Deductivism says that a mathematical sentence s should be understood as expressing the claim that s deductively follows from appropriate axioms. For instance, deductivists might construe “2+2=4” as “the sentence ‘2+2=4’ deductively follows from the axioms of arithmetic”. Deductivism promises a number of benefits. It captures the fairly common idea that mathematics is about “what can be deduced from the axioms”; it avoids an ontology of abstract mathematical objects; and it maintains that our access to mathematical truths requires nothing beyond (...) our ability to make logical deductions. Sections 1 and 2 define and motivate deductivism in more detail. Section 3 covers four authors (Russell, Hilbert, Pasch, Curry) who have endorsed deductivism at some point. Section 4 aims to clarify what semantic claim deductivists make. Sections 5–9 review objections to deductivism and possible replies. (shrink)

This entry is composed of three sections. In §1, we survey debates about what structural rationality is, including the emergence of the concept in the contemporary literature, its key characteristics, its relationship to substantive rationality, its paradigm instances, and the questions of whether these instances are unified and, if so, how. In §2, we turn to the debate about structural requirements of rationality – including controversies about whether they are “wide-scope” or “narrow-scope”, synchronic or diachronic, and whether they govern processes (...) or states; as well as examining various forms of skepticism about structural requirements of rationality. In §3, we turn to the debate about the normative significance of structural rationality, surveying central challenges for the view that structural rationality is normatively significant and the theoretical options that arise in light of these challenges. (shrink)

Henry Habberley Price, who published as H. H. Price, was born in 1899. From 1935 to 1959 he was Wykeham Professor of Logic at Oxford University. Price was a major figure in his lifetime well-known especially for the “clarity and elegance of style”, which, according to Martha Kneale (1996: xix), make his works readable in spite of changing fashions in philosophy. Many people’s acquaintance nowadays with Price’s philosophical work derives from his being a target in Austin’s (1962) famous attack on (...) the sense-datum theory. This restricted acquaintance with his output is one reason that Price has been ignored in recent philosophy. -/- Mainstream philosophy neglected him after the Second World War, perhaps partly because, when articulating his ideas, he mainly engaged with philosophers of the past, such as Locke and Hume. His thought was, however, valued by fellow philosophers such as Broad, Moore, Ayer, and generations of his students at Oxford, including Sellars, Armstrong, and Anscombe. -/- Although Price is seen mainly as a philosopher of perception, only two of his six books are about perception and he had a major influence, also publishing many articles, on a variety of topics, including some we cannot focus on here, e.g., our evidence of other minds (1938; 1930b: 195) and psychical research (1940c; 1953b; 1972; 1995; an interest he claims to share with Neo-Platonists [1968a: 447]). We can only provide a sketch of his rich contributions. After briefly sketching his life (§1), we discuss his philosophy’s general features (§2), contributions to the studies of perception (§3), properties (§5.1), recognition (§5), belief (§6), religious belief (§6.8), his revival and serious study of Hume (§4), and some remarkable anticipations (§7). (shrink)