34 ideas
| 2352 | The job of the philosopher is to distinguish facts about the world from conventions [Putnam] |
| Full Idea: It is the job of the philosopher to distinguish what is fact and what is convention in our theorising about the world. | |
| From: Hilary Putnam (Representation and Reality [1988], §7 p.112) | |
| A reaction: This may well be the entire truth about philosophy. It begins with the Nomos-Physis debate in ancient Athens, and it turns out to be the key issue in almost every area of metaphysics, epistemology, aesthetics and morality. |
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| Full Idea: Item x is said to be a sufficient truth-maker for truth-bearer p just in case necessarily if x exists then p is true. ...Every truth has a sufficient truth-maker. Hence, I take it, the sum of all sufficient truth-makers is a universal truth-maker. | |
| From: Peter Forrest (General Facts,Phys Necessity, and Metaph of Time [2006], 1) | |
| A reaction: Note that it is not 'necessary', because something else might make p true instead. |
| 2345 | Semantic notions do not occur in Tarski's definitions, but assessing their correctness involves translation [Putnam] |
| Full Idea: Although no semantic notions are used in Tarski's truth definitions themselves, they are used in deciding when such a definition is correct, namely the notion of translation. | |
| From: Hilary Putnam (Representation and Reality [1988], §4 p.66) |
| 2347 | Asserting the truth of an indexical statement is not the same as uttering the statement [Putnam] |
| Full Idea: If you say "I am going to drive this car", and I say "That's true", that is very different from my saying "I am going to drive this car". | |
| From: Hilary Putnam (Representation and Reality [1988], §4 p.68) |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| Full Idea: In current set theory, the search is on for new axioms to determine the size of the continuum. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §0) | |
| A reaction: This sounds the wrong way round. Presumably we seek axioms that fix everything else about set theory, and then check to see what continuum results. Otherwise we could just pick our continuum, by picking our axioms. |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| Full Idea: The extensional view of sets is preferable because it is simpler, clearer, and more convenient, because it individuates uniquely, and because it can simulate intensional notions when the need arises. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [She cites Fraenkel, Bar-Hillet and Levy for this] The difficulty seems to be whether the extensional notion captures our ordinary intuitive notion of what constitutes a group of things, since that needs flexible size and some sort of unity. |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| Full Idea: Most writers agree that if any sense can be made of the distinction between analytic and synthetic, then the Axiom of Extensionality should be counted as analytic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [Boolos is the source of the idea] In other words Extensionality is not worth discussing, because it simply tells you what the world 'set' means, and there is no room for discussion about that. The set/class called 'humans' varies in size. |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| Full Idea: If one is interested in analysis then infinite sets are indispensable since even the notion of a real number cannot be developed by means of finite sets alone. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: [Maddy is citing Fraenkel, Bar-Hillel and Levy] So Cantor's great breakthrough (Idea 13021) actually follows from the earlier acceptance of the real numbers, so that's where the departure from common sense started. |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| Full Idea: The Axiom of Infinity is a simple statement of Cantor's great breakthrough. His bold hypothesis that a collection of elements that had lurked in the background of mathematics could be infinite launched modern mathematics. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: It also embodies one of those many points where mathematics seems to depart from common sense - but then most subjects depart from common sense when they get more sophisticated. Look what happened to art. |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| Full Idea: The Power Set Axiom is indispensable for a set-theoretic account of the continuum, ...and in so far as those attempts are successful, then the power-set principle gains some confirmatory support. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.6) | |
| A reaction: The continuum is, of course, notoriously problematic. Have we created an extra problem in our attempts at solving the first one? |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| Full Idea: Jordain made consistent and ill-starred efforts to prove the Axiom of Choice. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This would appear to be the fate of most axioms. You would presumably have to use a different system from the one you are engaged with to achieve your proof. |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| Full Idea: Many theorems depend on the Axiom of Choice, including that a countable union of sets is countable, and results in analysis, topology, abstract algebra and mathematical logic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: The modern attitude seems to be to admit anything if it leads to interesting results. It makes you wonder about the modern approach of using mathematics and logic as the cutting edges of ontological thinking. |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| Full Idea: Resistance to the Axiom of Choice centred on opposition between existence and construction. Modern set theory thrives on a realistic approach which says the choice set exists, regardless of whether it can be defined, constructed, or given by a rule. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This seems to be a key case for the ontology that lies at the heart of theory. Choice seems to be an invaluable tool for proofs, so it won't go away, so admit it to the ontology. Hm. So the tools of thought have existence? |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| Full Idea: The Iterative Conception (Zermelo 1930) says everything appears at some stage. Given two objects a and b, let A and B be the stages at which they first appear. Suppose B is after A. Then the pair set of a and b appears at the immediate stage after B. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: Presumably this all happens in 'logical time' (a nice phrase I have just invented!). I suppose we might say that the existence of the paired set is 'forced' by the preceding sets. No transcendental inferences in this story? |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| Full Idea: The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system. |
| 2349 | Realists believe truth is correspondence, independent of humans, is bivalent, and is unique [Putnam] |
| Full Idea: Metaphysical realism about truth is a bundle of ideas: that it is a matter of Correspondence, that it exhibits Independence (of humans), Bivalence, and Uniqueness (there is only one ultimate truth). | |
| From: Hilary Putnam (Representation and Reality [1988], §7 p.107) | |
| A reaction: It requires robust truth, but not correspondence (which is too strict, and too imprecise). Not sure about bivalence, which seems an unwarranted imposition. The other two seem fine, to me. |
| 2351 | Aristotle says an object (e.g. a lamp) has identity if its parts stay together when it is moved [Putnam] |
| Full Idea: The parts of a lamp stay together when it is moved (which is one of Aristotle's criteria for objecthood). | |
| From: Hilary Putnam (Representation and Reality [1988], §7 p.110) | |
| A reaction: Metaphysics 1052a26 (just after the cross-reference) says a thing may be unified 'if its movement is single'. |
| 2331 | Functionalism says robots and people are the same at one level of abstraction [Putnam] |
| Full Idea: My "functionalism" insisted that a robot, a human being, a silicon creature and a disembodied spirit could all work much the same way when described at the relevant level of abstraction, and it is wrong to think the essence of mind is hardware. | |
| From: Hilary Putnam (Representation and Reality [1988], Int p.xii) | |
| A reaction: This is the key point about the theory - that it is an abstract theory of mind, saying nothing about substances. It drew, however, some misguided criticisms suggesting silly implementations. |
| 2348 | Is there just one computational state for each specific belief? [Putnam] |
| Full Idea: The idea that there is one computational state that every being who believes that there are lots of cats in the neighbourhood is in must be false. | |
| From: Hilary Putnam (Representation and Reality [1988], §5 p.84) | |
| A reaction: It is tempting to say that the mental states of such people must have SOMETHING in common, until you realise that all you can specify is that all their states are about cats. |
| 2332 | Functionalism can't explain reference and truth, which are needed for logic [Putnam] |
| Full Idea: Functionalism has as much trouble with physical accounts of reference as of meaning. Reference is the main tool used in formal theories of truth. But 'truth' isn't folk psychology, it is central to logic, which everyone wants. | |
| From: Hilary Putnam (Representation and Reality [1988], Int p.xiv) | |
| A reaction: All logic is defined in terms of truth and falsehood resulting from reasoning, but it could be that 'true' and 'false' have no more content that 1 and 0 in binary electronics. They are distinct, but empty. |
| 2071 | If concepts have external meaning, computational states won't explain psychology [Putnam] |
| Full Idea: Computational models of the brain/mind will not suffice for cognitive psychology. We cannot individuate concepts and beliefs without reference to the environment. Meanings aren't "in the head". | |
| From: Hilary Putnam (Representation and Reality [1988], p.73) | |
| A reaction: Mr Functionalism quits! |
| 2344 | If we are going to eliminate folk psychology, we must also eliminate folk logic [Putnam] |
| Full Idea: Why don't the eliminationists speak of "folk logic" as well as "folk psychology"? | |
| From: Hilary Putnam (Representation and Reality [1988], §4 p.60) | |
| A reaction: I think Putnam considers that if you can prove 'truth' to be a necessary feature of mental life, that connects mind and world, but marking a sentence as 'T' doesn't make any connections. |
| 2074 | Can we give a scientific, computational account of folk psychology? [Putnam] |
| Full Idea: The desire that grips Fodor, as it once gripped me, is the desire to make belief-desire psychology "scientific" by simply identifying it outright with computational psychology. | |
| From: Hilary Putnam (Representation and Reality [1988], p.7) | |
| A reaction: An "outright" identification looks very implausible. It seems that we should accept that belief-desire psychology is a very good guide to normal brain events, but a bad guide to unusual brain events. See Ideas 2987 and 7519. |
| 2343 | Reference may be different while mental representation is the same [Putnam] |
| Full Idea: The 'mental representations' of Earth speakers and Twin Earth speakers were not in any way different; the reference was different because the substances were different. Reference is fixed by the environment itself. | |
| From: Hilary Putnam (Representation and Reality [1988], §2 p.32) | |
| A reaction: There seems to be an elementary distinction here between what you think you are referring to, and what you are in fact referring to. "That man is the Prince of Wales" (pointing at the butler). |
| 2346 | Meaning and translation (which are needed to define truth) both presuppose the notion of reference [Putnam] |
| Full Idea: The notion of meaning, and hence of translation (needed to define truth), presupposes the notion of reference. | |
| From: Hilary Putnam (Representation and Reality [1988], §4 p.67) | |
| A reaction: It is plausible to see reference as the fundamental notion of language. With no anchors in reality, language would be 'private', in LW's sense. |
| 2354 | "Meaning is use" is not a definition of meaning [Putnam] |
| Full Idea: "Meaning is use" is not a definition of meaning. | |
| From: Hilary Putnam (Representation and Reality [1988], §7 p.119) | |
| A reaction: I agree. It probably fails to define meaning because it is false. A corkscrew is not the action of opening a wine bottle. |
| 2334 | Meaning holism tried to show that you can't get fixed meanings built out of observation terms [Putnam] |
| Full Idea: The doctrine of Quine called "meaning holism" offered arguments refuting logical positivist attempts to show that every term we can understand can be defined using a limited group of "observation terms". | |
| From: Hilary Putnam (Representation and Reality [1988], §1 p.08) | |
| A reaction: To seems a rather large jump from saying that sentences come in groups to full-blown 'holism' (involving every sentence). |
| 2335 | Understanding a sentence involves background knowledge and can't be done in isolation [Putnam] |
| Full Idea: If I say "Hawks fly", I do not intend my hearer to deduce that a hawk with a broken wing will fly. What we expect depends on the whole network of belief. Language describes experience as a network, not sentence by sentence. | |
| From: Hilary Putnam (Representation and Reality [1988], §1 p.09) | |
| A reaction: The shortcut through this is 'exactly what did you mean when you said "Hawks fly"?'. That is, get me closer to your proposition. |
| 2336 | Holism seems to make fixed definition more or less impossible [Putnam] |
| Full Idea: Holism immediately suggests that most terms cannot be defined, at least not in a way that is fixed once and for all. | |
| From: Hilary Putnam (Representation and Reality [1988], §1 p.09) | |
| A reaction: Perhaps there exists a single perfect definition for each holistic system, only graspable by a transcendent intellect. Or why can't there be a matching holistic system of definitions? |
| 2340 | We should separate how the reference of 'gold' is fixed from its conceptual content [Putnam] |
| Full Idea: The effect of my account, as of Kripke's, is to separate the question of how the reference of terms such as 'gold' is fixed from the question of their conceptual content. | |
| From: Hilary Putnam (Representation and Reality [1988], §2 p.38) | |
| A reaction: Too simple. 'Gold' isn't a proper name, like 'Hilary', which needs no more content than a serial number. Baptising a gold sample needs much more information than baptising a person. |
| 2341 | Like names, natural kind terms have their meaning fixed by extension and reference [Putnam] |
| Full Idea: It seems that the dominant "component" of natural kind words is the extension. The referential factor does almost all the work, and natural kind terms resemble names. | |
| From: Hilary Putnam (Representation and Reality [1988], §3 p.49) | |
| A reaction: My concept of 'tiger' does not mainly consist of the tigers. Does the concept contract as the tiger population dwindles? Prototypes, exemplars etc. See 'Concepts' |
| 2339 | Aristotle implies that we have the complete concepts of a language in our heads, but we don't [Putnam] |
| Full Idea: What is wrong with the Aristotelian picture (of meaning and reference based on concepts) is that it suggest that everything that is necessary for the use of language is stored in each individual mind, but no individual language works this way. | |
| From: Hilary Putnam (Representation and Reality [1988], §2 p.25) | |
| A reaction: Languages must partly work that way. You can't talk without a conceptual storehouse. In a small society I would expect every adult to know the full vocabulary. |
| 2338 | Reference (say to 'elms') is a social phenomenon which we can leave to experts [Putnam] |
| Full Idea: Reference is a social phenomenon. Individual speakers do not have to know how to distinguish robins, or elms, or aluminium. They can always rely on experts to do this for them. | |
| From: Hilary Putnam (Representation and Reality [1988], §2 p.22) | |
| A reaction: It can't just be a social phenomenon. The experts don't just enquire about standard usage, or defer to Hilary Putnam. |
| 2342 | "Water" is a natural kind term, but "H2O" is a description [Putnam] |
| Full Idea: "Water" functions as a natural kind term, but "H2O" is a description, synonymous with an account of its atoms. | |
| From: Hilary Putnam (Representation and Reality [1988], §3 p.50) |