17 ideas
| 8797 | The negation of all my beliefs about my current headache would be fully coherent [Sosa] |
| Full Idea: If I have a headache, I could have a set of beliefs that I do not have a headache, that I am not in pain, that no one is in pain, and so on. The resulting system of beliefs would cohere as fully as does my actual system of beliefs. | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §9) | |
| A reaction: I think this is a misunderstanding of coherentism. Beliefs are not to be formulated through a process of coherence, but are evaluated that way. A belief that I have headache just arrives; I then see that its denial is incoherent, so I accept it. |
| 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. |
| 13768 | Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington] |
| Full Idea: If your interest in logic is confined to applications to mathematics or other a priori matters, it is fine for validity to preserve certainty, ..but if you use conditionals when arguing about contingent matters, then great caution will be required. | |
| From: Dorothy Edgington (Conditionals [2001], 17.2.1) |
| 13770 | There are many different conditional mental states, and different conditional speech acts [Edgington] |
| Full Idea: As well as conditional beliefs, there are conditional desires, hopes, fears etc. As well as conditional statements, there are conditional commands, questions, offers, promises, bets etc. | |
| From: Dorothy Edgington (Conditionals [2001], 17.3.4) |
| 13764 | Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington] |
| Full Idea: Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'? | |
| From: Dorothy Edgington (Conditionals [2001], 17.1) | |
| A reaction: I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional. |
| 13765 | 'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington] |
| Full Idea: If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B). | |
| From: Dorothy Edgington (Conditionals [2001], 17.1) | |
| A reaction: This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true. |
| 8794 | There are very few really obvious truths, and not much can be proved from them [Sosa] |
| Full Idea: Radical foundationalism suffers from two weaknesses: there are not so many perfectly obvious truths as Descartes thought; and if we restrict ourselves to what it truly obvious, very little supposed common sense knowledge can be proved. | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §3) | |
| A reaction: It is striking how few examples can ever be found of self-evident a priori truths. However, if there are self-evident truths about direct experience (pace Descartes), that would give us more than enough. |
| 8796 | A single belief can trail two regresses, one terminating and one not [Sosa] |
| Full Idea: A single belief can trail at once regresses of both sorts: one terminating and one not. | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §6) | |
| A reaction: This makes foundationalism possible, while admitting the existence of regresses. It is a good point, and triumphalist anti-foundationalists can't just point out a regress and then smugly troop off to the pub. |
| 8799 | If mental states are not propositional, they are logically dumb, and cannot be foundations [Sosa] |
| Full Idea: If a mental state is not propositional, then how can it possibly serve as a foundation for belief? How can one infer or justify anything on the basis of a state that, having no propositional content, must be logically dumb? | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §11) | |
| A reaction: This may be the best objection to foundationalism. McDowell tries to argue that conceptual content is inherent in perception, thus giving the beginnings of inbuilt propositional content. But an organism awash with bare experiences knows nothing. |
| 8795 | Mental states cannot be foundational if they are not immune to error [Sosa] |
| Full Idea: If a mental state provides no guarantee against error, then it cannot serve as a foundation for knowledge. | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §4) | |
| A reaction: That assumes that knowledge entails certainty, which I am sure it should not. On a fallibilist account, a foundation could be incredibly secure, despite a barely imaginable scenario in which it turned out to be false. |
| 8798 | Vision causes and justifies beliefs; but to some extent the cause is the justification [Sosa] |
| Full Idea: Visual experience is recognized as both the cause and the justification of our visual beliefs. But these are not wholly independent. Presumably the justification that something is red derives partly from the fact that it originates in visual experience. | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §10) | |
| A reaction: Yes, but the fact that certain visual experiences originate in dreams is taken as grounds for denying their truth, not affirming it. So why do we distinguish them? I am thinking that only in the 'space of reasons' can a cause become a justification. |
| 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. |