What is the value of intellectual playfulness? Traditional characterizations of the ideal thinker often leave out playfulness; the ideal inquirer is supposed to be sober, careful, and conscientiousness. But elsewhere we find another ideal: the laughing sage, the playful thinker. These are models of intellectual playfulness. Intellectual playfulness, I suggest, is the disposition to try out alternate belief systems for fun – to try on radically different perspectives for the sheer pleasure of it. But what would the cog-nitive value be (...) of such playfulness? I suggest that intellectual playfulness function as, at the very least, a kind of intellectual insurance policy against epistemic traps. An epistemic trap is a belief system that re-directs good-faith inquiry to bad results. Am epistemic trap manipulates background beliefs to fend off contrary evidence. For example, a conspiracy theory might include a set of beliefs about how the mainstream media has been taken over by some vicious cabal. Normal epistemic attempts will be captured by a well-wrought epistemic trap, because normal attempts at inquiry are guided by these background beliefs -- which set what counts as a plausible path to explore, and what is implausible or beyond the pale. And a clever epistemic trap will manipulate those background beliefs for ill effect. Intellectual playfulness, on the other hand, isn’t motivated by an epistemic interest in the truth, but in the sheer pleasure of intellectual exploration. Since intellectual playfulness isn’t oriented towards the truth, it won’t be constrained by an agent’s background beliefs – it won’t, for example, prefer to investigate apparently more plausible pathways. Intellectual playfulness offers an opportunity to escape from epistemic traps. But intellectual playfulness has its own limitations. It will only drive us to explore belief systems when that exploration is fun. What we need is an array of differently-motivated exploratory tendencies – empathy, curiosity, playfulness – each of which will each cover for the others’ limitations. (shrink)

This paper tries to show that there is an important virtue that could be called “accountability.” This virtue is a trait of a person who embraces being held accountable and consistently displays excellence in relations in which the person is held accountable. After describing the virtue in more detail, including its motivational profile, some core features of this virtue are described. Empirical implications and an agenda for future research are briefly discussed. Possible objections to the virtue are considered and rebutted, (...) and relations to other virtues, particularly the personal virtue of justice, are discussed. In conclusion, we suggest that though this virtue has not received the attention it deserves in contemporary society, it has been more clearly recognized in other cultures. Some of the reasons for the partial eclipse of the virtue are understandable and justifiable, but there are good reasons to think our society would be improved if we paid more attention to accountability from a virtue perspective. (shrink)

Former discussions of biological generalizations have focused on the question of whether there are universal laws of biology. These discussions typically analyzed generalizations out of their investigative and explanatory contexts and concluded that whatever biological generalizations are, they are not universal laws. The aim of this paper is to explain what biological generalizations are by shifting attention towards the contexts in which they are drawn. I argue that within the context of any particular biological explanation or investigation, biologists employ two (...) types of generations. One type identifies causal regularities exhibited by particular kinds of biological entities. The other type identifies how these entities are distributed in the biological world. (shrink)

This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, (...) the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties). (shrink)

To eliminate racist prejudices, it is necessary to identify the root cause of racism. American slavery preceded racism, and it was closely associated with genocide. Accordingly, we seek the unique cause of the unique event of genocide + slavery. This was initially justified by religious prejudice, rather than colour prejudice. This religious justification was weakened when many Blacks converted to Christianity, after the trans-Atlantic slave trade. The curse of Kam, using quick visual cues to characterize Blacks as inferior Christians, was (...) inadequate. Hence, the church fell back on an ancient trick of using false history as secular justification for Christian superiority. This trick had resulted in a false history of science during the Crusades when scientific knowledge in translated Arabic texts was indiscriminately attributed to the early Greeks, without evidence. This false history enabled belief in religious superiority to mutate into a secular belief in White superiority. After colonialism, and the Aryan race conjecture, the belief in White superiority further mutated into a belief in Western civilizational superiority, openly propagated today by colonial education. Hence, to eliminate racist prejudice, it is necessary to engage simultaneously with the allied prejudices about Christian/White/Western superiority, based on the same false history of science. (shrink)

Previously we saw that racist prejudice is supported by false history. The false history of the Greek origins of mathematics is reinforced by a bad philosophy of mathematics. There is no evidence for the existence of Euclid. The “Euclid” book does not contain a single axiomatic proof, as was exposed over a century ago. Such was never the intention of the actual author. The book was brazenly reinterpreted, since axiomatic proof was a church political requirement, and used in church rational (...) theology adopted during the Crusades, as a counter to Islamic rational theology. Deductive proofs are MORE fallible than inductive or empirical proofs. Even a validly proved mathematical theorem, such as the “Pythagorean” theorem, is invalid knowledge in the real world. There is no concept of approximate truth in formal mathematics. Nevertheless, the myth of “superior” axiomatic proofs in the “Euclid” book continues to be reiterated by Western historians, and colonial education teaches axiomatic mathematics. Actually, superior practical value comes from the two “Pythagorean” calculations well known toIndian/Egyptian tradition, but unknown to Greeks. The advantage of related decolonized courses in mathematics has been pedagogically demonstrated. But understanding and political will are needed to change colonial/church education. (shrink)