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Review: R. M. Martin, Semiotics and Linguistic Structure. A Primer of Philosophic Logic

an object o, yields an understanding, called Val(p, t, i), of "what mental events, if actualized, would yield better apprehensions of o,, e.g., justifiable assertions about o," (p. 66). And a person "p is justified in asserting the existence of an objective domain o, when, on the basis of p's understanding Val(p, t, i), p can successfully construct increasingly sound, justifiable theory of o," (p. 84). Evidence and justification, then, ultimately rest with the internal or phenomenological character of observation and validation; it is so with empirical knowledge in physical theory, and it is so too with non-empirical knowledge in logic and mathematics. Contra Quine, Tragesser holds that logical principles are not ultimately confirmed by senseexperience (see the above and p. 110). With Quine, he holds that logical truths are not analytic, true by meaning, but rather true by virtue of the world (p. 111). But contra Quine, he holds that logic is not universal but equivocal. For, he argues, different theories about different domains of objects may call for different logics. In particular, he argues, the theory of extensive, geometric continua seems to call for a non-classical logic, drawing on Weyl and Brouwer; while the theory of the ego-independent physical world seems to call for a classical logic, drawing here on Frege and Husserl on ego-independent truths (pp. 93-106). Thus, a logical truth is true by virtue of the domain to which it applies. Drawing on Husserlian phenomenology and epistemology, Tragesser has characterized in an intelligent way an important approach to logical and mathematical knowledge, pursuing phenomenological foundations for the Platonistic tendencies of Godel and many others. He cites Husserl aptly throughout, and he draws frequent examples of logical or mathematical work from Frege, Church, Godel, Weierstrass, Weyl, and Brouwer as well as metalogical views from Quine, Tarski, Carnap, Hanson, and others. The writing is quite clear, non-technical, and generally easy to follow. Several parts would benefit, however, by being worked out in more detail. The details are not provided as to exactly how geometric continua require a non-classical logic and how physical theory needs a classical logic. Also, a reader might want more detailed formulations of a sample conception (describing the elements more precisely) and Val understanding (on which the author excuses himself from precise formulations of the key ingredients: p. 67). I close with a caution and an objection. Tragesser seems to mix "domains" of objects, posited as existing, with "possible worlds," in urging that logical truth cannot be truth "in all possible worlds" since different "worlds" or "domains" need different logics (p. 91). There may be a slip here, of which I would caution. Tragesser's view should be that the actual world harbors different domains with different logics; for the actual world should include all domains of actual entities, whether concrete or abstract, while possible worlds may include non-actual things. Behind such a slip might be a tendency, perhaps encouraged by some of Husserl's writings, to conflate phenomenology with epistemology, to take every experience as positing its object as somehow existing. But if there are objects of phantasy, they in no wise exist and are not experienced in phantasy as existing; still, they might have a logic, or so Meinong might have held. The objection concerns Tragesser's identifying his notion of Val with Husserl's notion of the "nucleus" of a noema (pp. 126-130), and the nucleus with the "A"', the item of sense presenting the object "in abstraction from all predicates" (p. 128). The nucleus is for Husserl the whole "sense" including the X plus predicate senses. The X is merely the sense of the presented object "itself," and is not the same as the complex understanding Val. The understanding of what would count as further apprehension of the same object should be placed in the background of the subject's consciousness.