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Factor analysis
I don't understand factor analysis well, but it seems as if answers to most questions are predicted by just one factor.

For instance, if you are an anti-naturalist, then it's likely that you are going to be a non-physicalist about mind, think that there is a further fact about personal identity, be a libertarian in free will, and believe in God. None of these answers is significantly predicted by any other factor. (Though I wonder what's fundamental: maybe if you believe in God, the others follow as far as your own reasoning is concerned.)

There are a few questions that are determined by more than one factor. Knowledge rationalism is predicted by:   anti-naturalism, realism, and rationalism itself.

But all in all, there seem to be just four basic determinative "personality" factors in philosophy: naturalism, realism, rationalism, and externalism. Aside from externalism, which speaks to the transformative influence of Kripke and Putnam, the other three are old chestnuts. I suppose naturalism is the newest of the other three, dating to the Scientific Revolution, or perhaps to nineteenth century materialism.

Factor analysis
Reply to Mohan Matthen
I wouldn't make claims nearly as strong as this.  Some of what you've said here definitely isn't right: e.g. there are many more non-naturalist atheists among the respondents than non-naturalist theists, so it's not true that if you're a non-naturalist you're likely to believe in god (though it's true that you're more likely to believe in god than if you're a naturalist).  Note also that we've left off correlation loadings under 0.25 for ease of reading, and these can certainly be quite significant.  There are also numerous questions whose responses aren't strongly predicted by the first four factors.

Finally, and perhaps most importantly, the factors depend strongly on the choice of questions, and it's perhaps not accidental that the editors are interested in questions about naturalism, realism, rationalism, and externalism.  Other equally reasonable choices of questions might well have produced a stronger role for factors involving e.g. epistemic anti-realism, deontology, logical classicalism (roughly our fifth, sixth, and seventh  factors), and many other things.

So I wouldn't make claims about "just four determinative personality factors".  But it's interesting to look at the factor structure all the same.