A priori knowledge: yes for mathematics (and possibly priors) only.
Abstract objects: Platonism
Aesthetic value: subjectively objective
Analytic-synthetic distinction: yes, math is analytic, everything else is synthetic
Epistemic justification: externalism
External world: it exists, I assume that's non-skeptical realism
Free will: leaning towards compatibilism
Knowledge: empiricism or rationalism? Both, for different types of knowledge.
Knowledge claims: invariantism (although contextualism may have some points)
Laws of nature: Humean or non-Humean? I wasn't able to find a concise summary of what this means.
Logic: classical (with Baysean probability theory, which is derived from classical logic and mathematics, applicable in most cases dealing with non-mathematical objects)
Mental content: internalism or externalism? I can't figure out what this means.
Meta-ethics: moral realism
Metaphilosophy: probably naturalism
Mind: not sure
Moral judgment: cognitivism
Moral motivation: internalism or externalism? I can't figure out what this means
Newcomb's problem: one box
Normative ethics: something like consequential virtue ethics
Perceptual experience: disjunctivism, qualia theory, representationalism, or sense-datum theory? These all seem to be talking about different things.
Personal identity: biological view, psychological view, or further-fact view? Probably further-fact view if it means what I'm guessing it means.
Politics: libertarianism
Proper names: Millian, to the extend this question is at all meaningful
Science: scientific realism (subject to the constrain that our current theories, at least, are as wrong as Newtonian physics)
Teletransporter (new matter): not sure
Time: A-theory or B-theory? This is at best a question of definitions and not a philosophical question.
Trolley problem (five straight ahead, one on side track, turn requires switching, what ought one do?): probably switch but with strong caveats
Truth: probably correspondence
Zombies: conceivable possibly metaphysically possible
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Philisophers: Locke, to a certain extent Mill and maybe Quine (I don't know enough about him to be sure).
The questions are at http://philpapers.org/surveys/oquestions.html. The correlations can be intensely interesting to those who understand philosophical jargon (http://philpapers.org/surveys/linear_most.pl) - it doesn't take too long to look them up as you go - and I actually found it to be a fun way to learn new philosophy. I know that there was a LW thread about this several months ago, but it didn't have a section for people here to respond to the survey. I would be very interested to see how people here would respond.
I'll repost the questions here:
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Original Survey Questions | PhilPapers Surveys
A priori knowledge: yes or no?
Abstract objects: Platonism or nominalism?
Aesthetic value: objective or subjective?
Analytic-synthetic distinction: yes or no?
Epistemic justification: internalism or externalism?
External world: idealism, skepticism, or non-skeptical realism?
Free will: compatibilism, libertarianism, or no free will?
God: theism or atheism?
Knowledge: empiricism or rationalism?
Knowledge claims: contextualism, relativism, or invariantism?
Laws of nature: Humean or non-Humean?
Logic: classical or non-classical?
Mental content: internalism or externalism?
Meta-ethics: moral realism or moral anti-realism?
Metaphilosophy: naturalism or non-naturalism?
Mind: physicalism or non-physicalism?
Moral judgment: cognitivism or non-cognitivism?
Moral motivation: internalism or externalism?
Newcomb's problem: one box or two boxes?
Normative ethics: deontology, consequentialism, or virtue ethics?
Perceptual experience: disjunctivism, qualia theory, representationalism, or sense-datum theory?
Personal identity: biological view, psychological view, or further-fact view?
Politics: communitarianism, egalitarianism, or libertarianism?
Proper names: Fregean or Millian?
Science: scientific realism or scientific anti-realism?
Teletransporter (new matter): survival or death?
Time: A-theory or B-theory?
Trolley problem (five straight ahead, one on side track, turn requires switching, what ought one do?): switch or don't switch?
Truth: correspondence, deflationary, or epistemic?
Zombies: inconceivable, conceivable but not metaphysically possible, or metaphysically possible?
===
And... which of the following philosophers do you identify with?
The philosophers available to choose from for the "which philosophers do you identify with?" question were:
Anscombe
Aquinas
Aristotle
Augustine
Berkeley
Carnap
Davidson
Descartes
Frege
Hegel
Heidegger
Hobbes
Hume
Husserl
Kant
Kierkegaard
Leibniz
Lewis
Locke
Marx
Mill
Moore
Nietzsche
Plato
Quine
Rawls
Rousseau
Russell
Socrates
Spinoza
Wittgenstein