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All the ideas for 'On the Question of Absolute Undecidability', 'Mirror Mirror - Is That All?' and 'works'

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43 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Organisms understand their worlds better if they understand themselves [Gulick]
     Full Idea: Organisms come to better understand their worlds by coming to better understand themselves and the ways in which their own structures engage their worlds.
     From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §III)
     A reaction: Van Gulick is defending a higher-order theory of consciousness, but this strikes me as a good rationale for the target of philosophy, which has increasingly (since Descartes) focused on understanding our own minds.
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Quinean metaphysics just lists the beings, which is a domain with no internal structure [Schaffer,J on Quine]
     Full Idea: The Quinean task in metaphysics is to say what exists. What exists forms the domain of quantification. The domain is a set (or class, or plurality) - it has no internal structure. In other words, the Quinean task is to list the beings.
     From: comment on Willard Quine (works [1961]) by Jonathan Schaffer - On What Grounds What 1.1
     A reaction: I really warm to this thesis. The Quinean version is what you get when you think that logic is the best tool for explicating metaphysics. Schaffer goes on to say that the only real aim for Quine is the cardinality of what exists!
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Set theory is full of Platonist metaphysics, so Quine aimed to keep it separate from logic [Quine, by Benardete,JA]
     Full Idea: Quine has showed us how set theory - now recognised to be positively awash in Platonistic metaphysics - can and should be prevented from infecting logic proper.
     From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Intro
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)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Quine wants V = L for a cleaner theory, despite the scepticism of most theorists [Quine, by Shapiro]
     Full Idea: Quine suggests that V = L be accepted in set theory because it makes for a cleaner theory, even though most set theorists are skeptical of V = L.
     From: report of Willard Quine (works [1961]) by Stewart Shapiro - Philosophy of Mathematics Ch.1
     A reaction: Shapiro cites it as a case of a philosopher trying to make recommendations to mathematicians. Maddy supports Quine.
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Two things can never entail three things [Quine, by Benardete,JA]
     Full Idea: Two things can never entail three things.
     From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.17
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
If we had to name objects to make existence claims, we couldn't discuss all the real numbers [Quine]
     Full Idea: Since one wants to say that real numbers exist and yet one cannot name each of them, it is not unreasonable to relinquish the connection between naming an object and making an existence claim about it.
     From: Willard Quine (works [1961]), quoted by Alex Orenstein - W.V. Quine Ch.2
     A reaction: One could say that same about people, such as 'the most recent citizen of Brazil'. Some sort of successful reference seems to be needed, such as 'the next prime beyond the biggest so far found'. Depends what your predicate is going to be.
5. Theory of Logic / G. Quantification / 1. Quantification
No sense can be made of quantification into opaque contexts [Quine, by Hale]
     Full Idea: Quine says that no good sense can be made of quantification into opaque contexts.
     From: report of Willard Quine (works [1961]) by Bob Hale - Abstract Objects Ch.2
     A reaction: This is because poor old Quine was trapped in a world of language, and had lost touch with reality. I can quantify over the things you are thinking about, as long as you are thinking about things that can be quantified over.
Finite quantification can be eliminated in favour of disjunction and conjunction [Quine, by Dummett]
     Full Idea: Quine even asserts that where we have no infinite domains, quantification can be eliminated in favour of finite disjunction and conjunction.
     From: report of Willard Quine (works [1961]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14
     A reaction: Thus ∃x is expressed as 'this or this or this...', and ∀ is expressed as 'this and this and this...' Dummett raises an eyebrow, but it sounds OK to me.
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)]
     Full Idea: Quine at first regarded substitutional quantification as incoherent, behind which there lurked use-mention confusions, but has over the years, given his nominalist dispositions, come to notice its appeal.
     From: report of Willard Quine (works [1961]) by Ruth Barcan Marcus - Nominalism and Substitutional Quantifiers p.166
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)
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
For Quine, intuitionist ontology is inadequate for classical mathematics [Quine, by Orenstein]
     Full Idea: Quine feels that the intuitionist's ontology of abstract objects is too slight to serve the needs of classical mathematics.
     From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3
     A reaction: Quine, who devoted his life to the application of Ockham's Razor, decided that sets were an essential part of the ontological baggage (which made him, according to Orenstein, a 'reluctant Platonist'). Dummett defends intuitionism.
Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein]
     Full Idea: Intuitionists will not admit any numbers which are not properly constructed out of rational numbers, ...but classical mathematics appeals to the real numbers (a non-denumerable totality) in notions such as that of a limit
     From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3
     A reaction: (See Idea 8454 for the categories of numbers). This is a problem for Dummett.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
A logically perfect language could express all truths, so all truths must be logically expressible [Quine, by Hossack]
     Full Idea: Quine's test of ontological commitment says that anything that can be said truly at all must be capable of being said in a logically perfect language, so there must be a paraphrase of every truth into the language of logic.
     From: report of Willard Quine (works [1961]) by Keith Hossack - Plurals and Complexes 2
     A reaction: A very nice statement of the Quinean view, much more persuasive than other statements I have encountered. I am suddenly almost converted to a doctrine I have hitherto despised. Isn't philosophy wonderful?
7. Existence / D. Theories of Reality / 11. Ontological Commitment / c. Commitment of predicates
Quine says we can expand predicates easily (ideology), but not names (ontology) [Quine, by Noonan]
     Full Idea: The highly intuitive methodological programme enunciated by Quine says that as our knowledge expands we should unhesitatingly expand our ideology, our stock of predicables, but should be much more wary about ontology, the name variables.
     From: report of Willard Quine (works [1961]) by Harold Noonan - Identity §3
     A reaction: I suddenly embrace this as a crucial truth. This distinction allows you to expand on truths without expanding on reality. I would add that it is also crucial to distinguish properties from predicates. A new predicate isn't a new property.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
For Quine everything exists theoretically, as reference, predication and quantification [Quine, by Benardete,JA]
     Full Idea: Theoretical entities (which is everything, according to Quine) are postulated by us in a threefold fashion as an object (1) to which we refer, (2) of which we predicate, and (3) over which we quantify.
     From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.12
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Quine says the predicate of a true statement has no ontological implications [Quine, by Armstrong]
     Full Idea: Quine's doctrine is that the predicate of a true statement carries no ontological implications.
     From: report of Willard Quine (works [1961]) by David M. Armstrong - Properties §1
     A reaction: Quine is ontologically committed to the subject of the statement (an object). The predicate seems to be an inseparable part of that object. Quine is, of course, a holist, so ontological commitment isn't judged in single statements.
8. Modes of Existence / B. Properties / 12. Denial of Properties
Quine suggests that properties can be replaced with extensional entities like sets [Quine, by Shapiro]
     Full Idea: Quine doubts the existence of properties, and, trying to be helpful, suggests that variables ranging over properties be replaced with variables ranging over respectable extensional entities like sets, so we can 'identify' a property with a singleton set.
     From: report of Willard Quine (works [1961]) by Stewart Shapiro - Higher-Order Logic 2.1
     A reaction: This strikes me as a classic modern heresy, a slippery slope that loses all grip on what a property is, replacing it with entities that mean nothing, but make the logic work.
Quine says that if second-order logic is to quantify over properties, that can be done in first-order predicate logic [Quine, by Benardete,JA]
     Full Idea: Quine assures us that if the specific mission of second-order logic is quantifying over properties, the task can readily be performed by first-order predicate logic, as in (Ex) x is a property, and (y) y has x.
     From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.10
Quine brought classes into semantics to get rid of properties [Quine, by McGinn]
     Full Idea: Quine brought classes into semantics in order to oust properties.
     From: report of Willard Quine (works [1961]) by Colin McGinn - Logical Properties Ch.3
     A reaction: Quine's view has always struck me as odd, as I don't see how you can decide what set something belongs to if you haven't already decided its properties. But then I take it that nature informs you of most properties, and set membership is not arbitrary.
Don't analyse 'red is a colour' as involving properties. Say 'all red things are coloured things' [Quine, by Orenstein]
     Full Idea: Quine proposes that 'red is a colour' does not require analysis, such as 'there is an x which is the property of being red and it is a colour' which needs an ontology of properties. We can just say that all red things are coloured things.
     From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.6
     A reaction: The question of the ontology of properties is here approached, in twentieth century style, as the question 'what is the logical form of property attribution sentences?' Quine's version deals in sets of prior objects, rather than abstract entities.
8. Modes of Existence / D. Universals / 2. Need for Universals
Universals are acceptable if they are needed to make an accepted theory true [Quine, by Jacquette]
     Full Idea: Abstract entities (universals) are admitted to an ontology by Quine's criterion if they must be supposed to exist (or subsist) in order to make the propositions of an accepted theory true.
     From: report of Willard Quine (works [1961]) by Dale Jacquette - Abstract Entity p.3
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
Quine is committed to sets, but is more a Class Nominalist than a Platonist [Quine, by Macdonald,C]
     Full Idea: Armstrong dubs Quine an 'Ostrich Nominalist' (what problem??), but Quine calls himself a Platonist, because he is committed to classes or sets as well as particulars. He is not an extreme nominalist, and might best be called a Class Nominalist.
     From: report of Willard Quine (works [1961], Ch.6 n15) by Cynthia Macdonald - Varieties of Things
     A reaction: For someone as ontologically austere as Quine to show 'commitment' to sets deserves some recognition. If he wants to be a Platonist, I say that's fine. What on earth is a set, apart from its members?
9. Objects / A. Existence of Objects / 4. Impossible objects
Definite descriptions can't unambiguously pick out an object which doesn't exist [Lycan on Quine]
     Full Idea: Meinong characteristically refers to his Objects using definite descriptions, such as 'the golden mountain'. But on his view there are many golden mountains, with different features. How can 'the golden mountain' then succeed in denoting a single Object?
     From: comment on Willard Quine (works [1961]) by William Lycan - The Trouble with Possible Worlds 01
     A reaction: Use of definite descriptions doesn't seem obligatory in this situation. 'Think of a golden mountain' - 'which one?' - 'never mind which one!'.
10. Modality / B. Possibility / 1. Possibility
Quine wants identity and individuation-conditions for possibilia [Quine, by Lycan]
     Full Idea: Quine notoriously demands identity and individuation-conditions for mere possibilia.
     From: report of Willard Quine (works [1961]) by William Lycan - The Trouble with Possible Worlds 01
     A reaction: Demanding individuation before speaking of anything strikes me as dubious. 'Whoever did this should own up'. 'There must be something we can do'. Obviously you need some idea of what you are talking about - but not much.
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
For Quine the only way to know a necessity is empirically [Quine, by Dancy,J]
     Full Idea: Quine argues that no necessity can be known other than empirically.
     From: report of Willard Quine (works [1961]) by Jonathan Dancy - Intro to Contemporary Epistemology 14.6
11. Knowledge Aims / A. Knowledge / 2. Understanding
In contrast with knowledge, the notion of understanding emphasizes practical engagement [Gulick]
     Full Idea: In contrast with standard notions of knowledge, the concept of understanding emphasizes the element of practical engagement from the outset.
     From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §II)
     A reaction: This could be the very interesting germ of a huge revolution in our approach to epistemology, which I find rather appealing. Plato's desire that knowledge should have 'logos' seems to me in the same area. It sounds rather internalist, which is good.
11. Knowledge Aims / A. Knowledge / 6. Knowing How
Knowing-that is a much richer kind of knowing-how [Gulick]
     Full Idea: Knowing-that is a much richer kind of knowing-how.
     From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §II)
     A reaction: This thought could rather rapidly revive the discredited notion of knowing-how. I think it might slot into an account of the mind in terms of levels, so that my internalist view of knowledge emerges at higher levels, built on more basic responses.
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Quine's empiricism is based on whole theoretical systems, not on single mental events [Quine, by Orenstein]
     Full Idea: Traditional empiricism takes impressions, ideas or sense data as the basic unit of empirical thought, but Quine takes account of the theoretical as well as the observational; the unit of empirical significance is whole systems of belief.
     From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.1
     A reaction: This invites either the question of what components make up the whole systems, or (alternatively) what sort of mental events decide to accept a system as a whole. Should Quine revert either to traditional empiricism, or to rationalism?
13. Knowledge Criteria / E. Relativism / 4. Cultural relativism
To proclaim cultural relativism is to thereby rise above it [Quine, by Newton-Smith]
     Full Idea: Truth, says the cultural relativist, is culture-bound. But if it were, then he, within his own culture, ought to see his own culture-bound truth as absolute. He cannot proclaim cultural relativism without rising above it.
     From: report of Willard Quine (works [1961]) by W.H. Newton-Smith - The Rationality of Science VII.10
14. Science / B. Scientific Theories / 3. Instrumentalism
For Quine, theories are instruments used to make predictions about observations [Quine, by O'Grady]
     Full Idea: Quine's epistemological position is instrumentalist. Our theories are instruments we use to make predictions about observations.
     From: report of Willard Quine (works [1961]) by Paul O'Grady - Relativism Ch.3
     A reaction: This is the pragmatist in Quine. It fits the evolutionary view to think that the bottom line is prediction. My theory about the Pelopponesian War seems an exception.
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
Is consciousness a type of self-awareness, or is being self-aware a way of being conscious? [Gulick]
     Full Idea: Is consciousness just a special type of self-awareness, or is being self-aware a special way of being conscious?
     From: Robert van Gulick (Mirror Mirror - Is That All? [2006], Intro)
     A reaction: This is a really good key question, which has hovered over the debate since Locke's definition of a person (as 'self-aware'). I take the self to be a mechanism of most brains, which is prior to consciousness. Maybe the two are inseparable.
15. Nature of Minds / B. Features of Minds / 1. Consciousness / f. Higher-order thought
Higher-order theories divide over whether the higher level involves thought or perception [Gulick]
     Full Idea: Higher-order thought (HOT) models treat metastates as thought-like, and higher-order perception (HOP) models regard them as at least quasi-perceptual and resulting from some form of inner monitoring or inner sense.
     From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §I)
     A reaction: I would understand 'thought' to at least partially involve judgements. The HOT theory (Carruthers) seems to suit epistemological foundationalists, who want truth to enter on the ground floor. This pushes me towards the HOP model (Lycan) as more plausible.
Higher-order models reduce the problem of consciousness to intentionality [Gulick]
     Full Idea: Higher-order models would effectively reduce the problem of consciousness to that of intentionality.
     From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §I)
     A reaction: This gives the bigger picture - that higher-order theories are the cutting edge of attempts to give a naturalistic, reductivist account of consciousness. That seems to be the only way to go, so we should encourage them in the enterprise.
Maybe qualia only exist at the lower level, and a higher-level is needed for what-it-is-like [Gulick]
     Full Idea: Some higher-order theorists say we have qualitative but unconscious mental states of color or pain (qualia), but there is nothing it is like to be in such a state, which needs higher-order awareness. The meta-states are devoid of qualia.
     From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §I.5)
     A reaction: He calls this the 'stranded qualia' problem. Clearly one begins to sharpen Ockham's Razor at this point, if the higher-level state isn't contributing something. I don't rule out unconscious qualia. The strength of a real pain is distorted in a dream.
19. Language / B. Reference / 1. Reference theories
Quine says there is no matter of fact about reference - it is 'inscrutable' [Quine, by O'Grady]
     Full Idea: Quine holds the doctrine of the 'inscrutability of reference', which means there is no fact of the matter about reference.
     From: report of Willard Quine (works [1961]) by Paul O'Grady - Relativism Ch.3
     A reaction: Presumably reference depends on conventions like pointing, or the functioning of words like "that", or the ambiguities of descriptions. If you can't define it, it doesn't exist? I don't believe him.
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
The principle of charity only applies to the logical constants [Quine, by Miller,A]
     Full Idea: Quine takes to the principle of charity to apply only to the translation of the logical constants.
     From: report of Willard Quine (works [1961]) by Alexander Miller - Philosophy of Language 8.7
     A reaction: Given how weird some people's view of the world seems to be, this very cautious approach has an interesting rival appeal to Davidson't much more charitable view, that people mostly speak truth. It depends whether you are discussing lunch or the gods.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
Essence gives an illusion of understanding [Quine, by Almog]
     Full Idea: Essence engenders a mere illusion of understanding
     From: report of Willard Quine (works [1961]) by Joseph Almog - Nature Without Essence Intro
     A reaction: [Almog quotes Quine, but doesn't give a reference] This is roughly the same as Popper's criticism of essentialism.
27. Natural Reality / G. Biology / 2. Life
From the teleopragmatic perspective, life is largely an informational process [Gulick]
     Full Idea: From the teleopragmatic perspective, life itself is largely an informational process.
     From: Robert van Gulick (Mirror Mirror - Is That All? [2006])
     A reaction: From the cynical perspective a human is just 'blood and foul smell in a bag', but that may not give you whole story. The point here is that the informational view will cover both the genetic and the mental levels of human life. True but unilluminating?