35 ideas
| 6267 | A culture needs to admit that knowledge is more extensive than just 'science' [Putnam] |
| Full Idea: The acknowledgement that the sphere of knowledge is wider than the sphere of 'science' seems to me to be a cultural necessity if we are to arrive at a sane and human view of ourselves or of science. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Intro) | |
| A reaction: A very nice remark, with which I intuitively agree, but then you are left with the problem of explaining how something can qualify as knowledge when it can't pass the stringent tests of science. How wide to we spread, and why? |
| 6272 | 'True' and 'refers' cannot be made scientically precise, but are fundamental to science [Putnam] |
| Full Idea: Some non-scientific knowledge is presupposed by science; for example, I have been arguing that 'refers' and 'true' cannot be made scientifically precise; yet truth is a fundamental term in logic - a precise science. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Lec VI) | |
| A reaction: We might ask whether we 'know' what 'true' and 'refers' mean, as opposed to being able to use them. If their usage doesn't count as knowledge, then we could still end up with all actual knowledge being somehow 'scientific'. |
| 6276 | 'The rug is green' might be warrantedly assertible even though the rug is not green [Putnam] |
| Full Idea: 'The rug is green' might be warrantedly assertible even though the rug is not green. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Pt Three) | |
| A reaction: The word 'warranted' seems to be ambiguous in modern philosophy. See Idea 6150. There seem to be internalist and externalist versions. It seems clear to say that a belief could be well-justified and yet false. |
| 6266 | We need the correspondence theory of truth to understand language and science [Putnam] |
| Full Idea: A correspondence theory of truth is needed to understand how language works, and how science works. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Intro) | |
| A reaction: Putnam retreated from this position to a more pragmatic one later on, but all my sympathies are with the present view, despite being repeatedly told by modern philosophers that I am wrong. See McGinn (Idea 6085) and Searle (Idea 3508). |
| 6277 | Correspondence between concepts and unconceptualised reality is impossible [Putnam] |
| Full Idea: The great nineteenth century argument against the correspondence theory of truth was that one cannot think of truth as correspondence to facts (or 'reality') because one would need to compare concepts directly with unconceptualised reality. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Pt Three) | |
| A reaction: Presumably the criticism was offered by idealists, who preferred a coherence theory. The defence is to say that there is a confusion here between a concept and the contents of a concept. The contents of a concept are designed to be facts. |
| 6264 | In Tarski's definition, you understand 'true' if you accept the notions of the object language [Putnam] |
| Full Idea: Anyone who accepts the notions of whatever object language is in question - and this can be chosen arbitrarily - can also understand 'true' as defined by Tarski for that object language. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Intro) | |
| A reaction: Thus if we say "'snow is white' is true iff snow is white", then if you 'accept the notion' that snow is white in English, you understand what 'true' means. This seems to leave you with the meaning of 'snow is white' being its truth conditions. |
| 6265 | Tarski has given a correct account of the formal logic of 'true', but there is more to the concept [Putnam] |
| Full Idea: What Tarski has done is to give us a perfectly correct account of the formal logic of the concept 'true', but the formal logic of the concept is not all there is to the notion of truth. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Intro) | |
| A reaction: I find this refreshing. A lot of modern philosophers seem to think that truth is no longer an interesting philosophical topic, because deflationary accounts have sidelined it, but I take the concept to be at the heart of metaphysics. |
| 6269 | Only Tarski has found a way to define 'true' [Putnam] |
| Full Idea: There is only one way anyone knows how to define 'true' and that is Tarski's way. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Lec II.5) | |
| A reaction: However, Davidson wrote a paper called 'On the Folly of Trying to Define Truth', which seems to reject even Tarski. Also bear in mind Putnam's earlier remark (Idea 6265) that there is more to truth than Tarski's definition. Just take 'true' as primitive. |
| 10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
| Full Idea: In 1938 Gödel proved that the Axiom of Choice is consistent with the other axioms of set theory. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: Hence people now standardly accept ZFC, rather than just ZF. |
| 10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
| Full Idea: Zermelo's Axiom of Choice asserts that for any set of non-empty sets that (pairwise) have no elements in common, then there is a set that 'simultaneously chooses' exactly one element from each set. Note that this is an existential claim. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: The Axiom is now widely accepted, after much debate in the early years. Even critics of the Axiom turn out to be relying on it. |
| 10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
| Full Idea: The Axiom of Choice seems clearly true from the Platonistic point of view, independently of how sets may be defined, but is rejected by those who think such existential claims must show how to pick out or define the object claimed to exist. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: The typical critics are likely to be intuitionists or formalists, who seek for both rigour and a plausible epistemology in our theory. |
| 10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
| Full Idea: The Trichotomy Principle (any number is less, equal to, or greater than, another number) turned out to be equivalent to the Axiom of Choice. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) | |
| A reaction: [He credits Sierpinski (1918) with this discovery] |
| 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
| Full Idea: The Axiom of Choice is a pure existence statement, without defining conditions. It was necessary to provide a foundation for Cantor's theory of transfinite cardinals and ordinal numbers, but its nonconstructive character engendered heated controversy. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I) |
| 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
| Full Idea: A structure is said to be a 'model' of an axiom system if each of its axioms is true in the structure (e.g. Euclidean or non-Euclidean geometry). 'Model theory' concerns which structures are models of a given language and axiom system. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
| A reaction: This strikes me as the most interesting aspect of mathematical logic, since it concerns the ways in which syntactic proof-systems actually connect with reality. Tarski is the central theoretician here, and his theory of truth is the key. |
| 10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
| Full Idea: In the late 1950s Tarski and Vaught defined and established basic properties of the relation of elementary equivalence between two structures, which holds when they make true exactly the same first-order sentences. This is fundamental to model theory. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
| A reaction: This is isomorphism, which clarifies what a model is by giving identity conditions between two models. Note that it is 'first-order', and presumably founded on classical logic. |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| Full Idea: The Löwenheim-Skolem Theorem, the earliest in model theory, states that if a countable set of sentences in a first-order language has a model, then it has a countable model. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) | |
| A reaction: There are 'upward' (sentences-to-model) and 'downward' (model-to-sentences) versions of the theory. |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| Full Idea: Before Tarski's work in the 1930s, the main results in model theory were the Löwenheim-Skolem Theorem, and Gödel's establishment in 1929 of the completeness of the axioms and rules for the classical first-order predicate (or quantificational) calculus. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) |
| 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
| Full Idea: Completeness is when, if a sentences holds in every model of a theory, then it is logically derivable from that theory. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V) |
| 10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
| Full Idea: 'Recursion theory' is the subject of what can and cannot be solved by computing machines | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Ch.9) | |
| A reaction: This because 'recursion' will grind out a result step-by-step, as long as the steps will 'halt' eventually. |
| 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
| Full Idea: In 1936 Church showed that Principia Mathematica is undecidable if it is ω-consistent, and a year later Rosser showed that Peano Arithmetic is undecidable, and any consistent extension of it. | |
| From: Feferman / Feferman (Alfred Tarski: life and logic [2004], Int IV) |
| 6280 | Realism is a theory, which explains the convergence of science and the success of language [Putnam] |
| Full Idea: Realism is an empirical theory; it explains the convergence of scientific theories, where earlier theories are often limiting cases of later theories (which is why theoretical terms preserve their reference); and it explains the success of language. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Pt Four) | |
| A reaction: I agree. Personally, I think of Plato's Theory of Forms and all religions as empirical theories. The response from anti-realists is generally to undermine confidence in the evidence which these 'empirical theories' are said to explain. |
| 6284 | If a tautology is immune from revision, why would that make it true? [Putnam] |
| Full Idea: If we held, say, 'All unmarried men are unmarried' as absolutely immune from revision, why would this make it true? | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Pt Four) | |
| A reaction: A very nice question. Like most American philosophers, Putnam accepts Quine's attack on the unrevisability of analytic truths. His point here is that defenders of analytic truths are probably desperate to preserve basic truths, but it won't work. |
| 6273 | Knowledge depends on believing others, which must be innate, as inferences are not strong enough [Putnam] |
| Full Idea: Our ability to picture how people are likely to respond may well be innate; indeed, our disposition to believe what other people tell us (which is fundamental to knowledge) could hardly be an inference, as that isn’t good enough for knowledge. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Lec VI) | |
| A reaction: An interesting claim. There could be an intermediate situation, which is a hard-wired non-conscious inference. When dismantled, the 'innate' brain circuits for assessing testimony could turn out to work on logic and evidence. |
| 6274 | Empathy may not give knowledge, but it can give plausibility or right opinion [Putnam] |
| Full Idea: Empathy with others may give less than 'Knowledge', but it gives more than mere logical or physical possibility; it gives plausibility, or (to revive Platonic terminology) it provides 'right opinion'. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Lec VI) | |
| A reaction: See Ideas 174 and 2140 for Plato. Putnam is exploring areas of knowledge outside the limits of strict science. Behind this claim seems to lie the Principle of Charity (3971), but a gang of systematic liars (e.g. evil students) would be a problem case. |
| 17084 | You can't decide which explanations are good if you don't attend to the interest-relative aspects [Putnam] |
| Full Idea: Explanation is an interest-relative notion …explanation has to be partly a pragmatic concept. To regard the 'pragmatics' of explanation as no part of the concept is to abdicate the job of figuring out what makes an explanation good. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], p. 41-2), quoted by David-Hillel Ruben - Explaining Explanation Ch 1 | |
| A reaction: I suppose this is just obvious, depending on how far you want to take the 'interest-relative' bit. If a fool is fobbed off with a trivial explanation, there must be some non-relative criterion for assessing that. |
| 6282 | Theory of meaning presupposes theory of understanding and reference [Putnam] |
| Full Idea: Theory of meaning presupposes theory of understanding and reference. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Pt Four) | |
| A reaction: How can you have a theory of understanding without a meaning that requires to be understood? Personally I think about the minds of small animals when pondering this, and that seems to put reference and truth at the front of the queue. |
| 6281 | Truth conditions can't explain understanding a sentence, because that in turn needs explanation [Putnam] |
| Full Idea: You can't treat understanding a sentence as knowing its truth conditions, because it then becomes unintelligible what that knowledge in turn consists in. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Pt Four) | |
| A reaction: The implication, I take it, is circularity; how can you specify truth conditions if you don't understand sentences? Putnam here agrees with Dummett that verification must be involved. Something has to be taken as axiomatic in all this. |
| 6278 | We should reject the view that truth is prior to meaning [Putnam] |
| Full Idea: I am suggesting that we reject the view that truth (based on the semantic theory) is prior to meaning. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Pt Three) | |
| A reaction: It is a nice question which of truth or meaning has logical priority. One might start by speculating about how and why animals think. A moth attracted to flame is probably working on truth without much that could be called 'meaning'. |
| 6271 | How reference is specified is not what reference is [Putnam] |
| Full Idea: A theory of how reference is specified isn't a theory of what reference is. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Lec V) | |
| A reaction: A simple and important point. We may achieve reference by naming, describing, grunting or pointing, but the question is, what have we achieved when we get there? |
| 6268 | The claim that scientific terms are incommensurable can be blocked if scientific terms are not descriptions [Putnam] |
| Full Idea: The line of reasoning of Kuhn and Feyerabend can be blocked by arguing (as I have in various places, and as Saul Kripke has) that scientific terms are not synonymous with descriptions. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Lec II.2) | |
| A reaction: A nice clear statement of the motivation for creating the causal theory of reference. See Idea 6162. We could still go back and ask whether we could block scientific relativism by rethinking how descriptions work, instead of abandoning them. |
| 6279 | A private language could work with reference and beliefs, and wouldn't need meaning [Putnam] |
| Full Idea: A language made up and used by a being who belonged to no community would have no need for such a concept as the 'meaning' of a term. To state the reference of each term and what the language speaker believes is to tell the whole story. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Pt Three) | |
| A reaction: A subtle response to Wittgenstein's claim (e.g. Ideas 4152,4158), but I am not sure what Putnam means. I would have thought that beliefs had to be embodied in propositions. They may not need 'meaning' quite as urgently as sentences, but still… |
| 6270 | The correct translation is the one that explains the speaker's behaviour [Putnam] |
| Full Idea: What it is to be a correct translation is to be the translation that best explains the behaviour of the speaker. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Lec III) | |
| A reaction: This seems fairly close to Quine, but rather puzzlingly uses the word 'correct'. If our criteria of translation are purely behavioural, there is no way we can be correct after one word ('gavagai'), so at what point does it become 'correct'? |
| 6283 | Language maps the world in many ways (because it maps onto other languages in many ways) [Putnam] |
| Full Idea: We could say that the language has more than one correct way of being mapped onto the world (it must, since it has more than one way of being correctly mapped onto a language which is itself correctly mapped onto the world). | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Pt Four) | |
| A reaction: This spells out nicely the significance of Quine's 'indeterminacy of translation'. Others have pointed out that the fact that language maps onto world in many ways need not be anti-realist; the world is endless, and language is limited. |
| 6275 | You can't say 'most speaker's beliefs are true'; in some areas this is not so, and you can't count beliefs [Putnam] |
| Full Idea: The maxim that 'most of a speaker's beliefs are true' as an a priori principle governing radical translation seems to me to go too far; first, I don't know how to count beliefs; second, most people's beliefs on some topics (philosophy) are probably false. | |
| From: Hilary Putnam (Meaning and the Moral Sciences [1978], Pt Three) | |
| A reaction: Putnam prefers a pragmatic view, where charity is applicable if behaviour is involved. Philosophy is too purely theoretical. The extent to which Charity should apply in philosophy seminars is a nice question, which all students should test in practice. |
| 21137 | Rawls rejected cosmopolitanism because it doesn't respect the autonomy of 'peoples' [Rawls, by Shorten] |
| Full Idea: Rawls rejected the cosmopolitan extension of his theory because he thought it failed to respect the political autonomy of 'peoples', which was his term of art for societies or political communities. | |
| From: report of John Rawls (The Law of Peoples [1999], p.115-8) by Andrew Shorten - Contemporary Political Theory 09 | |
| A reaction: Interesting that you might well start with the concept of 'a people', prior to some sort of social contract, but end up with rather alarming conflicts or indifference between rival peoples. Why should my people help in the famine next door? |