11 ideas
| 18073 | Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher] |
| Full Idea: Dummett argues that classical logic depends on the choice of the concept of truth as central to the theory of meaning, while for the intuitionist the concept of assertability occupies this position. | |
| From: report of Michael Dummett (The philosophical basis of intuitionist logic [1973]) by Philip Kitcher - The Nature of Mathematical Knowledge 06.5 | |
| A reaction: Since I can assert any nonsense I choose, this presumably means 'warranted' assertability, which is tied to the concept of proof in mathematics. You can reason about falsehoods, or about uninterpreted variables. Can you 'assert' 'Fx'? |
| 19057 | Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett] |
| Full Idea: Classical quantification represents an infinite conjunction or disjunction, and the truth-value is determined by the infinite sum or product of the instances ....but this presupposes that all the instances already possess determinate truth-values. | |
| From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.246) | |
| A reaction: In the case of the universal quantifier, Dummett is doing no more than citing the classic empiricism objection to induction - that you can't make the universal claim if you don't know all the instances. The claim is still meaningful, though. |
| 19055 | Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett] |
| Full Idea: An ability to state the condition for the truth of a sentence is, in effect, no more than an ability to express the content of the sentence in other words. | |
| From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.224) | |
| A reaction: Alternatively, if you give something other than a paraphrase of the sentence as its meaning (such as a proof of its truth), then you seem to have departed from your target sentence. Can we reduce and eliminate our sentences in this way? |
| 19056 | If a sentence is effectively undecidable, we can never know its truth conditions [Dummett] |
| Full Idea: If a sentence is effectively undecidable, the condition which must obtain for it to be true is not one which we are capable of recognising whenever it obtains, or of getting ourselves in a position to do so. | |
| From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.225) | |
| A reaction: The instances of 'undecidable' sentences are most clearly seen in mathematics, such as the Continuum Hypothesis or Goldbach's Conjecture, or anything involving vast infinite cardinals. But do you need precise truth-conditions for meaning? |
| 19054 | Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett] |
| Full Idea: If use constitutes meaning, it might seem that use is beyond criticism. ....But such an attitude can, ultimately, be supported onlly by the adoption of a holistic view of language. | |
| From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.218) | |
| A reaction: Dummett goes on to say that the rejection of the holistic view of mathematical meaning leads to his preference for intuitionistic logic. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 8404 | Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected [Field,H] |
| Full Idea: Some think singular causal claims should be explained in terms of general causal claims; some think the order should be reversed; some think a third thing (e.g. objective probability) will explain both; and some think they are only loosely connected. | |
| From: Hartry Field (Causation in a Physical World [2003], 2) | |
| A reaction: I think Ducasse gives the best account, which is the second option, of giving singular causal claims priority. Probability (Mellor) strikes me as a non-starter, and the idea that they are fairly independent seems rather implausible. |
| 8401 | Physical laws are largely time-symmetric, so they make a poor basis for directional causation [Field,H] |
| Full Idea: It is sometimes pointed out that (perhaps with a few minor exceptions) the fundamental physical laws are completely time-symmetric. If so, then if one is inclined to found causation on fundamental physical law, it isn't evident how directionality gets in. | |
| From: Hartry Field (Causation in a Physical World [2003], 1) | |
| A reaction: All my instincts tell me that causation is more fundamental than laws, and that directionality is there at the start. That, though, raises the nice question of how, if causation explains laws, the direction eventually gets left OUT! |
| 8400 | Identifying cause and effect is not just conventional; we explain later events by earlier ones [Field,H] |
| Full Idea: It is not just that the earlier member of a cause-effect pair is conventionally called the cause; it is also connected with other temporal asymmetries that play an important role in our practices. We tend to explain later events in terms of earlier ones. | |
| From: Hartry Field (Causation in a Physical World [2003], 1) | |
| A reaction: We also interfere with the earlier one to affect the later one, and not vice versa (Idea 8363). I am inclined to think that attempting to explain the direction of causation is either pointless or hopeless. |
| 8402 | The only reason for adding the notion of 'cause' to fundamental physics is directionality [Field,H] |
| Full Idea: Although it is true that the notion of 'cause' is not needed in fundamental physics, even statistical physics, still directionality considerations don't preclude this notion from being consistently added to fundamental physics. | |
| From: Hartry Field (Causation in a Physical World [2003], 1) | |
| A reaction: This only makes sense if the notion of cause already has directionality built into it, which I think is correct. The physicist might reply that they don't care about directionality, but the whole idea of an experiment seems to depend on it (Idea 8363). |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |