Idea: I do not explicitly learn the propositions that stand fast for me. I can discover them subsequently like the axis around which a body rotates. | |
| From: Ludwig Wittgenstein (On Certainty [1951], §152), quoted by Michael Williams - Problems of Knowledge Ch.14 | |
| A reaction: A nice metaphor for the way in which axioms are derived. It is also close to Quine's metaphor of the 'net' of understanding, with the centre area 'standing fast'. Not neat and tidy, though. |
| 8849 | Traditional foundationalism is radically internalist [Williams,M] |
| Full Idea: Traditional foundationalism is radically internalist. The justification-making factors for beliefs, basic and otherwise, are all open to view, and perhaps even actual objects of awareness. I am always in a position to know that I know. | |
| From: Michael Williams (Without Immediate Justification [2005], §1) | |
| A reaction: This is a helpful if one is trying to draw a map of the debate. An externalist foundationalism would have to terminate in the external fact which was the object of knowledge (via some reliable channel), but that is the truth, not the justification. |
| 8853 | Basic judgements are immune from error because they have no content [Williams,M] |
| Full Idea: Basic judgements threaten to buy their immunity from error at the cost of being drained of descriptive content altogether. | |
| From: Michael Williams (Without Immediate Justification [2005], §4) | |
| A reaction: This is probably the key objection to foundationalism. As you import sufficient content into basic experiences to enable them to actually justify a set of beliefs, you find you have imported all sorts of comparisons and classifications as well. |
| 8855 | Sensory experience may be fixed, but it can still be misdescribed [Williams,M] |
| Full Idea: The fact that experiential contents cannot be other than they are, as far as sensory awareness goes, does not imply that we cannot misdescribe them, as in misreporting the number of speckles on a speckled hen (Chisholm's example). | |
| From: Michael Williams (Without Immediate Justification [2005], §4) | |
| A reaction: [Chisholm 1942 is cited] Such experiences couldn't be basic beliefs if there was a conflict between their intrinsic nature and the description I used in discussing them. |
| 8852 | In the context of scepticism, externalism does not seem to be an option [Williams,M] |
| Full Idea: In the peculiar context of the skeptical challenge, it is easy to persuade oneself that externalism is not an option. | |
| From: Michael Williams (Without Immediate Justification [2005], §3) | |
| A reaction: This is because externalism sees justification as largely non-conscious, but when faced with scepticism, the justifications need to be spelled out, and therefore internalised. So are sceptical discussions basic, or freakish anomalies? |
| 3596 | Total doubt can't even get started [Wittgenstein, by Williams,M] |
| Full Idea: Wittgenstein remarked that if you tried to doubt everything, you would not get as far as doubting anything. | |
| From: report of Ludwig Wittgenstein (On Certainty [1951]) by Michael Williams - Problems of Knowledge Ch.14 |
| 9575 | Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege] |
| Full Idea: Husserl identifies a 'unitary mental act' where several contents are connected or related to one another, and also a difference-relation where two contents are related to one another by a negative judgement. | |
| From: report of Edmund Husserl (Philosophy of Arithmetic [1894], p.73-74) by Gottlob Frege - Review of Husserl's 'Phil of Arithmetic' p.322 | |
| A reaction: Frege is setting this up ready for a fairly vicious attack. Where Hume has a faculty for spotting resemblances, it is not implausible that we should also be hard-wired to spot differences. 'You look different; have you changed your hair style?' |
| 21214 | We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol] |
| Full Idea: Husserl said that the clarification of any concept is made by determining its psychological origin. He is concerned with the psychological origins of the operation of calculating cardinal numbers. | |
| From: report of Edmund Husserl (Philosophy of Arithmetic [1894]) by Victor Velarde-Mayol - On Husserl 2.2 | |
| A reaction: This may not be the same as the 'psychologism' that Frege so despised, because Husserl is offering a clarification, rather than the intrinsic nature of number concepts. It is not a theory of the origin of numbers. |
| 9819 | Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl] |
| Full Idea: Husserl substitutes his account of the process of concept-formation for a delineation of the concept. It is above all in making this substitution that psychologism is objectionable (and Frege opposed it so vehemently). | |
| From: comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.2 | |
| A reaction: While this is a powerful point which is a modern orthodoxy, it hardly excludes a study of concept-formation from being of great interest for other reasons. It may not appeal to logicians, but it is crucial part of the metaphysics of nature. |
| 9851 | Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl] |
| Full Idea: Husserl saw that abstracted units, though featureless, must in some way retain their distinctness, some shadowy remnant of their objects. So he wanted to correlate like-numbered sets, not just register their identity, but then abstractionism fails. | |
| From: comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.12 | |
| A reaction: Abstractionism is held to be between the devil and the deep blue sea, of depending on units which are identifiable, when they are defined as devoid of all individuality. We seem forced to say that the only distinction between them is countability. |
| 4721 | If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein] |
| Full Idea: If you are not certain of any fact, you cannot be certain of the meaning of your words either. | |
| From: Ludwig Wittgenstein (On Certainty [1951], §114) | |
| A reaction: A wonderfully challenging aphorism. I suspect that it is true, but not really a problem. We all know the meaning of 'Loch Ness Monster', as long as we don't get too fussy. And for local objects I am happy that I know the facts. |