Rolf George

Theory of science

VOLUME I: THEORY OF FUNDAMENTALS AND THEORY OF ELEMENTS (PART I) VOLUME TWO: THEORY OF ELEMENTS (PART II) VOLUME THREE: THEORY OF KNOWLEDGE AND THE ART OF DISCOVERY VOLUME FOUR: THEORY OF SCIENCE PROPER

Bolzano's consequence, relevance, and enthymemes

Historians of logic tend to view their task as the application of modern insights and symbolic techniques to old texts. Perhaps they do this on the assumption that what is good in these works must be an adumbration of what was recently done and is now well known. This holds, at any rate, for most discussions of Bolzano’s theory of logical consequence.’ In the present paper I shall reverse this procedure and comment on some problems and beliefs of contemporary logic from what I take to be Bolzano’s point of view. This will have the advantage of bringing out more forcefully than a straight exegesis what his view was and will also, I hope, put in doubt certain contemporary dogmas. I begin by applying his definition of consequence to propositional logic. Bolzano did not entertain this branch of logic, and to this extent my account is ahistorical. That it is, nonetheless, a straight extension of his theory is shown by the fact that all 23 theorems about consequence which he proves in his Theory of Science hold in this application.2 I then consider how C. I. Lewis’s so-called “independent proof” for A & --A F B fares in this system (it fails). After some comments on the proof, I show that in Bolzano-consequence premisses and conclusion share a subsentence (a necessary condition of relevance). There follows a discussion of enthymemes and a general procedure for generating the so-called “missing premiss”. At the end I sketch a taxonomy of consequence relations and briefly remark on earlier interpretations of Bolzano’s work. In using the first person plural (from now on) I mean to speak for those who think Bolzano’s approach sound, a group that includes at least Bolzano and myself.

Bolzano and the Problem of Psychologism

Husserl’s discussion of psychologism in his Logical Investigations led to a heated debate in German academic philosophy. While he, and earlier Frege, had been concerned only with psychologism in logic (and this variety will be my only concern in this essay), it was discovered that many other philosophical and humanist disciplines had been infected as well. It was found that there was metaphysical, ontological, epistemological, logical, ethical, aesthetic, sociological, religious, historical, mathematical, pedagogical and linguistic psychologism. Psychologisms were sub-classified into empiricist, a prioristic, sensualist, rationalist, critical, theological, evolutionary, pragmatist, transcendental. They could be old, new, false, genuine, objective, subjective, extreme or moderate, to cite from the lists in Martin Kusch’s excellent account of psychologism (1995, p. 108). In almost all cases it ranged from regrettable to abject. Philosophers accused each other of this transgression. It must have been satisfying to find residual psychologism even in those who explicitly denounced it. Even Husserl was fingered, and accused in turn of “logicism” by Wilhelm Wundt, which term here meant that Husserl intended to reduce psychology to logic, and turn it into a “psychology without psychology” (Wundt p. 580, cited from Kusch, 1995, p. 180.). The term “psychological logicism”, in contrast to “logical psychologism,” had come to refer to the practice, as old as philosophy itself, of beginning with the logical analysis of thought, and postulating mental faculties or functions, like understanding, reason etc., that would account for the various logical accomplishments and capacities (cf. Kreiser, p. 237).

A posts cript on fallacies

Bolzano is justly esteemed for his opposition to psychologism in logic. It is most fitting, therefore, that his defmition of consequence has enabled us to strike a blow at the residual psychologism that is found in the customary treatment on enthymemes.’ We shall now do the same for the so-called formal fallacies. Our discussion is a response to Gerald Massey’s claim that “fallacies . . . are perhaps of more interest to psychologists and psychiatrists than to logicians and philosophers.“* The outline of Massey’s argument is as follows: He holds that the “cardinal principle that undergirds the application of formal logic to natural languages” is that “arguments that instantiate valid argument forms are valid.“’ The naive account of formal fallacy supposes that demonstrations of invalidity proceed analogously, i.e., by showing that the argument in question instantiates an invalid form, a mistake “so common as virtually to escape notice.“4 This does not work, for, merely to point out that an argument is an instance, for example, of “asserting the consequent” will not establish its invalidity, since some arguments of that form are valid, e.g., ‘A 3 A, A != A’. To show invalidity, Massey holds, one needs to show not just that an argument is an instance of an invalid form, but that it fails to instance a valid form, a vastly more difficult undertaking which flounders on the “apparently unfinished state of contemporary logic . . . . For even if it could somehow be established that no translation of an argument into formal systems yields a valid argument form, how could one hope to prove the same result about all possible systems?“5 There is then no logical theory of fallacy. But, he thinks, one can still speak of fallacies in a different, namely a psychological, sense. Consider the following example:

Bolzano as Logician

Bernard Bolzano stands out with Frege as one of the great logicians of the nineteenth century. His approach to logic, set out in the Theory of Science of 1837, marks a fundamental reorientation of the subject on many fronts, one that is as radical as any in the history of the field. In sharp contrast to many of his contemporaries, Bolzano insisted upon a rigorous separation of logic from psychology. It should be possible, he thought, to characterize propositions, ideas, inferences, and the axiomatic organization of sciences without reference to a thinking subject. Consistently pursuing this approach to logic and methodology, Bolzano developed important accounts of formal semantics and formal axiomatics. A talented mathematician, Bolzano developed his logic in conjunction with his mathematical research. Among the first to work on the foundations of mathematics in the modern sense of the term, he made a number of key discoveries in analysis, topology, and set theory and had a significant influence on the development of mathematics in the nineteenth century. This chapter discusses Bolzanos logic along with some of his work in the foundations of mathematics that has some bearing on logic.

Review Essays: Snails Rolled Up Contrary to All Sense@@@The Philosophy of Right and Left: Incongruent Counterparts and the Nature of Space.

To The Argument Of 1768.- To The Arguments Of 1770 And 1783.- On The First Ground Of The Distinction Of Regions In Space (1768).- Selection From Section 15 Of Dissertation On The Form And Principles Of The Sensible And Intelligible World (1770).- Selection From The Prolegomena To Any Future Metaphysics (1783).- On Higher Space.- The Paradox Of Incongruous Counterparts.- Tractatus 6.36111.- Incongruent Counterparts And Absolute Space.- The Fourth Dimension.- The Ozma Problem And The Fall Of Parity.- The Difference Between Right And Left.- Kant Incongruous Counterparts, And The Nature Of Space And Space-Time.- Hands, Knees, And Absolute Space.- Incongruous Counterparts, Intrinsic Features, And The Substantiviality Of Space.- Incongruent Counterparts.- Showing And Telling: Can The Difference Between Right And Left Be Explained In Words?.- Right, Left, And The Fourth Dimension.- On the Other Hand...: A Reconsideration of Kant, Incongruent Counterparts, and Absolute Space.- Replies To Sklar And Earman.- Kant On Incongruent Counterparts.- The Role of Incongruent Counterparts in Kants Transcendental Idealism.- Incongruent Counterparts And Things In Themselves.- Contemporary Contributors.

Do the Poor Really Pay for the Higher Education of the Rich

In the last several years, ethicists have discussed problems of medical, professional, business and environmental ethics with much animation, and political philosophers have shown more interest than before in details of public policy. Yet this “applied turn,” as it has been called, has not swept much philosophical attention in the direction of taxation and public finance, though they offer numerous conceptual challenges. Nor have these subjects engaged the attention of those in the critical thinking business, though distortions in representing them are common enough.