44 ideas
| 2319 | Metaphysics is the clarification of the ontological relationships between different areas of thought [Kim] |
| Full Idea: Metaphysics is the domain where different languages, theories, explanations, and conceptual systems come together and have their mutual ontological relationships sorted out and clarified. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §3 p.066) |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| Full Idea: Gödel's proof wrought an abrupt turn in the philosophy of mathematics. We had supposed that truth, in mathematics, consisted in provability. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Willard Quine - Forward to Gödel's Unpublished | |
| A reaction: This explains the crisis in the early 1930s, which Tarski's theory appeared to solve. |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| Full Idea: Gödel's incompleteness results of 1931 show that all axiom systems precise enough to satisfy Hilbert's conception are necessarily incomplete. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1215 | |
| A reaction: [Hallett italicises 'necessarily'] Hilbert axioms have to be recursive - that is, everything in the system must track back to them. |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| Full Idea: The inherent limitations of the axiomatic method were first brought to light by the incompleteness theorems. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Koellner - On the Question of Absolute Undecidability 1.1 |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| Full Idea: Second Incompleteness Theorem: roughly, nice theories that include enough basic arithmetic can't prove their own consistency. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 1.5 | |
| A reaction: On the face of it, this sounds less surprising than the First Theorem. Philosophers have often noticed that it seems unlikely that you could use reason to prove reason, as when Descartes just relies on 'clear and distinct ideas'. |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| Full Idea: Gödel showed PA cannot be proved consistent from with PA. But 'reflection principles' can be added, which are axioms partially expressing the soundness of PA, by asserting what is provable. A Global Reflection Principle asserts full soundness. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Halbach,V/Leigh,G.E. - Axiomatic Theories of Truth (2013 ver) 1.2 | |
| A reaction: The authors point out that this needs a truth predicate within the language, so disquotational truth won't do, and there is a motivation for an axiomatic theory of truth. |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| Full Idea: Where Gödel's First Theorem sabotages logicist ambitions, the Second Theorem sabotages Hilbert's Programme. | |
| From: comment on Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 36 | |
| A reaction: Neo-logicism (Crispin Wright etc.) has a strategy for evading the First Theorem. |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| Full Idea: My undecidable arithmetical sentence ...is not at all absolutely undecidable; rather, one can always pass to 'higher' systems in which the sentence in question is decidable. | |
| From: Kurt Gödel (On Formally Undecidable Propositions [1931]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.1 | |
| A reaction: [a 1931 MS] He says the reals are 'higher' than the naturals, and the axioms of set theory are higher still. The addition of a truth predicate is part of what makes the sentence become decidable. |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| Full Idea: Gödel's far-reaching work on the nature of logic and formal systems reveals that there can be no single consistent theory from which all mathematical truths can be derived. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.8 |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| Full Idea: Gödel's theorem states that either arithmetic is incomplete, or it is inconsistent. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Georges Rey - Contemporary Philosophy of Mind 8.7 |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| Full Idea: First Incompleteness Theorem: any properly axiomatised and consistent theory of basic arithmetic must remain incomplete, whatever our efforts to complete it by throwing further axioms into the mix. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 1.2 | |
| A reaction: This is because it is always possible to formulate a well-formed sentence which is not provable within the theory. |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| Full Idea: The vast continent of arithmetical truth cannot be brought into systematic order by laying down a fixed set of axioms and rules of inference from which every true mathematical statement can be formally derived. For some this was a shocking revelation. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by E Nagel / JR Newman - Gödel's Proof VII.C | |
| A reaction: Good news for philosophy, I'd say. The truth cannot be worked out by mechanical procedures, so it needs the subtle and intuitive intelligence of your proper philosopher (Parmenides is the role model) to actually understand reality. |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| Full Idea: Gödel's Second Incompleteness Theorem says that true unprovable sentences are clearly semantic consequences of the axioms in the sense that they are necessarily true if the axioms are true. So semantic consequence outruns provability. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Robert Hanna - Rationality and Logic 5.3 |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| Full Idea: First Incompleteness Theorem: If S is a sufficiently powerful formal system, then if S is consistent then S is syntactically incomplete. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Gödel found a single sentence, effectively saying 'I am unprovable in S', which is neither provable nor refutable in S. |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| Full Idea: Second Incompleteness Theorem: If S is a sufficiently powerful formal system, then if S is consistent then S cannot prove its own consistency | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems much less surprising than the First Theorem (though it derives from it). It was always kind of obvious that you couldn't use reason to prove that reason works (see, for example, the Cartesian Circle). |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| Full Idea: The original Gödel construction gives us a sentence that a theory shows is true if and only if it satisfies the condition of being unprovable-in-that-theory. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 20.5 |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| Full Idea: An approximation of Gödel's Theorem imagines a statement 'This system of mathematics can't prove this statement true'. If the system proves the statement, then it can't prove it. If the statement can't prove the statement, clearly it still can't prove it. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 | |
| A reaction: Gödel's contribution to this simple idea seems to be a demonstration that formal arithmetic is capable of expressing such a statement. |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10) | |
| A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity. |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08) | |
| A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning. |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| Full Idea: Gödel defended impredicative definitions on grounds of ontological realism. From that perspective, an impredicative definition is a description of an existing entity with reference to other existing entities. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Stewart Shapiro - Thinking About Mathematics 5.3 | |
| A reaction: This is why constructivists must be absolutely precise about definition, where realists only have to do their best. Compare building a car with painting a landscape. |
| 2317 | Reductionism is good on light, genes, temperature and transparency [Kim, by PG] |
| Full Idea: Examples where reductionism seems to give a good account of things are light, genes, temperature and transparency. | |
| From: report of Jaegwon Kim (Mind in a Physical World [1998], §1 p.025) by PG - Db (ideas) | |
| A reaction: This a fairly simple examples, thoroughly confirmed by science a long time ago. Life is a nicer example, because it is more complex and less obvious, but pretty much beyond dispute these days. |
| 2310 | Supervenience is linked to dependence [Kim] |
| Full Idea: It is customary to associate supervenience with the idea of dependence or determination. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §1 p.011) | |
| A reaction: It is only 'customary' because, in principle, the supervenience might just be a coincidence. I might follow someone everywhere because I love them (dependence) or because they force me to (determination). There's always a reason. |
| 2315 | Mereological supervenience says wholes are fixed by parts [Kim] |
| Full Idea: Mereological supervenience is the doctrine that wholes are fixed by the properties and relations that characterise their parts. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §1 p.018) | |
| A reaction: Presumably this would be the opposite of 'holism'. Personally I would take mereological supervenience to be not merely correct, but to be metaphysically necessary. Don't ask me to prove it, of course. |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01) |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02) |
| 2329 | Causal power is a good way of distinguishing the real from the unreal [Kim] |
| Full Idea: A plausible criterion for distinguishing what is real from what is not real is the possession of causal power. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §4 p.119) |
| 2320 | Properties can have causal powers lacked by their constituents [Kim] |
| Full Idea: Macroproperties can, and in general do, have their own causal powers, powers that go beyond the causal powers of their microconstituents. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §3 p.085) | |
| A reaction: I don't see why the macro-powers 'go beyond' the sum of the micro-powers. Admittedly one molecule can't be slippery, but slipperiness can be totally reduced to molecule behaviour. |
| 530 | There are two contradictory arguments about everything [Kim] |
| Full Idea: There are two contradictory arguments about everything. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], B06a), quoted by (who?) - where? |
| 13314 | Protagoras says arguments on both sides are always equal [Kim, by Seneca] |
| Full Idea: Protagoras declares that it is possible to argue either side of any question with equal force, even the question whether or not one can equally argue either side of any question! | |
| From: report of Jaegwon Kim (Mind in a Physical World [1998]) by Seneca the Younger - Letters from a Stoic 088 | |
| A reaction: This is perhaps the most famous sceptical argument in the ancient world (though, note, Protagoras is most famous for his relativism rather than his scepticism). It is, of course, wrong. The arguments are sometimes equal, but often they are not. |
| 2065 | Not every person is the measure of all things, but only wise people [Plato on Kim] |
| Full Idea: We do not agree that every person is the measure of all things, but only wise people. | |
| From: comment on Jaegwon Kim (Mind in a Physical World [1998], B01) by Plato - Theaetetus 183c | |
| A reaction: I fully agree with this, but only because I have an optimistic view that rational people converge on the truth. |
| 1550 | Why didn't Protagoras begin by saying "a tadpole is the measure of all things"? [Plato on Kim] |
| Full Idea: Why didn't he start 'Truth' off by saying "A pig is the measure of all things", or "a baboon",…or " tadpole"? That would have been a magnificently haughty beginning. | |
| From: comment on Jaegwon Kim (Mind in a Physical World [1998], B01) by Plato - Theaetetus 161d1 |
| 2318 | Agency, knowledge, reason, memory, psychology all need mental causes [Kim, by PG] |
| Full Idea: The following all require a belief in mental causation: agency (mind causes events), knowledge (perception causes beliefs), reasoning (one belief causes another), memory (events cause ideas), psychology (science of mental causes). | |
| From: report of Jaegwon Kim (Mind in a Physical World [1998], §2 p.031) by PG - Db (ideas) | |
| A reaction: A very good list, which I cannot fault, and to which I cannot add. The question is: is there any mental activity left over which does NOT require causation? Candidates are free will, and the contingent character of qualia. I say the answer is, no. |
| 2325 | It seems impossible that an exact physical copy of this world could lack intentionality [Kim] |
| Full Idea: It seems to me inconceivable that a possible world exists that is an exact physical duplicate of this world but lacking wholly in intentionality. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §4 p.101) | |
| A reaction: Personally I can't conceive of such a world lacking qualia either. The physical entails the mental, say I. |
| 2324 | Intentionality as function seems possible [Kim] |
| Full Idea: There has been much scepticism about a functionalist account of intentionality, particularly from Putnam (recently) and Searle, but, like many others, I don't see any principled objections to such an account. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §4 p.101) | |
| A reaction: I agree. I don't believe that intentionality is a candidate for being one of those many 'magic' qualities which are supposed to make the reduction of mind to brain impossible. |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| Full Idea: Gödel in his completeness theorem for first-order logic showed that a certain set of syntactically specifiable rules was adequate to capture all first-order valid arguments. No semantics (e.g. reference, truth, validity) was necessary. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Georges Rey - Contemporary Philosophy of Mind 8.2 | |
| A reaction: This implies that a logic machine is possible, but we shouldn't raise our hopes for proper rationality. Validity can be shown for purely algebraic arguments, but rationality requires truth as well as validity, and that needs propositions and semantics. |
| 2314 | Maybe intentionality is reducible, but qualia aren't [Kim] |
| Full Idea: It is possible to hold that phenomenal properties (qualia) are irreducible, while holding intentional properties, including propositional attitudes, to be reducible (functionally, or biologically). | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §1 p.017) | |
| A reaction: This is the position which Kim has settled for, but I find it baffling. If the universe is full of irreducibles that is one thing, but if everything in the universe is reducible except for one tiny item, that is implausible. |
| 2313 | Emergentism says there is no explanation for a supervenient property [Kim] |
| Full Idea: The emergentism (of Searle), like ethical intuitionism, views mind-body supervenience as something that admits no explanation - it is a brute fact. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §1 p.013) | |
| A reaction: This is why 'emergence' is no sort of theory, and is really old-fashioned dualism in a dubious naturalistic disguise. If mind 'emerges', there is presumably a causal mechanism for that. |
| 2328 | The only mental property that might be emergent is that of qualia [Kim] |
| Full Idea: If emergentism is correct about anything, it is more likely to be correct about qualia than about anything else. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §4 p.103) | |
| A reaction: I'm puzzled by a view that says that nearly all of the mind is reducible, but one tiny aspect of it is 'emergent'. What sort of ontology is envisaged by that? |
| 2309 | Non-Reductive Physicalism relies on supervenience [Kim] |
| Full Idea: Many philosophers saw in mind-body supervenience a satisfying metaphysical statement of physicalism without reductionism. This widely influential position is now known as "nonreductive physicalism". | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §1 p.008) | |
| A reaction: If two things supervene on one another, then we should be asking why. Occasionalism and Parallelism are presumably not the answer. Coldness supervenes on ice. |
| 2311 | Maybe strong supervenience implies reduction [Kim] |
| Full Idea: Maybe strong supervenience is inconsistent with the irreducibility of the supervenient properties to their subvenient bases. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §1 p.012) | |
| A reaction: If two things are really very very supervenient on one another (superdupervenient?), then you have to ask WHY? If there isn't identity, then there is surely a highly lawlike connection? |
| 2308 | Identity theory was overthrown by multiple realisations and causal anomalies [Kim] |
| Full Idea: The two principle arguments which overthrew the mind-brain identity theory were the multiple realization argument of Hilary Putnam, and the anomalist argument of Davidson, which contained the seeds of functionalism and anomalous monism. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §1 p.002) | |
| A reaction: The first argument strikes me as significant and interesting, but Davidson seems weak. It makes the unsubstantiated claim that mind is outside the laws of physics, and irreducible. |
| 2322 | Multiple realisation applies to other species, and even one individual over time [Kim] |
| Full Idea: Multiple realization goes deeper and wider than biological species, and even in the same individual the neural realizer, or correlate, of a given mental state or function may change over time through maturation and brain injuries. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §4 p.095) | |
| A reaction: The tricky question here is what you mean by 'change'. How different must a pattern of neurons be before you say it is of a different type? How do you individuate a type? |
| 2327 | Knowledge and inversion make functionalism about qualia doubtful [Kim] |
| Full Idea: My doubts about functionalist accounts of qualia are based on the much discussed arguments from qualia inversions, and from epistemic considerations. | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §4 p.102) | |
| A reaction: With a colour inversion experience changes but function doesn't. But maybe function does change if you ask the right questions. 'Is this a warm colour?' It certainly strikes me that qualia contain useful (epistemic) information. |
| 2323 | Emotions have both intentionality and qualia [Kim] |
| Full Idea: It has been customary to distinguish between two broad categories of mental phenomena, the intentional and the phenomenal, without excluding those that have both (e.g. emotions). | |
| From: Jaegwon Kim (Mind in a Physical World [1998], §4 p.101) | |
| A reaction: This has become the conventional modern account of the mind. It seems a little too simple to say that the mind is characterised by two clearcut phenomena like this. I suspect that his picture will be modified in time. |