196 ideas
7623 | For ancient Greeks being wise was an ethical value [Putnam] |
2352 | The job of the philosopher is to distinguish facts about the world from conventions [Putnam] |
6782 | Realism is the only philosophy of science that doesn't make the success of science a miracle [Putnam] |
6267 | A culture needs to admit that knowledge is more extensive than just 'science' [Putnam] |
6272 | 'True' and 'refers' cannot be made scientically precise, but are fundamental to science [Putnam] |
6276 | 'The rug is green' might be warrantedly assertible even though the rug is not green [Putnam] |
4714 | Putnam's epistemic notion of truth replaces the realism of correspondence with ontological relativism [Putnam, by O'Grady] |
6266 | We need the correspondence theory of truth to understand language and science [Putnam] |
7617 | Before Kant, all philosophers had a correspondence theory of truth [Putnam] |
6277 | Correspondence between concepts and unconceptualised reality is impossible [Putnam] |
4716 | The correspondence theory is wrong, because there is no one correspondence between reality and fact [Putnam, by O'Grady] |
8828 | Truth is rational acceptability [Putnam] |
7616 | Truth is an idealisation of rational acceptability [Putnam] |
18951 | For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam] |
6264 | In Tarski's definition, you understand 'true' if you accept the notions of the object language [Putnam] |
6265 | Tarski has given a correct account of the formal logic of 'true', but there is more to the concept [Putnam] |
6269 | Only Tarski has found a way to define 'true' [Putnam] |
2345 | Semantic notions do not occur in Tarski's definitions, but assessing their correctness involves translation [Putnam] |
2347 | Asserting the truth of an indexical statement is not the same as uttering the statement [Putnam] |
18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
18952 | '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam] |
18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
18958 | In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam] |
9944 | We understand some statements about all sets [Putnam] |
18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
13655 | The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro] |
9915 | V = L just says all sets are constructible [Putnam] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
17824 | The master science is physical objects divided into sets [Maddy] |
8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
18954 | Before the late 19th century logic was trivialised by not dealing with relations [Putnam] |
18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
10066 | Putnam coined the term 'if-thenism' [Putnam, by Musgrave] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
17505 | Using proper names properly doesn't involve necessary and sufficient conditions [Putnam] |
18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
14203 | Intension is not meaning, as 'cube' and 'square-faced polyhedron' are intensionally the same [Putnam] |
14207 | If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam] |
9913 | The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
9937 | I do not believe mathematics either has or needs 'foundations' [Putnam] |
9939 | It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam] |
18182 | The extension of concepts is not important to me [Maddy] |
18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
10718 | A natural number is a property of sets [Maddy, by Oliver] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
3663 | How can you contemplate Platonic entities without causal transactions with them? [Putnam] |
8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
9940 | Maybe mathematics is empirical in that we could try to change it [Putnam] |
9914 | It is unfashionable, but most mathematical intuitions come from nature [Putnam] |
17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
9941 | Science requires more than consistency of mathematics [Putnam] |
18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
6280 | Realism is a theory, which explains the convergence of science and the success of language [Putnam] |
17644 | Metaphysical realism is committed to there being one ultimate true theory [Putnam] |
2349 | Realists believe truth is correspondence, independent of humans, is bivalent, and is unique [Putnam] |
9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
22181 | Putnam says anti-realism is a bad explanation of accurate predictions [Putnam, by Okasha] |
14214 | If we try to cure the abundance of theories with causal links, this is 'just more theory' [Putnam, by Lewis] |
17648 | It is an illusion to think there could be one good scientific theory of reality [Putnam] |
14205 | The sentence 'A cat is on a mat' remains always true when 'cat' means cherry and 'mat' means tree [Putnam] |
7610 | A fact is simply what it is rational to accept [Putnam] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
7618 | Very nominalistic philosophers deny properties, though scientists accept them [Putnam] |
18957 | Nominalism only makes sense if it is materialist [Putnam] |
2351 | Aristotle says an object (e.g. a lamp) has identity if its parts stay together when it is moved [Putnam] |
18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
17643 | Shape is essential relative to 'statue', but not essential relative to 'clay' [Putnam] |
11908 | Putnam bases essences on 'same kind', but same kinds may not share properties [Mackie,P on Putnam] |
14380 | The distinction between necessary and essential properties can be ignored [Rocca] |
18890 | Putnam smuggles essentialism about liquids into his proof that water must be H2O [Salmon,N on Putnam] |
4718 | If necessity is always relative to a description in a language, then there is only 'de dicto' necessity [Putnam, by O'Grady] |
10269 | Mathematics eliminates possibility, as being simultaneous actuality in sets [Putnam] |
9169 | A statement can be metaphysically necessary and epistemologically contingent [Putnam] |
5819 | Conceivability is no proof of possibility [Putnam] |
6284 | If a tautology is immune from revision, why would that make it true? [Putnam] |
17642 | The old view that sense data are independent of mind is quite dotty [Putnam] |
6273 | Knowledge depends on believing others, which must be innate, as inferences are not strong enough [Putnam] |
6274 | Empathy may not give knowledge, but it can give plausibility or right opinion [Putnam] |
7620 | Some kind of objective 'rightness' is a presupposition of thought itself [Putnam] |
18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |
17508 | Science aims at truth, not at 'simplicity' [Putnam] |
14204 | Naïve operationalism would have meanings change every time the tests change [Putnam] |
17084 | You can't decide which explanations are good if you don't attend to the interest-relative aspects [Putnam] |
7705 | The Twin Earth theory suggests that intentionality is independent of qualia [Jacquette on Putnam] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
2590 | Dispositions need mental terms to define them [Putnam] |
3460 | Superactors and superspartans count against behaviourism [Putnam, by Searle] |
2591 | Total paralysis would mean that there were mental states but no behaviour at all [Putnam] |
2588 | Is pain a functional state of a complete organism? [Putnam] |
2589 | Functionalism is compatible with dualism, as pure mind could perform the functions [Putnam] |
2592 | Functional states correlate with AND explain pain behaviour [Putnam] |
5495 | Instances of pain are physical tokens, but the nature of pain is more abstract [Putnam, by Lycan] |
2331 | Functionalism says robots and people are the same at one level of abstraction [Putnam] |
2071 | If concepts have external meaning, computational states won't explain psychology [Putnam] |
2332 | Functionalism can't explain reference and truth, which are needed for logic [Putnam] |
2348 | Is there just one computational state for each specific belief? [Putnam] |
2587 | Temperature is mean molecular kinetic energy, but they are two different concepts [Putnam] |
2344 | If we are going to eliminate folk psychology, we must also eliminate folk logic [Putnam] |
6376 | Neuroscience does not support multiple realisability, and tends to support identity [Polger on Putnam] |
2330 | If humans and molluscs both feel pain, it can't be a single biological state [Putnam, by Kim] |
2074 | Can we give a scientific, computational account of folk psychology? [Putnam] |
7611 | Rationality is one part of our conception of human flourishing [Putnam] |
2605 | If everything uses mentalese, ALL concepts must be innate! [Putnam] |
2606 | No machine language can express generalisations [Putnam] |
4099 | If Twins talking about 'water' and 'XYZ' have different thoughts but identical heads, then thoughts aren't in the head [Putnam, by Crane] |
12026 | We say ice and steam are different forms of water, but not that they are different forms of H2O [Forbes,G on Putnam] |
3208 | Does 'water' mean a particular substance that was 'dubbed'? [Putnam, by Rey] |
14200 | 'Water' on Twin Earth doesn't refer to water, but no mental difference can account for this [Putnam] |
2343 | Reference may be different while mental representation is the same [Putnam] |
9168 | I can't distinguish elm trees, but I mean by 'elm' the same set of trees as everybody else [Putnam] |
5820 | 'Water' has an unnoticed indexical component, referring to stuff around here [Putnam] |
7612 | Reference is social not individual, because we defer to experts when referring to elm trees [Putnam] |
7613 | Concepts are (at least in part) abilities and not occurrences [Putnam] |
6282 | Theory of meaning presupposes theory of understanding and reference [Putnam] |
2346 | Meaning and translation (which are needed to define truth) both presuppose the notion of reference [Putnam] |
6281 | Truth conditions can't explain understanding a sentence, because that in turn needs explanation [Putnam] |
6278 | We should reject the view that truth is prior to meaning [Putnam] |
2354 | "Meaning is use" is not a definition of meaning [Putnam] |
2336 | Holism seems to make fixed definition more or less impossible [Putnam] |
2334 | Meaning holism tried to show that you can't get fixed meanings built out of observation terms [Putnam] |
2335 | Understanding a sentence involves background knowledge and can't be done in isolation [Putnam] |
6271 | How reference is specified is not what reference is [Putnam] |
2340 | We should separate how the reference of 'gold' is fixed from its conceptual content [Putnam] |
2341 | Like names, natural kind terms have their meaning fixed by extension and reference [Putnam] |
17506 | I now think reference by the tests of experts is a special case of being causally connected [Putnam] |
2338 | Reference (say to 'elms') is a social phenomenon which we can leave to experts [Putnam] |
14202 | Neither individual nor community mental states fix reference [Putnam] |
9170 | We need to recognise the contribution of society and of the world in determining reference [Putnam] |
14201 | Maybe the total mental state of a language community fixes the reference of a term [Putnam] |
2339 | Aristotle implies that we have the complete concepts of a language in our heads, but we don't [Putnam] |
3893 | Often reference determines sense, and not (as Frege thought) vice versa [Putnam, by Scruton] |
6268 | The claim that scientific terms are incommensurable can be blocked if scientific terms are not descriptions [Putnam] |
5817 | Language is more like a cooperative steamship than an individual hammer [Putnam] |
6279 | A private language could work with reference and beliefs, and wouldn't need meaning [Putnam] |
6270 | The correct translation is the one that explains the speaker's behaviour [Putnam] |
6283 | Language maps the world in many ways (because it maps onto other languages in many ways) [Putnam] |
14206 | There are infinitely many interpretations of a sentence which can all seem to be 'correct' [Putnam] |
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] |
7624 | The word 'inconsiderate' nicely shows the blurring of facts and values [Putnam] |
11191 | The hidden structure of a natural kind determines membership in all possible worlds [Putnam] |
17507 | Natural kind stereotypes are 'strong' (obvious, like tiger) or 'weak' (obscure, like molybdenum) [Putnam] |
11904 | Express natural kinds as a posteriori predicate connections, not as singular terms [Putnam, by Mackie,P] |
2342 | "Water" is a natural kind term, but "H2O" is a description [Putnam] |
17645 | An alien might think oxygen was the main cause of a forest fire [Putnam] |
11192 | If causes are the essence of diseases, then disease is an example of a relational essence [Putnam, by Williams,NE] |
11190 | Archimedes meant by 'gold' the hidden structure or essence of the stuff [Putnam] |
5818 | If water is H2O in the actual world, there is no possible world where it isn't H2O [Putnam] |