13 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. |
| 8808 | Involuntary beliefs can still be evaluated [Feldman/Conee] |
| Full Idea: Examples confirm that beliefs may be both involuntary and subject to epistemic evaluation. | |
| From: R Feldman / E Conee (Evidentialism [1985], II) | |
| A reaction: This is an extremely important point, which summarises the situation with beliefs that arise from (apparent) immediate perception. A belief cannot possibly be knowledge if it has been triggered, but no effort was made to evaluate it. |
| 8807 | Evidentialism is the view that justification is determined by the quality of the evidence [Feldman/Conee] |
| Full Idea: What we call 'evidentialism' is the view that the epistemic justification of a belief is determined by the quality of the believer's evidence for the belief. | |
| From: R Feldman / E Conee (Evidentialism [1985], I) | |
| A reaction: The immediate question is whether the believer knows the quality of their evidence. A detective might not recognise the crucial clue (like the dog not barking). The definition of 'quality' had better not turn out to be circular. Forgotten evidence? |
| 8809 | Beliefs should fit evidence, and if you ought to believe it, then you are justified [Feldman/Conee] |
| Full Idea: One epistemically ought to have the doxastic attitudes that fit one's evidence. Being epistemically obligatory is equivalent to being epistemically justified. | |
| From: R Feldman / E Conee (Evidentialism [1985], III) | |
| A reaction: It is normal for someone to refuse to accept something, when another person believes the evidence is overwhelming. Evaluation of evidence must include an assessment of what other evidence might turn up. |
| 8810 | If someone rejects good criticism through arrogance, that is irrelevant to whether they have knowledge [Feldman/Conee] |
| Full Idea: If an arrogant young physicist refuses to recognise valid criticisms from a senior colleague, his or her character has nothing to do with the epistemic status of their belief in the theory. | |
| From: R Feldman / E Conee (Evidentialism [1985], III) | |
| A reaction: This rejects the idea that epistemic justification is essentially a matter of virtues and vices of character. That view is a version of reliabilism, and hence of externalism. I agree with the criticism, but epistemic virtues are still significant. |
| 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. |
| 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. |