[2014:] …3.12 factor analysis: To better understand these correlations, we perform exploratory factor analysis (1904; 1983) and principal component analysis (Pearson 1901; 2002) on the target faculty responses using a range of methods. The aim of both of these types of statistical analyses is to isolate a relatively small number of factors or components (we will use these terms interchangeably) that can be used to predict as much as possible of the variation in a larger number of observed variables (in this case, answers to survey questions). Any given factor is a linear combination f the observed variables. The numerical loading for each variable is the correlation between the factor and the variable.
Table 15 shows the components we extracted using principal component analysis. A Varimax rotation (which produces mutually uncorrected factors that tend to be highly loaded on a limited number of variables) was applied. We restricted the analysis to 30 answers in total (one per question). Some answers were combined: Relativism and Contextualism were combined, as were Idealism and Skepticism. Otherwise, the number of answers was reduced by eliminating one or more answer per question. This was necessary in order to remove uninteresting dependencies between answers. The number of extracted components was restricted to 7.
…While interpreting the results of such analyses is inherently difficult, the first 5 components showed in Table 15 are not too hard to characterize. The first component, dominated by theism, a rejection of naturalism, libertarianism about free will, and non-physicalism about the mind, seems to reflect a rejection of a naturalistic world view. The second component combines realism and cognitivism about moral judgements with objectivism about esthetic values. It is also associated with Platonism. It seems to reflect a propensity to acknowledge the objectivity of normative and evaluative facts and the reality of controversial entities in ontology. The third component combines a priori knowledge, analytic truths, and rationalism. The connection may be explained by the fact that a priori knowledge is typically associated with either analytic truths or rational intuition. The 4th component seems to be the kind of anti-realism associated with epistemic theories of truth, while the fifth component clearly captures a broadly externalist tendency. We will label the preceding components “anti -naturalism”, “objectivism/Platonism”, “rationalism”, “anti-realism”, and “externalism.” The labels are only rough approximations, however, and it is should be noted that these components are only imperfectly correlated with explicit endorsement of naturalism, rationalism, and so on.
Components 6 and 7 must be interpreted with additional care because they differ between the analyses conducted. It is also harder to put a label on them. Component 6 groups the view that one dies in the teletransporter case with deontology, the A-theory of time, and the view that one should not switch in the trolley case. The views on the trolley case and on deontology have a natural connection, but the connection between these views and the views on the teletransporter and time issues is more mysterious. The 7th component is dominated by two-boxing on Newcomb’s problem, upholding classical logic, and invariantism about knowledge claims. Again, it is unclear exactly what this component captures.
Table 16 shows the main correlations between background questions and the 7 extracted components. The correlations between our two last components identification with certain philosophers suggest that these components might reflect the views of these philosophers.
…The correlations and principal component analysis reported in the preceding sections suggest that philosophical views tend to come in packages. Our analysis reveals 5 major choice points in logical space: naturalism vs anti-naturalism, objectivism/Platonism vs subjectivism, rationalism vs empiricism, realism vs anti-realism (of the kind associated with epistemic theories of truth), internalism vs externalism. Of course, the packages depend on the choice of questions, and different surveys may have yielded different packages. Still, much of one’s position on the questions we asked appears to be determined by one’s view on these 5 issues. Positions on these issues are substantially affected by respondents’ professional backgrounds, their specializations, and their orientations as philosophers.