18 ideas
18951 | For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam] |
Full Idea: For a language L there is a predicate 'true-in-L' which one can employ for all scientific purposes in place of intuitive truth, and this predicate admits of a precise definition using only the vocabulary of L itself plus set theory. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.2) | |
A reaction: He refers, of course, to Tarski's theory. I'm unclear of the division between 'scientific purposes' and the rest of life (which is why some people embrace 'minimal' theories of ordinary truth). I'm struck by set theory being a necessary feature. |
18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
Full Idea: In modern notation we can consider potential logical principles that Aristotle never considered because of his general practice of looking at inferences each of whose premises involved exactly two class-names. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
A reaction: Presumably you can build up complex inferences from a pair of terms, just as you do with pairs in set theory. |
18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
Full Idea: On its modern interpretation, the validity of the inference 'All S are M; All M are P; so All S are P' just expresses the transitivity of the relation 'subclass of'. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.1) | |
A reaction: A simple point I've never quite grasped. Since lots of syllogisms can be expressed as Venn Diagrams, in which the circles are just sets, it's kind of obvious really. So why does Sommers go back to 'terms'? See 'Term Logic'. |
18952 | '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam] |
Full Idea: The symbol '⊃' (read 'if...then') is used with the definition 'Px ⊃ Qx' ('if Px then Qx') is short for '¬(Px & ¬Qx)'. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
A reaction: So ⊃ and → are just abbreviations, and not really a proper part of the language. Notoriously, though, this is quite a long way from what 'if...then' means in ordinary English, and it leads to paradoxical oddities. |
18958 | In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam] |
Full Idea: In the theory of types, 'x ∈ y' is well defined only if x and y are of the appropriate type, where individuals count as the zero type, sets of individuals as type one, sets of sets of individuals as type two. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.6) |
18954 | Before the late 19th century logic was trivialised by not dealing with relations [Putnam] |
Full Idea: It was essentially the failure to develop a logic of relations that trivialised the logic studied before the end of the nineteenth century. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
A reaction: De Morgan, Peirce and Frege were, I believe, the people who put this right. |
18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
Full Idea: The natural understanding of first-order logic is that in writing down first-order schemata we are implicitly asserting their validity, that is, making second-order assertions. ...Thus even quantification theory involves reference to classes. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
A reaction: If, as a nominalist, you totally rejected classes, presumably you would get by in first-order logic somehow. To say 'there are no classes so there is no logical validity' sounds bonkers. |
18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
Full Idea: Today, the tendency among philosophers is to assume that in no sense does logic itself have an empirical foundation. I believe this tendency is wrong. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.9) | |
A reaction: I agree, not on the basis of indispensability to science, but on the basis of psychological processes that lead from experience to logic. Russell and Quine are Putnam's allies here, and Frege is his opponent. Putnam developed a quantum logic. |
18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
Full Idea: Instead of identifying functions with certain sets, I might have identified sets with certain functions. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.9) |
18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
Full Idea: I don't think all substitution-instances of a valid schema are 'true'; some are clearly meaningless, such as 'If all boojums are snarks and all snarks are egglehumphs, then all boojums are egglehumphs'. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
A reaction: This seems like a very good challenge to Quine's claim that it is only form which produces a logical truth. Keep deductive and semantic consequence separate, with two different types of 'logical truth'. |
18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example) should today be investigated in an 'if-then' spirit. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.7) | |
A reaction: This attitude goes back to Hilbert, but it fits with Quine's view of what is indispensable for science. It is hard to see a reason for the cut-off, just looking at the logic of expanding sets. |
18957 | Nominalism only makes sense if it is materialist [Putnam] |
Full Idea: Nominalists must at heart be materialists, or so it seems to me: otherwise their scruples are unintelligible. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.5) | |
A reaction: This is modern nominalism - the rejection of abstract objects. I largely plead guilty to both charges. |
18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
Full Idea: Physics is full of references to such 'non-physical' entities as state-vectors, Hamiltonians, Hilbert space etc. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.2) | |
A reaction: I take these to be concepts which are 'abstracted' from the physical facts, and so they don't strike me as being much of an ontological problem, or an objection to nominalism (which Putnam takes them to be). |
18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |
Full Idea: Scientists want successful predictions in order to confirm their theories; they do not want theories in order to obtain the predictions, which are in some cases of not the slightest interest in themselves. | |
From: Hilary Putnam (Philosophy of Logic [1971], Ch.8) | |
A reaction: Equally, we might only care about the prediction, and have no interest at all in the theory. Farmers want weather predictions, not a PhD in meteorology. |
22439 | There are only duties if there are rights, so truth is only for those with a right to it [Constant] |
Full Idea: A duty is that on the part of one being which corresponds to the rights of another. Where there are no rights there are no duties. To tell the truth is therefore a duty, but only to the one who has the right to the truth. | |
From: Benjamin Constant (On Political Reactions [1797], p.123), quoted by Immanuel Kant - On a supposed right to lie p.28 | |
A reaction: We can't claim a right to have all questions answered truthfully (because there is a right to privacy), but we might claim a right not to be lied to (as long as we accept a refusal to answer). Kant rejected this idea. |
22440 | Unconditional truth-telling makes a society impossible [Constant] |
Full Idea: The moral principle 'it is a duty to tell the truth' would, if taken unconditionally and singly, make any society impossible. | |
From: Benjamin Constant (On Political Reactions [1797], p.124), quoted by Immanuel Kant - On a supposed right to lie p.28 | |
A reaction: He gives the well known example of the murderer at the door asking if your friend is inside. Compare everyone becoming perfectly telepathic. Our society would collapse, but a new society would learn to live with it. |
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. |
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. |