Mathematics has a great variety ofapplications in the physical sciences.This simple, undeniable fact, however,gives rise to an interestingphilosophical problem:why should physical scientistsfind that they are unable to evenstate their theories without theresources of abstract mathematicaltheories? Moreover, theformulation of physical theories inthe language of mathematicsoften leads to new physical predictionswhich were quite unexpected onpurely physical grounds. It is thought by somethat the puzzles the applications of mathematicspresent are artefacts of out-dated philosophical theories about thenature of mathematics. In this paper I argue (...) that this is not so.I outline two contemporary philosophical accounts of mathematics thatpay a great deal of attention to the applicability of mathematics and showthat even these leave a large part of the puzzles in question unexplained. (shrink)

Mathematics has a great variety ofapplications in the physical sciences.This simple, undeniable fact, however,gives rise to an interestingphilosophical problem:why should physical scientistsfind that they are unable to evenstate their theories without theresources of abstract mathematicaltheories? Moreover, theformulation of physical theories inthe language of mathematicsoften leads to new physical predictionswhich were quite unexpected onpurely physical grounds. It is thought by somethat the puzzles the applications of mathematicspresent are artefacts of out-dated philosophical theories about thenature of mathematics. In this paper I argue (...) that this is not so.I outline two contemporary philosophical accounts of mathematics thatpay a great deal of attention to the applicability of mathematics and showthat even these leave a large part of the puzzles in question unexplained. (shrink)

Scientific concepts and conceptual systems (theories) are particular forms of higher mental activity. They are cognitive organs that provide the ability of systematic cognition of phenomena, which are not available to the grasp of ordinary sense organs. They are tools of scientific “groping” of phenomena. Scientific concepts free perceptual and cognitive activity from determination of ordinary sense organs by providing a high degree of cognitive abstraction and generalization. Scientific cognition, like perceptual activity, is actualized by consciousness but outside the consciousness.

Let us begin with the simple observation that applied mathematics can be very tough! It is a common occurrence that basic physical principle instructs us to construct some syntactically simple set of differential equations, but it then proves almost impossible to extract salient information from them. As Charles Peirce once remarked, you can’t get a set of such equations to divulge their secrets by simply tilting at them like Don Quixote. As a consequence, applied mathematicians are often forced to pursue (...) roundabout and shakily rationalized expedients if any useful progress is to be made. Often these provisional and quasi-empirical procedures within applied mathematics loom large in motivating the “anti-realist” or “anti-unificationist” conclusions of Nancy Cartwright and allied authors. (shrink)

The objective of this essay is to provide the beginning of a principled classification of some of the ways space is intelligently used. Studies of planning have typically focused on the temporal ordering of action, leaving as unaddressed questions of where to lay down instruments, ingredients, work-in-progress, and the like. But, in having a body, we are spatially located creatures: we must always be facing some direction, have only certain objects in view, be within reach of certain others. How we (...) manage the spatial arrangement of items around us is not an afterthought: it is an integral part of the way we think, plan, and behave. The proposed classification has three main categories: spatial arrangements that simplify choice; spatial arrangements that simplify perception; and spatial dynamics that simplify internal computation. The data for such a classification is drawn from videos of cooking, assembly and packing, everyday observations in supermarkets, workshops and playrooms, and experimental studies of subjects playing Tetris, the computer game. This study, therefore, focuses on interactive processes in the medium and short term: on how agents set up their workplace for particular tasks, and how they continuously manage that workplace. (shrink)

In his seminal 1960 paper, the physicist Eugene Wigner formulated the question of the applicability of mathematics in physics in a way nobody had before. This formulation has been entirely overlooked due to an exclusive concern with solving Wigner’s problem and explaining the effectiveness of mathematics in the natural sciences, in one way or another. Many have attempted to attribute Wigner’s unjustified conclusion—that mathematics is unreasonably effective in the natural sciences—to his formalist views on mathematics. My goal is to show (...) that this reading misses out on Wigner’s highly original formulation of the problem which is presented throughout his body of work in physics as well as in philosophy. This formulation, as I will show, leads us in a new direction in solving the applicability problem. (shrink)

In his seminal 1960 paper, the physicist Eugene Wigner formulated the question of the applicability of mathematics in physics in a way nobody had before. This formulation has been entirely overlooked due to an exclusive concern with solving Wigner’s problem and explaining the effectiveness of mathematics in the natural sciences, in one way or another. Many have attempted to attribute Wigner’s unjustified conclusion—that mathematics is unreasonably effective in the natural sciences—to his formalist views on mathematics. My goal is to show (...) that this reading misses out on Wigner’s highly original formulation of the problem which is presented throughout his body of work in physics as well as in philosophy. This formulation, as I will show, leads us in a new direction in solving the applicability problem. (shrink)

E.V. Ilyenkov is widely considered to be the most important Soviet philosopher in the post-Stalin period. He is known largely for his original conception of the ideal, which he deployed against both idealist and crude materialist forms of reductionism, including official Soviet Diamat. This conception was articulated in its most developed form in ‘Dialectics of the Ideal’, which was written in the mid-1970s but prevented from publication in its complete form until thirty years after the author’s death. The translation before (...) you provides for the first time the complete, unabridged and unedited text of ‘Dialectics of the Ideal’ in English translation, including the author’s own subsequent comments on the text. (shrink)

The question of the identity of thought and being occupies an important place in the history of philosophy. Engels, addressing this question, wrote: "Is our thought capable of knowing the real world, can we in our ideas and concepts of the real world form a true reflection of reality? In philosophical language this question is called the question of the identity of thought and being. The vast majority of philosophers answer this question affirmatively.".

A traditional view of perception and action makestwo assumptions: that the causal flow betweenperception and action is primarily linear or one-way,and that they are merely instrumentally related toeach other, so that each is a means to the other.Either or both of these assumptions can be rejected. Behaviorism rejects the instrumental but not theone-way aspect of the traditional view, thus leavingitself open to charges of verificationism. Ecologicalviews reject the one-way aspect but not theinstrumental aspect of the traditional view, so thatperception and (...) action are seen as instrumentallyinterdependent. It is argued here that a betteralternative is to reject both assumptions, resultingin a two-level interdependence view in whichperception and action co-depend on dynamicallycircular subpersonal relations and as a result may bemore than merely instrumentally interdependent. Thisis illustrated by reference to motor theories ofperception and control theories of action. (shrink)