The Portuguese language version of social phobia and Anxiety Inventory: analysis of items and internal consistency in a Brazilian sample of 1,014 undergraduate students

OBJECTIVE: Theoretical and empirical analysis of items and internal consistency of the Portuguese-language version of Social Phobia and Anxiety Inventory (SPAI-Portuguese). METHODS: Social phobia experts conducted a 45-item content analysis of the SPAI-Portuguese administered to a sample of 1,014 university students. Item discrimination was evaluated by Student's t test; interitem, mean and item-to-total correlations, by Pearson coefficient; reliability was estimated by Cronbach's alpha. RESULTS: There was 100% agreement among experts concerning the 45 items. On the SPAI-Portuguese 43 items were discriminative (p < 0.05). A few inter-item correlations between both subscales were below 0.2. The mean inter-item correlations were: 0.41 on social phobia subscale; 0.32 on agoraphobia subscale and 0.32 on the SPAI-Portuguese. Item-to-total correlations were all higher then 0.3 (p < 0.001). Cronbach's alphas were: 0.95 on the SPAI-Portuguese; 0.96 on social phobia subscale; 0.85 on agoraphobia subscale. CONCLUSION: The 45-item content analysis revealed appropriateness concerning the underlying construct of the SPAI-Portuguese (social phobia, agoraphobia) with good discriminative capacity on 43 items. The mean inter-item correlations and reliability coefficients demonstrated the SPAI-Portuguese and subscales internal consistency and multidimensionality. No item was suppressed in the SPAI-Portuguese but the authors suggest that a shortened SPAI, in its different versions, could be an even more useful tool for research settings in social phobia.

The mathematics of McTaggart's paradox

Mc Taggart's celebrated proof of the unreality of time is a chain of implications whose final step asserts that the A-series (i.e. the classification of events as past, present or future) is intrinsically contradictory. This is widely believed to be the heart of the argument, and it is where most attempted refutations have been addressed; yet, it is also the only part of the proof which may be generalised to other contexts, since none of the notions involved in it is specifically temporal. In fact, as I show in the first part of the paper, McTaggart's refutation of the A-series can be easily interpreted in mathematical terms; subsequently, in order to strengthen my claim, I apply the same framework by analogy to the cases of space, modality, and personal identity. Therefore, either McTaggart's proof as a whole may be extended to each of these notions, or it must embed some distinctly temporal element in one of the steps leading up to the contradiction of the A-series. I conclude by suggesting where this element might lay, and by hinting at what I believe to be the true logical fallacy of the proof.

HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.