104 ideas
| 3240 | There is more insight in fundamental perplexity about problems than in their supposed solutions [Nagel] |
| Full Idea: Certain forms of perplexity (say about freedom, knowledge and the meaning of life) seem to me to embody more insight than any of the supposed solutions to those problems. | |
| From: Thomas Nagel (The View from Nowhere [1986], Intro) | |
| A reaction: Obviously false solutions won't embody much insight. This sounds good, but I suspect that the insight is in the recognition of the facts which give rise to the perplexity. I can't think of anything in favour of perplexity for its own sake. |
| 3269 | If your life is to be meaningful as part of some large thing, the large thing must be meaningful [Nagel] |
| Full Idea: Those seeking to give their lives meaning usually envision a role in something larger than themselves, …but such a role can't confer significance unless that enterprise is itself significant. | |
| From: Thomas Nagel (The Absurd [1971], §3) | |
| A reaction: Which correctly implies that this way of finding meaning for one's life is doomed. |
| 3242 | Philosophy is the childhood of the intellect, and a culture can't skip it [Nagel] |
| Full Idea: Philosophy is the childhood of the intellect, and a culture that tries to skip it will never grow up. | |
| From: Thomas Nagel (The View from Nowhere [1986], Intro) | |
| A reaction: Can he really mean that a mature culture doesn't need philosophy? |
| 3241 | It seems mad, but the aim of philosophy is to climb outside of our own minds [Nagel] |
| Full Idea: We are trying to climb outside of our own minds, an effort that some would regard as insane and that I regard as philosophically fundamental. | |
| From: Thomas Nagel (The View from Nowhere [1986], Intro) | |
| A reaction: It is not only philosophers who do this. It is an essential feature of the mind, and is inherent in the concept of truth. |
| 1489 | Modern philosophy tends to be a theory-constructing extension of science, but there is also problem-solving [Nagel] |
| Full Idea: Philosophy is now dominated by a spirit of theory construction which sees philosophy as continuous with science, but the other problem-centred style is still in existence and it is important to keep it alive. | |
| From: Thomas Nagel (The Philosophical Culture [1995], §6) |
| 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. |
| 3248 | Realism invites scepticism because it claims to be objective [Nagel] |
| Full Idea: The search for objective knowledge, because of its commitment to realism, cannot refute scepticism and must proceed under its shadow, and scepticism is only a problem because of the realist claims of objectivity. | |
| From: Thomas Nagel (The View from Nowhere [1986], V.1) |
| 20989 | Views are objective if they don't rely on a person's character, social position or species [Nagel] |
| Full Idea: A view or form of thought is more objective than another if it relies less on the specifics of the individual's makeup and position in the world, or on the character of the particular type of creature he is. | |
| From: Thomas Nagel (The View from Nowhere [1986], Intro) | |
| A reaction: Notice that this defines comparative objectivity, rather than an absolute. I take it that something must be entirely objective to qualify as a 'fact', and so anything about which there is a consensus that it is a fact can be taken as wholly objective. |
| 22354 | Things cause perceptions, properties have other effects, hence we reach a 'view from nowhere' [Nagel, by Reiss/Sprenger] |
| Full Idea: First we realise that perceptions are caused by things, second we realise that properties have other effects (as well as causing perceptions), and third we conceive of a thing's true nature without perspectives. That is the 'view from nowhere'. | |
| From: report of Thomas Nagel (The View from Nowhere [1986], p.14) by Reiss,J/Spreger,J - Scientific Objectivity 2.1 | |
| A reaction: [My summary of their summary] This is obviously an optimistic view. I''m not sure how he can justify three precise stages, given than animals probably jump straight to the third stage, and engage with the nature's of things. |
| 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 |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 4242 | Pure supervenience explains nothing, and is a sign of something fundamental we don't know [Nagel] |
| Full Idea: Pure, unexplained supervenience is never a solution to a problem but a sign that there is something fundamental we don't know. | |
| From: Thomas Nagel (The Psychophysical Nexus [2000], §III) | |
| A reaction: This seems right. It is not a theory or an explanation, merely the observation of a correlation which will require explanation. Why are they correlated? |
| 3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
| Full Idea: The supposition that a diamond or organism should truly have emergent properties is that they appear at certain complex levels of organisation, but are not explainable (even in principle) in terms of any more fundamental properties of the system. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |
| 3249 | Modern science depends on the distinction between primary and secondary qualities [Nagel] |
| Full Idea: The distinction between primary and secondary qualities is the precondition for the development of modern physics and chemistry. | |
| From: Thomas Nagel (The View from Nowhere [1986], V.3) |
| 22429 | We achieve objectivity by dropping secondary qualities, to focus on structural primary qualities [Nagel] |
| Full Idea: At the end [of the three stages of objectivity] the secondary qualities drop out of our picture of the external world, and the underlyiing primary qualities such as shape, size, weight, and motion are thought of structurally. | |
| From: Thomas Nagel (The View from Nowhere [1986], II) | |
| A reaction: This is the orthodox view for realists about the external world, and I largely agree. The only problem I see is that secondary qualities contain information, such as the colour of rotting fruit - but then colour is not an essential feature of rot. |
| 3296 | Sense-data are a false objectification of what is essentially subjective [Nagel] |
| Full Idea: The private object or sense datum view is an instance of the false objectification of what is essentially subjective. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.207) |
| 3247 | Epistemology is centrally about what we should believe, not the definition of knowledge [Nagel] |
| Full Idea: The central problem of epistemology is what to believe and how to justify one's beliefs, not the impersonal problem of whether my beliefs can be said to be knowledge. | |
| From: Thomas Nagel (The View from Nowhere [1986], V.1) | |
| A reaction: Wrong. The question of whether what one has is 'knowledge' is not impersonal at all - it is having the social status of a knower or expert. |
| 3271 | We can't control our own beliefs [Nagel] |
| Full Idea: Our beliefs are always due to factors outside of our control. | |
| From: Thomas Nagel (Moral Luck [1976], p.27) |
| 3270 | Justifications come to an end when we want them to [Nagel] |
| Full Idea: Justifications come to an end when we are content to have them end. | |
| From: Thomas Nagel (The Absurd [1971], §3) | |
| A reaction: This is the correct account, with the vital proviso that where justification comes to an end is usually a social matter. Robinson Crusoe doesn't care whether he 'knows' - he just acts on his beliefs. |
| 3252 | Scepticism is based on ideas which scepticism makes impossible [Nagel] |
| Full Idea: The sceptic reaches scepticism through thoughts that scepticism makes unthinkable. | |
| From: Thomas Nagel (The View from Nowhere [1986], V.6) |
| 1490 | You would have to be very morally lazy to ignore criticisms of your own culture [Nagel] |
| Full Idea: One would have to be very morally lazy to be unconcerned with the possibility that the prevailing morality of one's culture had something fundamentally wrong with it. | |
| From: Thomas Nagel (MacIntyre versus the Enlightenment [1988], 203) |
| 3251 | Observed regularities are only predictable if we assume hidden necessity [Nagel] |
| Full Idea: Observed regularities provide reason to believe that they will be repeated only to the extent that they provide evidence of hidden necessary connections, which hold timelessly. | |
| From: Thomas Nagel (The View from Nowhere [1986], V.5) |
| 3295 | Inner v outer brings astonishment that we are a particular person [Nagel] |
| Full Idea: The problem of reconciling the objective and subjective points of view takes its purest form in a sense of incredulity that one should be anyone in particular. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.206) | |
| A reaction: Nice observation. This idea has always struck me forcibly, and seems to be one of those basic intuitions which motivates philosophy, and yet the subject has almost nothing to say about it. Of course you are you, or you wouldn't be amazed by it… |
| 2957 | Brain bisection suggests unity of mind isn't all-or-nothing [Nagel, by Lockwood] |
| Full Idea: Nagel argues (because of brain bisection experiments) that we should jettison our commonsense assumption that the unity of consciousness is an all-or-nothing affair. | |
| From: report of Thomas Nagel (Brain Bisection and Unity of Consciousness [1971]) by Michael Lockwood - Mind, Brain and the Quantum p.84 | |
| A reaction: It seems wrong to call it 'commonsense'. It is an assumption that precedes any judgement, but if you rapidly grasp that your mind is in your brain, it becomes common sense that you can cut lumps out of your mind. |
| 3286 | An organism is conscious if and only if there is something it is like to be that organism [Nagel] |
| Full Idea: An organism only has conscious mental states if and only if there is something that it is like to be that organism. | |
| From: Thomas Nagel (What is it like to be a bat? [1974], p.166) | |
| A reaction: It is hard to argue with this, but one should push on and ask what features of its consciousness make it such that there is a 'what it is like'. What is it like to have a subconscious mind, or be deeply asleep, or drive while daydreaming? |
| 3285 | We may be unable to abandon personal identity, even when split-brains have undermined it [Nagel] |
| Full Idea: As a result of the evidence of split-brains, it is possible that the ordinary, simple idea of a single person will come to seem quaint some day, …but we may be unable to abandon the idea, no matter what we discover. | |
| From: Thomas Nagel (Brain Bisection and Unity of Consciousness [1971], p.164) | |
| A reaction: I'm not sure what grounds you can have for a claim that we can't abandon our current view of selves, even when the new reality will be utterly different. Rather conservative? I would expect future concepts to roughly match future reality. |
| 3293 | If you assert that we have an ego, you can still ask if that future ego will be me [Nagel] |
| Full Idea: The metaphysical ego, if it is a continuing individual with its identity over time, is just one more thing about which the same problem can be raised - will that ego still be me? | |
| From: Thomas Nagel (Subjective and Objective [1979], p.200) | |
| A reaction: You can worry too much about some philosophical questions. If it is me now, and it has continuing individual identity over time, I'm not going to lose sleep over the possibility that it might nevertheless somehow cease to be me. I'm overrated. |
| 3244 | Personal identity cannot be fully known a priori [Nagel] |
| Full Idea: The full conditions of personal identity cannot be extracted from the concept of a person at all: they cannot be arrived at a priori. | |
| From: Thomas Nagel (The View from Nowhere [1986], III.2) | |
| A reaction: However, if you turn to experience to get the hang of what a person is, it is virtually impossible to disentangle the essentials from the accidental features of being a person. How essential are memories or reasoning or hopes or understandings or plans? |
| 3245 | The question of whether a future experience will be mine presupposes personal identity [Nagel] |
| Full Idea: The identity of the self must have some sort of objectivity, otherwise the subjective question whether a future experience will be mine or not will be contentless. | |
| From: Thomas Nagel (The View from Nowhere [1986], III.3) | |
| A reaction: This sounds a bit circular and question-begging. If there is no objective self, then the question of whether a future experience will be mine would be a misconceived question. I sympathise with Nagel's attempt to show how personal identity is a priori. |
| 3246 | I can't even conceive of my brain being split in two [Nagel] |
| Full Idea: It is hard to think of myself as being identical with my brain. If my brain is to be split, with one half miserable and the other half euphoric, my expectations can take no form, as my idea of myself doesn't allow for divisibility. | |
| From: Thomas Nagel (The View from Nowhere [1986], III.4) | |
| A reaction: Nagel is trying to imply that there is some sort of conceptual impossibility here, but it may just be very difficult. I can think about my lovely lunch while doing my miserable job. Does Nagel want to hang on to a unified thing which doesn't exist? |
| 3292 | The most difficult problem of free will is saying what the problem is [Nagel] |
| Full Idea: The most difficult problem of free will is saying what the problem is. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.198) |
| 3288 | Can we describe our experiences to zombies? [Nagel] |
| Full Idea: The goal of an objective phenomenology would be to describe, at least in part, the subjective character of experiences in a form comprehensible to beings incapable of having those experiences. | |
| From: Thomas Nagel (What is it like to be a bat? [1974], p.179) | |
| A reaction: This seems a bizarre expectation. We can already explain visual experience to the blind up to a point, but no one is dreaming of an "objective phenomenology" which will give blind people total understanding, just by reading about it in braille. |
| 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. |
| 4883 | Nagel's title creates an impenetrable mystery, by ignoring a bat's ways that may not be "like" anything [Dennett on Nagel] |
| Full Idea: Nagel's title invites us to ignore all the different ways in which bats might accomplish their cunning feats without its "being like" anything for them. We create an impenetrable mystery for ourselves if we assume that Nagel's title makes sense. | |
| From: comment on Thomas Nagel (What is it like to be a bat? [1974]) by Daniel C. Dennett - Kinds of Minds Ch.6 | |
| A reaction: This could well be correct about bats, but the question applies to humans as well, and we can't deny that "what it is like" is a feature of some creatures' realities. On the fringes of our own consciousness there are mental events that are "like" nothing. |
| 3287 | We can't be objective about experience [Nagel] |
| Full Idea: If the subjective character of experience is fully comprehensible only from one point of view, then any shift to greater objectivity does not take us nearer to the real nature of the phenomenon: it takes us further away from it. | |
| From: Thomas Nagel (What is it like to be a bat? [1974], p.174) | |
| A reaction: We can, however, talk to one another about our subjectivity, and compare notes, and such 'inter-subjectivity' may be one approach to objectivity. We must concede Nagel's point, but we also miss something about a stone if we must remain outside of it. |
| 4989 | Physicalism should explain how subjective experience is possible, but not 'what it is like' [Kirk,R on Nagel] |
| Full Idea: A physicalist account of conscious experience must explain how it is possible for a physical system to be a conscious subject, but not 'what it is like' for some organism. | |
| From: comment on Thomas Nagel (What is it like to be a bat? [1974]) by Robert Kirk - Mind and Body §4.2 | |
| A reaction: You can't entirely evade Nagel's challenge. We are trying to discover the 'neural correlate of consciousness', which will explain why we are conscious, but we also want to know why we experience green for one wavelength, and red for another. |
| 4001 | The meaning of a word contains all its possible uses as well as its actual ones [Nagel] |
| Full Idea: The meaning of a word contains all its possible uses, true and false, not only its actual ones. | |
| From: Thomas Nagel (What Does It All Mean? [1987], Ch.5) | |
| A reaction: It has always seemed to me that meaning is not use, because you can't use it if it hasn't already got a meaning. What use is a meaningless word? |
| 6479 | Noninterference requires justification as much as interference does [Nagel] |
| Full Idea: Noninterference requires justification as much as interference does. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.10) | |
| A reaction: I'm not convinced by this, as a simple rule. If I spend my whole life doing just the minimum for my own survival, I don't see why I should have to justify that, and I don't see a state is obliged to justify it either. |
| 6450 | Morality must be motivating, and not because of pre-moral motives [Nagel] |
| Full Idea: My own view is that moral justification must be capable of motivating, but not in virtue of reliance on pre-moral motives. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.5) | |
| A reaction: This may well be the core and essence of Kantian moral theory. I'm inclined to think of it as 'Kant's dream', which is of ultra-rational beings who are driven by pure rationality as a motivator. People who fit this bill tend to be academics. |
| 3284 | There is no one theory of how to act (or what to believe) [Nagel] |
| Full Idea: To look for a single general theory of how to decide the right thing to do is like looking for a single theory of how to decide what to believe. | |
| From: Thomas Nagel (The Fragmentation of Value [1977], p.135) | |
| A reaction: Depends on your level of generality. Values and virtues are general guides which should be brought to every action, with 'higher' values guiding choice of what is relevant. |
| 3257 | Total objectivity can't see value, but it sees many people with values [Nagel] |
| Full Idea: A purely objective view has no way of knowing whether anything has any value, but actually its data include the appearance of value to individuals with particular perspectives, including oneself. | |
| From: Thomas Nagel (The View from Nowhere [1986], VIII.2) | |
| A reaction: I would have thought that a very objective assessment of someone's health is an obvious revelation of value, irrespective of anyone's particular perspective. |
| 3265 | We don't worry about the time before we were born the way we worry about death [Nagel] |
| Full Idea: We do not regard the period before we were born in the same way that we regard the prospect of death. | |
| From: Thomas Nagel (The View from Nowhere [1986], XI.3) | |
| A reaction: This is a challenge to Epicurus, who said death is no worse than pre-birth. This idea may be true of the situation immediately post-death, but a thousand years from now it is hard to distinguish them. |
| 3263 | If our own life lacks meaning, devotion to others won't give it meaning [Nagel] |
| Full Idea: If no one's life has any meaning in itself, how can it acquire meaning through devotion to the meaningless lives of others? | |
| From: Thomas Nagel (The View from Nowhere [1986], XI.2) | |
| A reaction: This is one of the paradoxes of compassion. The other is that the virtue requires other people to be in need of help, which can't be a desirable situation. |
| 3256 | Pain doesn't have a further property of badness; it gives a reason for its avoidance [Nagel] |
| Full Idea: The objective badness of pain is not some mysterious further property that all pains have, but just the fact that there is reason for anyone capable of viewing the world objectively to want it to stop. | |
| From: Thomas Nagel (The View from Nowhere [1986], VIII.2) | |
| A reaction: Presumably all pains (e.g. of grief and of toothache) have something in common, to qualify as pains. It must be more than being disliked, because we can dislike a food. |
| 3272 | Moral luck can arise in character, preconditions, actual circumstances, and outcome [Nagel] |
| Full Idea: Moral luck involves one's character, the antecedent circumstances of the act, the actual circumstances of the act, and the outcome of the act. | |
| From: Thomas Nagel (Moral Luck [1976], p.28) | |
| A reaction: Meaning, I take it, that there can be luck in any one of those four. A neat slicing up that doesn't quite fit the real world, where things flow. Helpful, though. |
| 6447 | Game theory misses out the motivation arising from the impersonal standpoint [Nagel] |
| Full Idea: I do not favour the route taken by Hobbes's modern descendants, using game theory, since I believe the impersonal standpoint makes an essential contribution to individual motivation which must be addressed by any ethically acceptable theory. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.4) | |
| A reaction: The assumption of self-seeking at the core of game theory seems very bizarre, and leads to moral approval of free riders. Nagel offers the best response, which is the Kantian impersonal view. Nagel may be optimistic about motivation, though. |
| 3261 | Something may be 'rational' either because it is required or because it is acceptable [Nagel] |
| Full Idea: "Rational" may mean rationally required or rationally acceptable | |
| From: Thomas Nagel (The View from Nowhere [1986], X.4) |
| 3258 | If cockroaches can't think about their actions, they have no duties [Nagel] |
| Full Idea: If cockroaches cannot think about what they should do, there is nothing they should do. | |
| From: Thomas Nagel (The View from Nowhere [1986], VIII.3) |
| 6446 | In ethics we abstract from our identity, but not from our humanity [Nagel] |
| Full Idea: In pursuit of the kind of objectivity needed in the physical sciences, we abstract even from our humanity; but nothing further than abstraction from our identity (that is, who we are) enters into ethical theory. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.2) | |
| A reaction: The 'brief' summary of this boils down to a nice and interesting slogan. It epitomises the modern Kantian approach to ethics. But compare Idea 4122, from Bernard Williams. |
| 3282 | The general form of moral reasoning is putting yourself in other people's shoes [Nagel] |
| Full Idea: I believe the general form of moral reasoning is to put yourself in other people's shoes. | |
| From: Thomas Nagel (Equality [1977], §9) |
| 3294 | As far as possible we should become instruments to realise what is best from an eternal point of view [Nagel] |
| Full Idea: The right thing to do is to turn oneself as far as possible into an instrument for the realisation of what is best 'sub specie aeternitatis'. | |
| From: Thomas Nagel (Subjective and Objective [1979], p.204) |
| 3254 | If we can decide how to live after stepping outside of ourselves, we have the basis of a moral theory [Nagel] |
| Full Idea: If we can make judgements about how we should live even after stepping outside of ourselves, they will provide the material for moral theory. | |
| From: Thomas Nagel (The View from Nowhere [1986], VIII.1) |
| 3264 | We should see others' viewpoints, but not lose touch with our own values [Nagel] |
| Full Idea: One should occupy a position far enough outside your own life to reduce the importance of the difference between yourself and other people, yet not so far outside that all human values vanish in a nihilistic blackout (i.e.aim for a form of humility). | |
| From: Thomas Nagel (The View from Nowhere [1986], XI.2) |
| 6477 | I can only universalise a maxim if everyone else could also universalise it [Nagel] |
| Full Idea: It is implicit in the categorical imperative that I can will that everyone should adopt as a maxim only what everyone else can also will that everyone should adopt as a maxim. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.5) | |
| A reaction: This is a nice move, because it shifts the theory away from a highly individualistic Cartesian view of morality towards the idea that morality is a community activity. |
| 3255 | We find new motives by discovering reasons for action different from our preexisting motives [Nagel] |
| Full Idea: There are reasons for action, and we must discover them instead of deriving them from our preexisting motives - and in that way we can acquire new motives superior to the old. | |
| From: Thomas Nagel (The View from Nowhere [1986], VIII.1) |
| 3262 | Utilitarianism is too demanding [Nagel] |
| Full Idea: Utilitarianism is too demanding. | |
| From: Thomas Nagel (The View from Nowhere [1986], X.5) |
| 3268 | If a small brief life is absurd, then so is a long and large one [Nagel] |
| Full Idea: If life is absurd because it only lasts seventy years, wouldn't it be infinitely absurd if it lasted for eternity? And if we are absurd because we are small, would we be any less absurd if we filled the universe? | |
| From: Thomas Nagel (The Absurd [1971], §1) |
| 3278 | An egalitarian system must give priority to those with the worst prospects in life [Nagel] |
| Full Idea: What makes a system egalitarian is the priority it gives to the claims of those whose overall life prospects put them at the bottom. | |
| From: Thomas Nagel (Equality [1977], §6) |
| 6448 | A legitimate system is one accepted as both impartial and reasonably partial [Nagel] |
| Full Idea: A legitimate system is one which reconciles the two universal principles of impartiality and reasonable partiality so that no one can object that his interests are not being accorded sufficient weight or that the demands on him are excessive. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.4) | |
| A reaction: This seems an appealing principle, and a nice attempt at stating the core of Kantian liberalism. It is obviously influenced by Scanlon's contractualist view, in the idea that 'no one can object', because everyone sees the justification. |
| 3275 | Equality was once opposed to aristocracy, but now it opposes public utility and individual rights [Nagel] |
| Full Idea: Egalitarianism was once opposed to aristocratic values, but now it is opposed by adherents of two non-aristocratic values: utility (increase benefit, even if unequally) and individual rights (which redistribution violates). | |
| From: Thomas Nagel (Equality [1977], §2) |
| 3281 | The ideal of acceptability to each individual underlies the appeal to equality [Nagel] |
| Full Idea: The ideal of acceptability to each individual underlies the appeal to equality. | |
| From: Thomas Nagel (Equality [1977], §8) |
| 3277 | In judging disputes, should we use one standard, or those of each individual? [Nagel] |
| Full Idea: In assessing equality of claims, it must be decided whether to use a single, objective standard, or whether interests should be ranked by the person's own estimation. Also should they balance momentary or long-term needs? | |
| From: Thomas Nagel (Equality [1977], §6) |
| 3274 | Equality can either be defended as good for society, or as good for individual rights [Nagel] |
| Full Idea: The communitarian defence of equality says it is good for society as a whole, whereas the individualistic defence defends equality as a correct distributive principle. | |
| From: Thomas Nagel (Equality [1977], §2) |
| 3273 | Equality nowadays is seen as political, social, legal and economic [Nagel] |
| Full Idea: Contemporary political debate recognises four types of equality: political, social, legal and economic. | |
| From: Thomas Nagel (Equality [1977], §1) | |
| A reaction: Meaning equality of 1) power and influence, 2) status and respect, 3) rights and justice, 4) wealth. |
| 6478 | Democracy is opposed to equality, if the poor are not a majority [Nagel] |
| Full Idea: As things are, democracy is the enemy of comprehensive equality, once the poor cease to be a majority. | |
| From: Thomas Nagel (Equality and Partiality [1991], Ch.9) | |
| A reaction: This is obvious once you think about it, but it is well worth saying, because it is tempting to think that we live in an 'equal' society, merely because we are equal in things such as voting rights and equality before the law. |
| 3276 | A morality of rights is very minimal, leaving a lot of human life without restrictions or duties [Nagel] |
| Full Idea: The morality of rights tends to be a limited, even minimal, morality. It leaves a great deal of human life ungoverned by moral restrictions or requirements. | |
| From: Thomas Nagel (Equality [1977], §5) |
| 3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |
| Full Idea: Given what heat is and what water is, it is literally impossible for water to be heated beyond a certain point at normal atmospheric pressure without boiling. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |
| 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) |