Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Mirror Mirror - Is That All?' and 'Philosophical Insignificance of A Priori Knowledge'

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19 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 / G. Scientific Philosophy / 3. Scientism
All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau]
     Full Idea: I would say that all worthwhile philosophy consists of synthetic theorizing, evaluated against experience.
     From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §1)
     A reaction: This is the view that philosophy is just science at a high level of abstraction, and he explicitly rejects 'conceptual analysis' as a fruitful activity. I need to take a stance on this one, but find I am in a state of paralysis. Welcome to philosophy...
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 / 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 / 11. Ontological Commitment / e. Ontological commitment problems
Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau]
     Full Idea: Our empirically best-supported theories may commit us to certain abstract mathematical entities, but this does not necessarily mean that this is what justifies our commitment. That we are committed doesn't explain why we should be.
     From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §4)
     A reaction: A nice point. It is only a slightly gormless scientism which would say that we have to accept whatever scientists demand. Who's in charge here - scientists, mathematicians or philosophers? Don't answer that...
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 / A. A Priori Knowledge / 9. A Priori from Concepts
A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau]
     Full Idea: I am a fully paid up-naturalist, but I see no reason to deny that a priori knowledge is possible. My view is that a priori knowledge is unimportant (esp to philosophy). If there is a priori knowledge, it is analytic, true by the structure of our concepts.
     From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §1)
     A reaction: It is one thing to say it is the structure of our concepts, and another to infer that it is unimportant. I take the structure of our concepts to be a shadow cast by the structure of the world. E.g. the structure of numbers reveals the world.
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Intuition and thought-experiments embody substantial information about the world [Papineau]
     Full Idea: Naturalists can allow for thought-experiments in philosophy. Intuitions play an important role, but only because they embody substantial information about the world.
     From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §3)
     A reaction: In this sense, intuitions are just memories which are too complex for us to articulate. They are not the intuitions of 'pure reason'. It is hard to connect the intuitive spotting of a proof with memories of the physical world.
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 / A. Nature of Meaning / 5. Meaning as Verification
Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau]
     Full Idea: Verificationism about concepts implies that thinkers will not share concepts with adherents of theories they reject. Those who reject the phlogiston theory will not possess the same concept as adherents, so cannot say 'there is no phlogiston'.
     From: David Papineau (Philosophical Insignificance of A Priori Knowledge [2010], §6)
     A reaction: The point seems to be more general - that it is hard to see how you can have a concept of anything which doesn't actually exist, if the concept is meant to rest on some sort of empirical verification.
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?