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All the ideas for 'On the Question of Absolute Undecidability', 'Vagueness: a global approach' and 'The View from Nowhere'

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40 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
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.
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
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?
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
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.
2. Reason / A. Nature of Reason / 5. Objectivity
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)
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.
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.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
     Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro)
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
     Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1)
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Indeterminacy is in conflict with classical logic [Fine,K]
     Full Idea: I now believe that the existence of indeterminacy is in conflict with classical logic.
     From: Kit Fine (Vagueness: a global approach [2020], 3)
     A reaction: I think that prior to this Fine had defended classical logic. Presumably the difficulty is over Bivalence. Nietzsche spotted this problem, despite not being a logician. Logic has to simplify the world. Hence philosophy is quite different from logic.
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Classical semantics has referents for names, extensions for predicates, and T or F for sentences [Fine,K]
     Full Idea: A precise language is often assigned a classical semantics, in which the semantic value of a name is its referent, the semantic value of a predicate is its extension (the objects of which it is true), and the value of a sentence is True or False.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: Helpful to have this clear statement of how predicates are treated. This extensionalism in logic causes trouble when it creeps into philosophy, and people say that 'red' just means all the red things. No it doesn't.
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
     Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
     Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable).
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
     A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
     Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem].
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1)
     A reaction: Each expansion brings a limitation, but then you can expand again.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
     Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
7. Existence / D. Theories of Reality / 10. Vagueness / a. Problem of vagueness
Local indeterminacy concerns a single object, and global indeterminacy covers a range [Fine,K]
     Full Idea: Vagueness concerns 'local' indeterminacy, such as whether one man in the lineup is bald, and 'global' indeterminacy, applying to a range of cases, as when it is indeterminate how 'bald' applies to the lineup. But how do these relate?
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: This puts the focus either on objects or on predicates which are vague.
Conjoining two indefinites by related sentences seems to produce a contradiction [Fine,K]
     Full Idea: If 'P is red' and 'P is orange' are indefinite, then 'P is red and P is orange' seems false, because red and orange are exclusive. But if two conjoined indefinite sentences are false, that makes 'P is red and P is red' false, when it should be indefinite.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: [compressed] This is the problem of 'penumbral connection', where two indefinite values are still logically related, by excluding one another. Presumably 'P is red and P is of indefinite shape' can be true? Doubtful about this argument.
Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen [Fine,K]
     Full Idea: Standard notions of vagueness all accept borderline cases, and presuppose a higher standpoint from which a judgement of being borderline F, rather than simply being F or being not F, can be made.
     From: Kit Fine (Vagueness: a global approach [2020], 3)
     A reaction: He says that the concept of borderline cases is an impediment to understanding vagueness. Proposing a third group when you are struggling to separate two other groups doesn't seem helpful, come to think of it. Limbo cases.
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
Identifying vagueness with ignorance is the common mistake of confusing symptoms with cause [Fine,K]
     Full Idea: We can see Epistemicism [vagueness as ignorance] as a common and misguided tendency to identify a cause with its symptoms. We are unsure how to characterise vagueness, and identify it with the resulting ignorance, instead of explaining it.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: Love it. This echoes my repeated plea in these reactions to stop identifying features of reality with the functions which embody them or the patterns they create. We need to explain them, and must dig deeper.
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
Supervaluation can give no answer to 'who is the last bald man' [Fine,K]
     Full Idea: Under supervaluation there should always be someone who is the last bald man in the sequence, but there is always an acceptable way to make some other man the last bald man.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: Fine seems to take this as a conclusive refutation of the supervaluation approach. Fine says (p.41) that supervaluation says there is a precisification for every instance.
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
We do not have an intelligible concept of a borderline case [Fine,K]
     Full Idea: We simply have no intelligible notion of local indeterminacy or of a borderline case.
     From: Kit Fine (Vagueness: a global approach [2020], 2)
     A reaction: He mentions cases which are near a borderline, and cases which are hard to decide, but denies that these are intrinsically borderline. If there are borderline cases between red and orange, what are the outer boundaries of the border?
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / b. Primary/secondary
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)
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.
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
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.
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
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)
14. Science / C. Induction / 4. Reason in Induction
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)
16. Persons / B. Nature of the Self / 4. Presupposition of Self
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?
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.
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
It seems absurd that there is no identity of any kind between two objects which involve survival [Fine,K]
     Full Idea: Pace Parfit and others, it boggles the mind that survival could be independent of any relation of identity between the currently existing object and the objects that subsequently exist.
     From: Kit Fine (Vagueness: a global approach [2020], 3)
     A reaction: Yes. If the self or mind just consists of a diachronic trail of memories such that the two ends of the trail have no connection at all, that isn't the kind of survival that any of us want. I want to live my life, not a life.
16. Persons / D. Continuity of the Self / 4. Split Consciousness
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?
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
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.
22. Metaethics / B. Value / 2. Values / e. Death
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.
22. Metaethics / B. Value / 2. Values / f. Altruism
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.
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
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.
23. Ethics / D. Deontological Ethics / 1. Deontology
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)
23. Ethics / D. Deontological Ethics / 2. Duty
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)
23. Ethics / D. Deontological Ethics / 3. Universalisability
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)
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)
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
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)
23. Ethics / E. Utilitarianism / 3. Motivation for Altruism
Utilitarianism is too demanding [Nagel]
     Full Idea: Utilitarianism is too demanding.
     From: Thomas Nagel (The View from Nowhere [1986], X.5)
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
We identify laws with regularities because we mistakenly identify causes with their symptoms [Fine,K]
     Full Idea: There is a common tendency to identify a cause with its symptoms. Hence we are not sure how to characterise a law, and so we identify it with the regularities to which it gives rise.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: A lovely clear identification of my pet hate, which is superficial accounts of things, which claim to be the last word, but actually explain nothing.