But it is also true that the final question posed by Lukasiewicz in this regard—‘how are true functoral propositions possible?’—can never be answered by an abstract, formal logic, a logic without gnoseology. For to respond to this question requires discovery of the logical principle, or common root, that underlies both sorts of propositions: empirical and qualitative (since formal) propositions, which can be immediately confronted with the facts (such as the ‘premises’ and ‘conclusions’', the subject‑predicate constituents of the traditional Aristotelian syllogism), and functoral propositions, which do not immediately confront the facts. This in turn requires a truly general theory of logic, as free as possible of any tacitly accepted presuppositions, and therefore a logic‑gnoseology that tells us, for example, the meaning of ‘factuality’ and ‘fact’ as compared to ‘logicity’ and ‘reason’. And it so happens that the neo‑positivist formalist, because of the very coherence of his formalistic discourse, is compelled despite himself (like the formalist-dialectician Hegel) to resort to an actual use of the principle of noncontradiction quite different from and much more concrete than that theorized by him in terms of the ‘tautological’ or ‘contradictory’ character of mere molecular or analytic propositions. (Just as, again despite himself, Hegel actually used a determinate and therefore non‑contradictory dialectic quite different from his theoretical use of a pure tauto‑heterology or dialectical unity of ‘pure thoughts’, ‘considered in and for themselves’ apart from experience, with its necessity of distinction and lack of contradiction.) But to do this, of course, it is necessary to pose the logico-gnoseological problem of the relationship between thought and reality, which means the relationship between reason and matter, and not to disregard, for fear of metaphysics, this and other problems that are no longer, if indeed they ever were, the province of metaphysics. It is, in fact, difficult to deny that such problems properly belong to the domain of any philosophy worthy of the name: philosophy as a science which, through the most anti‑dogmatic method possible, seeks to eliminate and resolve the greatest possible number of presuppositions or otherwise unexplained facts and thus to arrive at the greatest possible unity of things.
It seems clear that the materialist critique of a priori reasoning is the method that can broach these problems with the greatest protection against dogmatism, whether logical‑metaphysical or logical-formalist, whether old or new. If only because any other ‘method’, whether idealist, neo‑scholastic, spiritualist, vulgar materialist, existentialist, or whatever, contains so many gratuitous presuppositions of its own that it is unable to confront with critical efficacy the presuppositions—admitted with the understanding that they do not impugn it, since they are of extra‑logical order, namely ontological, gnoseological, epistemological, etc.—of the highly compromised modern formal logic, or pure logic of science, that symbolic or mathematical logic claims to be. Even apart from the fact that the proclaimed neutrality of this logic with respect to extra‑logical questions facilitates the alliances forged by its followers not only with idealism and existentialism, but even with Catholic spiritualism (Bocheński, Boenher, etc.).
In actual fact, it is only in appearance that the followers of Carnap doubt and reject ‘logical’ problems, as in the case of the necessity of distinguishing the logical from the factual meaning of truth. This, as well as Preti’s excessively self‑evident transition from logic to epistemology as far as scientific laws are concerned, are symptoms of an internal philosophical torment that can be critically apprehended primarily, if not solely, by the modern materialist who acknowledges only scientific knowledge (physical and ‘moral’) and is therefore interested exclusively in the philosophical foundation of this knowledge, with no reservation whatever.
That is why only the materialist genuinely senses the limits of this pure logic of modern science and, while not lumping things together indiscriminately, and therefore while not confusing it with any of its crude predecessors, like Machism, objectively and critically denounces its philosophical insufficiencies.
SOURCE: Della Volpe, Galvano. Logic as a Positive Science, translated by Jon Rothschild (London: NLB, 1980), Appendix 3: On Logical Positivism, pp. 247-265; this excerpt pp. 263-265 (concluding paragraphs). (Original: Logica come scienza positiva, 1969.)
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