36 ideas
| 2653 | If the parts of the universe are subject to the law of nature, the whole universe must also be subject to it [Cicero] |
| Full Idea: If the parts of the universe are subject to the law of nature, then the universe itself must be subject to this law. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.86) |
| 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. |
| 2628 | Why would mind mix with matter if it didn't need it? [Cicero] |
| Full Idea: If the gods have no need of the sensible world, why mix up mind with water and water with mind, if mind can exist by itself without any need of matter? | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.24) | |
| A reaction: This question migrates into our puzzles about why a separate mental substance would be produced by evolution. If it is device physical systems use to promote themselves, mental substance is reduced to an inferior and dependent role. |
| 20814 | Eloquence educates, exhorts, comforts, distracts and unites us, and raises us from savagery [Cicero] |
| Full Idea: How wonderful is the power of eloquence! It enables us to learn and to teach. We use it to exhort and persuade, to comfort the unfortunate, to distract the timid and calm the passionate. It unites us in law and society, and raises us from savagery. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], 2.147) | |
| A reaction: [compressed] Cicero would have been well aware of the doubts about rhetoric felt by Socrates (and possibly Plato). Cicero was probably the greatest Roman orator. |
| 2640 | We have the death penalty, but still have thousands of robbers [Cicero] |
| Full Idea: We have robbers by the thousand, although they have the penalty of death before their eyes. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.86) |
| 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. |
| 2652 | Some regard nature simply as an irrational force that imparts movement [Cicero] |
| Full Idea: Some regard nature as an irrational force which merely imparts a mechanical motion to material bodies. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.81) |
| 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. |
| 2645 | Why shouldn't the gods fear their own destruction? [Cicero] |
| Full Idea: Why should the gods not be apprehensive of their own possible dissolution? | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.114) |
| 2627 | I wonder whether loss of reverence for the gods would mean the end of all virtue [Cicero] |
| Full Idea: I do not know whether, if our reverence for the gods were lost, we should not also see the end of good faith, of human brotherhood, and even of justice itself, which is the keystone of all the virtues. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.3) |
| 2651 | God doesn't obey the laws of nature; they are subject to the law of God [Cicero] |
| Full Idea: God is not subject to obey the laws of nature. It is nature that is subject to the laws of God. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.77) |
| 2634 | It seems clear to me that we have an innate idea of the divine [Cicero] |
| Full Idea: Let us take it as agreed that we have a preconception or "an innate idea" (as I have called it) or a prior knowledge of the divine. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.44) |
| 2636 | Many primitive people know nothing of the gods [Cicero] |
| Full Idea: There must be many wild and primitive peoples who have no idea of the gods at all. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.62) |
| 2655 | If the barbarians of Britain saw a complex machine, they would be baffled, but would know it was designed [Cicero] |
| Full Idea: If someone were to take the celestial globe of Posidonius and show it to the people of Britain, would a single one of those barbarians fail to see that it was the product of a conscious intelligence? | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.88) |
| 2656 | Chance is no more likely to create the world than spilling lots of letters is likely to create a famous poem [Cicero] |
| Full Idea: If someone thinks chance made the world, he should also think that if an infinite number of the letters of the alphabet were shaken together and poured out on the ground it would be possible for them to spell out the whole 'Annals' of Ennius. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.93) |
| 2647 | It is obvious from order that someone is in charge, as when we visit a gymnasium [Cicero] |
| Full Idea: If one comes into a gymnasium and sees everything properly arranged and carried on in order, one does not imagine these arrangements to be accidental, but infers that there is someone in command whose orders are obeyed. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.15) |
| 2650 | If a person cannot feel the power of God when looking at the stars, they are probably incapable of feeling [Cicero] |
| Full Idea: If any man cannot feel the power of God when he looks upon the stars, then I doubt whether he is capable of any feeling at all. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], II.55) |
| 2657 | If everything with regular movement and order is divine, then recurrent illnesses must be divine [Cicero] |
| Full Idea: Are we to find a divinity in every regular movement and in everything which happens in a constant order? If so, we shall have to say that tertian and quartan agues are divine because their course and recurrence is absolutely uniform. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], III.24) |
| 2638 | Either the gods are identical, or one is more beautiful than another [Cicero] |
| Full Idea: Are the gods all exactly the same? If not, then one must be more beautiful than another. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.80) |
| 2635 | The gods are happy, so virtuous, so rational, so must have human shape [Cicero] |
| Full Idea: We agree the gods are happy, and no happiness is possible without virtue: there is no virtue without reason: and reason is associated only with the human form: then it must follow that the gods themselves have human shape. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.48) |
| 2641 | Why believe in gods if you have never seen them? [Cicero] |
| Full Idea: Did you ever actually see a god? Then why do you believe that gods exist? | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], I.88) |
| 2659 | The lists of good men who have suffered and bad men who have prospered are endless [Cicero] |
| Full Idea: Time would fail me if I tried to list all the good men for whom things have turned out badly. So it would if I tried to mention all the wicked who have prospered. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], III.80) |
| 2658 | The gods blame men for having vices, but they could have given us enough reason to avoid them [Cicero] |
| Full Idea: You gods say that the fault lies in the vices of mankind. But you could have endowed men with reason in a form which would exclude all vice and crime. | |
| From: M. Tullius Cicero (On the Nature of the Gods ('De natura deorum') [c.44 BCE], III.76) |