Whatever his faults as man and philosopher may have been, Bertrand Russell stands as a model of how to do and write philosophy in English. My own publications have often fallen short of this ideal of breadth and lucidity—although not all of them at all points. Perhaps still more markedly, recent philosophy has been strikingly lacking in imagination and bold speculation; few philosophical traditions have made themselves into paradigms of derivative and dull "normal science" (in the sense of Thomas Kuhn) as has Anglo-American philosophy of the last decades. With a veneer of symbol-studded rigor, and faux-scientific attachments to a supposedly common sense and well-understood world of physical matter, there is a surprising—and I think unattractive and wrong-headed—common attachment to everything "naturalized." That is everything, including philosophical concepts, is to be intellectually dealt with as the sciences have recently treated nature—often based upon a rather naïve and simplistic idea of what science does.

Nevertheless, the methods of thinking and writing as clearly as one can, perhaps using some tools borrowed from mathematics and the natural sciences, can be of enormous value to philosophy. This is something that non-analytical and especially Continental philosophers have not always grasped. Plato, Aristotle, Descartes, Pascal, Leibniz, Kant and many others were keenly aware of the relevance of an extensive knowledge of science and mathematics for philosophy. We must not only rush to deal with big issues and the big picture, but also be aware that we are wrestling with difficult issues that are often tantalizingly (but not impossibly) beyond our grasp.

There is no royal road to doing philosophy: neither the theory of language nor reveling in the shockingly diverse use of it, for example. Carefully formulated "valid" arguments often turn out to be simplistic ones whose symbolic forms are valid but whose concepts are unexamined, and the use of elaborate symbolic machinery has more often than not obscured the fact that it is a distracting, conceptual Rube Goldberg contraption. The sometimes intentionally obscure and amusingly literary creations of our European bretheren, their discourses on texts, praxis, and semiosis everywhere, and objective things and values nowhere, does not produce—or perhaps even aim for—that basic philosophical currency, (rational) understanding. Just as philosophy is essentially broad, interrelating seemingly distinct issues and subfields—such as metaphysics and ethics—so too its method is essentially eclectic. There is no magical key, no tool or trick at the ready, which can singlehandedly end our puzzlement. Some tools, used deftly, are perhaps better than others.

While European philosophy since Hegel has often made a fetish of the history of philosophy and scholarship about it, much Anglo-American philosophy since Frege and Moore has taken the opposite tack and pretended to ignore or even inveigh against it. The history of philosophy is not just an account of who said exactly what, nor even of how the distant past affected the past and even us. The history of philosophy instead constitutes a list of mining claims about where the gold might lie. These claims are visibly scattered all about, and it is quite hard to tell when there is no or little gold—or even tin—beneath them. Some are mere guesses or suggestions by past miners of varying abilities about some unlikely place that may contain philosophical riches (but by admittedly clever and even wise people), and some are sites on which deep mines have been dug, but in which it is hard for us modern folk now to move around. It seems foolish to ignore, as a policy, all of these claims, and go off to dig where our impulses direct us. We should think hard about which mines once produced apparently high quality ore—and why. We should triangulate among the once rich but now mined-out sites before we start digging again. Likewise, we should not just open any old mine or claim stake and think that we will find riches. No matter how carefully we dig, we cannot get gold out of some dirt.

If there are cuprits in recent philosophy, it is these: historicists and anti-historicists, pro- and anti-symbolists, linguists and anti-linguists, scientists and anti-scientists, and so on. This has often been overlaid with a patina of timidity, conformism, narrowness of education and interest, and "professionalism."

Art, emotions

2.  Logic and the Philosophy Of Mathematics. If there is any area in which I should have well-developed views, it is these. I am not sure I really do, but here goes. I think that the current, fashionable definition of logic roughly as the theory of logical consequence among sentences is extremely problematic. I think that any good definition of logic will have within it the germ of an explanation of why creatures that can think at all should reason in certain ways, or why certain methods of reasoning are preferable for certain (perhaps universal) purpose over others. In other words, a correct definition of logic will somehow be linked with how we should think, and especially with the mental habits we should cultivate by which one thought follows another. Such a conception, or constraints on the nature, of logic and how it should be defined has four consequences that are unpopular or even reviled. First, it relates logic to normativity—perhaps even to a kind of ethics of thought. Second, it takes "logic" as embracing not just deductive logic for sentences, but all methods of thought worth developing, including inductive logic, science, imagination, and speculation (Peircean abduction). If we extend thought to include any states of mind that are "cognitive"—directed to or directly related to objects we can think about—then logic includes as well some guidance about the formation of our cognitive emotions. (This probably links logic to art.) Third, it "psychologizes" logic: it connects logic to thought processes, rather than to abstract relationships among "sentences." Nevertheless, this is an ideal theory about how any creature that can think should think, and not about how humans do think, or even how humans should think. Fourth, it makes logic not just a theory about relationships among, or ideal sequences of, sentences, propositions, or sentence-like entities, but also makes logic applicable to anything that we can think about. This likely includes concepts and other "parts" of the sentence-like entities toward which we have states of mind like belief. There is thus also a normativity to our concepts, and how we form concepts. We should have many, diverse, and precise concepts that are indeed applicable to the world as we think they are—and we should have concepts that are about all areas of human activity where it is useful for a thinking entity to have concepts. I should have concepts of maples as opposed to oaks, and of sonata-allegro as opposed to rondo musical forms, of "anger" as opposed to dislike—and more particularly for logic as a theory of ideal methods of thought, I should have certain highly developed habits of making more precise, altogether discarding, and differentiating concepts.

Within deductive logic, I have certain views that are quite standard and usual, and some that are probably quite odd. Within the standard presentations of what is considered logic, I tend to believe that "classical" logic is the only one worthy of the name: one with standard connectives (and, or, if…then, in their standard semantic interpretation), and with two "values": true or false. Perhaps because of my "psychologistic" tendencies, I do not like to understand and present logics purely in their convenient extensional formulations. Rather, I like to think of logic in an intensional way, with terms and operations that connect to concepts (or even properties) and not to things or sets of things. It may turn out that the calculus for describing intensional logic properly, a logic of thoughts and concepts, is not markedly different from a logic of things. I have long been enamored of a Fregean logic of sense and denotation, as understood by Alonzo Church, but like—I believe--him I reject the reduction of intension (and thus meaning) to constructs like possible worlds that are ultimately extensional.

However I believe that standard accounts of predicate logic do a profound disservice to the real structure of thought (and possibly to the structure of the world): they divide the world up into things ("individuals," or their names) and properties (or their names, predicates) which these individuals "have." While convenient, and following linguistic custom, this is ultimately unclear and unjustified. Which things are individuals? There are no "things" and their "properties." There is ultimately only structure. Structures, when clearly understood, are ultimately (purely) relational and mathematically-describable. Mathematics just is the theory of all forms of well-defined structure.

All ideal understanding is ultimately mathematical. Consequently, logic (even or especially as augmented with set theory) cannot epistemologically explain or metaphysically ground mathematics. Philosophers’ understanding of the relationship of mathematics to logic is quite deluded, I think, as many mathematicians have dismissively presumed. We do not grasp or ideally understand mathematical structure through logical structure. If anything, we can understand logic through mathematical structure (a Peircean anti-logicism).

In the teaching of logic—although I do typically focus narrowly on deductive logic (one can’t do everything in a semester)—I am historicist, philosophical, pluralistic, diagram-inclined and semantics-inclined, and when I teach predicate logic (more or less in the usual way), move as quickly as I can to getting stuidents to think clearly about relations, since that is where the idea of structure lives. I try to teach logic as a live philosophical discipline with philosophical issues lurking all about, and of our current views in logic as the product of an often capricious and intrinsically interesting history that is interwoven with the history of philosophy and mathematics. (Even highly educated know too little, I believe, about the history of science, mathematics, and technology—living only in a kind of obvious present, and assuming that the current view in science or mathematics, whatever that is, to be correct, well-understood, philosophically unproblematic, or otherwise optimal.)