52 ideas
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| Full Idea: I uphold the belief that for clear questions posed by reason, reason can also find clear answers. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.5 | |
| A reaction: [written in 1961] This contradicts the implication normally taken from his much earlier Incompleteness Theorems. |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| Full Idea: Impredicative Definitions are definitions of an object by reference to the totality to which the object itself (and perhaps also things definable only in terms of that object) belong. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], n 13) |
| 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| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Willard Quine - Forward to Gödel's Unpublished | |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. |
| 17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
| Full Idea: Gödel proved the completeness of first order predicate logic in his doctoral dissertation of 1930. | |
| From: report of Kurt Gödel (Completeness of Axioms of Logic [1930]) by Michal Walicki - Introduction to Mathematical Logic History E.2.2 |
| 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. |
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| Full Idea: We have something like perception of the objects of set theory, shown by the axioms forcing themselves on us as being true. I don't see why we should have less confidence in this kind of perception (i.e. mathematical intuition) than in sense perception. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.483), quoted by Michčle Friend - Introducing the Philosophy of Mathematics 2.4 | |
| A reaction: A famous strong expression of realism about the existence of sets. It is remarkable how the ingredients of mathematics spread themselves before the mind like a landscape, inviting journeys - but I think that just shows how minds cope with abstractions. |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| Full Idea: Gödel proved the classical relative consistency of the axiom V = L (which implies the axiom of choice and the generalized continuum hypothesis). This established the full independence of the continuum hypothesis from the other axioms. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Hilary Putnam - Mathematics without Foundations | |
| A reaction: Gödel initially wanted to make V = L an axiom, but the changed his mind. Maddy has lots to say on the subject. |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| Full Idea: In the superior realist and simple theory of types, the place of the axiom of reducibility is not taken by the axiom of classes, Zermelo's Aussonderungsaxiom. | |
| From: report of Kurt Gödel (Russell's Mathematical Logic [1944], p.140-1) by Bernard Linsky - Russell's Metaphysical Logic 6.1 n3 | |
| A reaction: This is Zermelo's Axiom of Separation, but that too is not an axiom of standard ZFC. |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| Full Idea: Gödel proved the completeness of standard formalizations of first-order logic, including Frege's original one. However, an implication of his famous theorem on the incompleteness of arithmetic is that second-order logic is incomplete. | |
| From: report of Kurt Gödel (works [1930]) by Michael Dummett - The Philosophy of Mathematics 3.1 | |
| A reaction: This must mean that it is impossible to characterise arithmetic fully in terms of first-order logic. In which case we can only characterize the features of abstract reality in general if we employ an incomplete system. We're doomed. |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| Full Idea: 'Mathematical Logic' is a precise and complete formulation of formal logic, and is both a section of mathematics covering classes, relations, symbols etc, and also a science prior to all others, with ideas and principles underlying all sciences. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.447) | |
| A reaction: He cites Leibniz as the ancestor. In this database it is referred to as 'theory of logic', as 'mathematical' seems to be simply misleading. The principles of the subject are standardly applied to mathematical themes. |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| Full Idea: One may, on good grounds, deny that reference to a totality necessarily implies reference to all single elements of it or, in other words, that 'all' means the same as an infinite logical conjunction. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.455) |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| Full Idea: At that time (c.1930) a concept of objective mathematical truth as opposed to demonstrability was viewed with greatest suspicion and widely rejected as meaningless. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 28.2 | |
| A reaction: [quoted from a letter] This is the time of Ramsey's redundancy account, and before Tarski's famous paper of 1933. It is also the high point of Formalism, associated with Hilbert. |
| 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. |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| Full Idea: Gödel was quick to point out that his original incompleteness theorems did not produce instances of absolute undecidability and hence did not undermine Hilbert's conviction that for every precise mathematical question there is a discoverable answer. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: The normal simplistic view among philosophes is that Gödel did indeed decisively refute the optimistic claims of Hilbert. Roughly, whether Hilbert is right depends on which axioms of set theory you adopt. |
| 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. |
| 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. |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| Full Idea: In order to be sure that new expression can be translated into expressions not containing them, it is necessary to have a survey of all possible expressions, and this can be furnished only by syntactical considerations. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.448) | |
| A reaction: [compressed] |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| Full Idea: The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.271), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 03.4 |
| 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 |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| Full Idea: The generalized Continuum Hypothesis says that there exists no cardinal number between the power of any arbitrary set and the power of the set of its subsets. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| Full Idea: Gödel proved that the Continuum Hypothesis was not inconsistent with the axioms of set theory. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| Full Idea: Gödel proved that (if set theory is consistent) we cannot refute the continuum hypothesis, and Cohen proved that (if set theory is consistent) we cannot prove it either. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by William D. Hart - The Evolution of Logic 10 |
| 17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
| Full Idea: Eventually Gödel ...expressed the hope that there might be a generalised completeness theorem according to which there are no absolutely undecidable sentences. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: This comes as a bit of a shock to those who associate him with the inherent undecidability of reality. |
| 10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
| Full Idea: The concept of truth of sentences in a language cannot be defined in the language. This is the true reason for the existence of undecidable propositions in the formal systems containing arithmetic. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 21.6 | |
| A reaction: [from a letter by Gödel] So they key to Incompleteness is Tarski's observations about truth. Highly significant, as I take it. |
| 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. |
| 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 |
| 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. |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| Full Idea: It has turned out that the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.449) | |
| A reaction: A nice statement of the famous result, from the great man himself, in the plainest possible English. |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| Full Idea: Classes and concepts may be conceived of as real objects, ..and are as necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions, with neither case being about 'data'. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.456) | |
| A reaction: Note that while he thinks real objects are essential for mathematics, be may not be claiming the same thing for our knowledge of logic. If logic contains no objects, then how could mathematics be reduced to it, as in logicism? |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| Full Idea: Evidently the 'given' underlying mathematics is closely related to the abstract elements contained in our empirical ideas. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], Suppl) | |
| A reaction: Yes! The great modern mathematical platonist says something with which I can agree. He goes on to hint at a platonic view of the structure of the empirical world, but we'll let that pass. |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| Full Idea: Impredicative definitions are admitted into ordinary mathematics. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) | |
| A reaction: The issue is at what point in building an account of the foundations of mathematics (if there be such, see Putnam) these impure definitions should be ruled out. |
| 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. |
| 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. |
| 8388 | Causation is either direct realism, Humean reduction, non-Humean reduction or theoretical realism [Tooley] |
| Full Idea: The main approaches to causation I shall refer to as direct realism, Humean reductionism, non-Humean reductionism, and indirect or theoretical realism. | |
| From: Michael Tooley (Causation and Supervenience [2003], 2) | |
| A reaction: The first simply observes causation (Anscombe), the second reduces it to regularity (Hume), the third reduces it to other natural features (Fair, Salmon, Dowe), the fourth takes an instrumental approach (Armstrong, Tooley). I favour the third approach. |
| 8389 | Causation distinctions: reductionism/realism; Humean/non-Humean states; observable/non-observable [Tooley] |
| Full Idea: The three main distinctions concerning causation are between reductionism and realism; between Humean and non-Humean states of affairs; and between states that are immediately observable and those that are not. | |
| From: Michael Tooley (Causation and Supervenience [2003], 2) | |
| A reaction: I favour reductionism over realism, because I like the question 'If x is real, what is it made of?' I favour non-Humean states of affairs, because I think constant conjunction is very superficial. I presume the existence of non-observable components. |
| 8416 | Reductionists can't explain accidents, uninstantiated laws, probabilities, or the existence of any laws [Tooley] |
| Full Idea: Reductionist accounts of causation cannot distinguish laws from accidental uniformities, cannot allow for basic uninstantiated laws, can't explain probabilistic laws, and cannot even demonstrate the existence of laws. | |
| From: Michael Tooley (Causality: Reductionism versus Realism [1990], 2) | |
| A reaction: I am tempted to say that this is so much the worse for the idea of laws. Extensive regularities only occur for a reason. Probabilities aren't laws. Hypothetical facts will cover uninstantiated laws. Laws are just patterns. |
| 8393 | We can only reduce the direction of causation to the direction of time if we are realist about the latter [Tooley] |
| Full Idea: A reductionist can hold that the direction of causation is to be defined in terms of the direction of time; but this response is only available if one is prepared to adopt a realist view of the direction of time. | |
| From: Michael Tooley (Causation and Supervenience [2003], 4.2.1.2) | |
| A reaction: A nice illustration of the problems that arise if we try to be reductionist about everything. Personally I prefer my realism to be about time rather than about causation. Time, I would say, makes causation possible, not the other way around. |
| 8390 | Causation is directly observable in pressure on one's body, and in willed action [Tooley] |
| Full Idea: The arguments in favour of causation being observable appeal especially to the impression of pressure upon one's body, and to one's introspective awareness of willing, together with the perception of the event which one willed. | |
| From: Michael Tooley (Causation and Supervenience [2003], 3) | |
| A reaction: [He cites Evan Fagels] Anscombe also cites words which have causality built into their meaning. This would approach would give priority to mental causation, and would need to demonstrate that similar things happen out in the world. |
| 8418 | Quantum physics suggests that the basic laws of nature are probabilistic [Tooley] |
| Full Idea: Quantum physics seems to lend strong support to the idea that the basic laws of nature may well be probabilistic. | |
| From: Michael Tooley (Causality: Reductionism versus Realism [1990], 3.2.1) | |
| A reaction: Groan. Quantum physics should be outlawed from all philosophical discussions. The scientists don't understand it themselves. I'm certainly not going to build my worldview on it. I don't accept that these probabilities could count as 'laws'. |
| 8392 | Probabilist laws are compatible with effects always or never happening [Tooley] |
| Full Idea: If laws of causation are probabilistic then the law does not entail any restrictions upon the proportion of events that follow a cause: ...it can have absolutely any value from zero to one. | |
| From: Michael Tooley (Causation and Supervenience [2003], 4.1.3) | |
| A reaction: This objection applies to an account of laws of nature, and also to definitions of causes as events which increase probabilities. One needn't be fully committed to natural necessity, but it must form some part of the account. |
| 8399 | The actual cause may not be the most efficacious one [Tooley] |
| Full Idea: A given type of state may be causally efficacious, but not as efficacious as an alternative states, so it is not true that even a direct cause need raise the probability of its effect. | |
| From: Michael Tooley (Causation and Supervenience [2003], 6.2.4) | |
| A reaction: My intuition is that explaining causation in terms of probabilities entirely misses the point, which mainly concerns explaining the sense of necessitation in a cause. This idea give me a good reason for my intuition. |
| 8391 | In counterfactual worlds there are laws with no instances, so laws aren't supervenient on actuality [Tooley] |
| Full Idea: If a counterfactual holds in a possible world, that is presumably because a law holds in that world, which means there could be basic causal laws that lack all instances. But then causal laws cannot be totally supervenient on the history of the universe. | |
| From: Michael Tooley (Causation and Supervenience [2003], 4.1.2) | |
| A reaction: A nice argument, which sounds like trouble for Lewis. One could deny that the laws have to hold in the counterfactual worlds, but then we wouldn't be able to conceive them. |
| 8394 | Explaining causation in terms of laws can't explain the direction of causation [Tooley] |
| Full Idea: The most serious objection to any account of causation in terms of nomological relations alone is that it can't provide any account of the direction of causation. | |
| From: Michael Tooley (Causation and Supervenience [2003], 5.1) | |
| A reaction: Cf. Idea 8393. I am not convinced that there could be an 'account' of the direction of causation, so I am inclined to take it as given. If we take 'powers' (active properties) as basic, they would have a direction built into them. |
| 8398 | Causation is a concept of a relation the same in all worlds, so it can't be a physical process [Tooley] |
| Full Idea: Against the view that causation is a particular physical process, might it not be argued that the concept of causation is the concept of a relation that possesses a certain intrinsic nature, so that causation must be the same in all possible worlds? | |
| From: Michael Tooley (Causation and Supervenience [2003], 5.4) | |
| A reaction: This makes the Humean assumption that laws of nature might be wildly different. I think it is perfectly possible that physical processes are the only way that causation could occur. Alternatively, the generic definition of 'cause' is just very vague. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |