23 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). |
| 21506 | A coherence theory of justification can combine with a correspondence theory of truth [Bonjour] |
| Full Idea: There is no manifest absurdity in combining a coherence theory of justification with a correspondence theory of truth. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.1) | |
| A reaction: His point is to sharply (and correctly) distinguish coherent justification from a coherence theory of truth. Personally I would recommend talking of a 'robust' theory of truth, without tricky commitment to 'correspondence' between very dissimilar things. |
| 21509 | There will always be a vast number of equally coherent but rival systems [Bonjour] |
| Full Idea: On any plausible conception of coherence, there will always be many, probably infinitely many, different and incompatible systems of belief which are equally coherent. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.5) | |
| A reaction: If 'infinitely many' theories are allowed, that blocks the coherentist hope that widening and precisifying the system will narrow down the options and offer some verisimilitude. If we stick to current English expression, that should keep them finite. |
| 21503 | Empirical coherence must attribute reliability to spontaneous experience [Bonjour] |
| Full Idea: An empirical coherence theory needs, for the beliefs of a cognitive system to be even candidates for empirical justification, that the system must contain laws attributing a high degree of reliability to a variety of spontaneous cognitive beliefs. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 7.1) | |
| A reaction: Wanting such a 'law' seems optimistic, and not in the spirit of true coherentism, which can individually evaluate each experiential belief. I'm not sure Bonjour's Observation Requirement is needed, since it is incoherent to neglect observations. |
| 21511 | A well written novel cannot possibly match a real belief system for coherence [Bonjour] |
| Full Idea: It is not even minimally plausible that a well written novel ...would have the degree of coherence required to be a serious alternative to anyone's actual system of beliefs. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.5) | |
| A reaction: This seems correct. 'Bleak House' is wonderfully consistent, but its elements are entirely verbal, and nothing occupies the space between the facts that are described. And Lady Dedlock is not in Debrett. I think this kills a standard objection. |
| 21510 | The objection that a negated system is equally coherent assume that coherence is consistency [Bonjour] |
| Full Idea: Sometimes it is said that if one has an appropriately coherent system, an alternative system can be produced simply be negating all of the components of the first system. This would only be so if coherence amounted simply to consistency. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.5) | |
| A reaction: I associate Russell with this original objection to coherentism. I formerly took this to be a serious problem, and am now relieved to see that it clearly isn't. |
| 21505 | A coherent system can be justified with initial beliefs lacking all credibility [Bonjour] |
| Full Idea: It is simply not necessary in order for [the coherence] view to yield justification to suppose that cognitively spontaneous beliefs have some degree of initial or independent credibility. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 7.2) | |
| A reaction: This is thoroughly and rather persuasively criticised by Erik Olson. But he always focuses on the coherence of a 'system' with multiple beliefs. I take the credibility of each individual belief to need coherent assessment against a full background. |
| 21504 | The best explanation of coherent observations is they are caused by and correspond to reality [Bonjour] |
| Full Idea: The best explanation for a stable system of beliefs which rely on observation is that the beliefs are caused by what they depict, and the system roughly corresponds to the independent reality it describes. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 8.3) | |
| A reaction: [compressed] Anyone who links best explanation to coherence (and to induction) warms the cockles of my heart. Erik Olson offers a critique, but doesn't convince me. The alternative is to find a better explanation (than reality), or give up. |
| 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. |
| 21508 | Anomalies challenge the claim that the basic explanations are actually basic [Bonjour] |
| Full Idea: The distinctive significance of anomalies lies in the fact that they undermine the claim of the allegedly basic explanatory principles to be genuinely basic. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.3) | |
| A reaction: This seems plausible, suggesting that (rather than an anomaly flatly 'falsifying' a theory) an anomaly may just demand a restructuring or reconceptualising of the theory. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |