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The Fully Generalized and Strengthened Logocentric Predicament
The attempt to formulate the foundations of logic is rendered arduous by a … “logocentric” predicament. In order to give an account of logic, we must presuppose and employ logic. (Sheffer, 1926: p. 228)
Logic is not a theory but a reflexion of the world. Logic is transcendental. (Wittgenstein, 1981: p. 169, prop. 6.13)
I. Prologue
The most fundamental problem in the philosophy of logic is what, in 1926, Harry M. Sheffer (inventor of the Sheffer stroke function) aptly called “the logocentric predicament,” as per the first epigraph of this essay, which I’ll reformulate as follows:
in order either to justify or explain logic, logic must be presupposed and used, hence logic is unjustifiable and inexplicable.
In fact, the logocentric predicament has several interestingly different specific sub-versions, including Lewis Carroll’s famous “What-the-Tortoise-Said-to-Achilles” syllogistic regress problem (Carroll, 1895), W.V.O. Quine’s equally famous argument against the conventionalist theory of logical truth (Quine, 1976), and the particularly interesting problem of justifying deduction (Dummett, 1973/1978; Haack, 1976), which I’ll reformulate as follows:
1. Logical deduction can be justified either deductively or non-deductively.
2. But on the one hand, a deductive justification of logical deduction is circular.
3. And on the other hand, a non-deductive justification of logical deduction—for example, an inductive, holistic, intuitive, pragmatic, etc., justification—is insufficient.
4. Therefore, logical deduction is unjustifiable.
In his pre-Tractarian 1913 “Notes on Logic,” thirteen years before Sheffer’s article and sixty years before Dummett’s and Haack’s articles, Ludwig Wittgenstein brilliantly and presciently recognized the logocentric predicament and its specific sub-problem of justifying deduction:
Deductions only proceed according to the laws of deduction but these laws cannot justify deduction. (Wittgenstein, 1979: p. 93e)
Indeed, the most illuminating way of construing Wittgenstein’s theory of the nature of logic in the Tractatus Logico-Philosophicus, is that it’s essentially an extended attempt to solve the logocentric predicament and also its specific sub-problem of justifying deduction, the pair of which can now, a century later, be understood as sub-species and sub-sub-species respectively, of what I’ll call the fully generalized and strengthened logocentric predicament.
But what, more precisely, is the fully generalized and strengthened logocentric predicament, and can it be adequately solved?
In the next section, I’ll answer both of those questions decisively and unequivocally, in nineteen short steps.
II. The Fully Generalized and Strengthened Logocentric Predicament, and Its Unique Adequate Solution
1. In order either to justify or explain logic, logic must be presupposed and used.
2. Therefore, every attempted justification or explanation of logic is circular.
3. Due to this circularity, logic is unjustifiable and inexplicable.
4. Now, step 3 is a variety of skepticism about logic.
5. Like step 3, every actual or possible variety of skepticism about logic whatsoever must be justified by arguments and supported by reasons.
6. But, every actual or possible justification whatsoever of any claim or theory by means of arguments and reasons, presupposes and uses logic.
7. Therefore, every actual or possible variety of skepticism about logic, including step 3, is self-refuting.
8. The classical thesis of logical psychologism says that logic can be
either (i) subjectively reduced to purely mentalistic facts about individual human mental states,
or (ii) materialistically reduced to purely physical facts,
or (iii) relativistically reduced to purely conventional and social facts about human communities,
or (iv) non-cognitively reduced to purely instrumental practical facts about humanity and its interests (Hanna, 2006a: ch. 1, 2008, 2015a).
9. But, every actual or possible attempted reduction of logic is an attempted reductive explanation of logic.
10. Now, every actual or possible explanation of anything whatsoever presupposes and uses logic.
11. Therefore, every actual or possible attempted reduction of logic presupposes and uses pre-reduced, un-reduced logic.
12. Therefore, every actual or possible attempted reduction of logic is self-refuting.
13. Therefore, logic is
(i) presupposed and used by every actual or possible justification or explanation whatsoever,
(ii) absolutely skepticism-resistant, and
(iii) mentalistically, materialistically, relativistically, and non-cognitively irreducible.
14. Steps 1-13 jointly constitute the fully generalized and strengthened logocentric predicament, which can also be briefly reformulated as follows:
there is no actual or possible theoretical or purely instrumental practical standpoint on logic that can be rationally external to logic itself, which is the same as to say that every actual or possible theoretical or purely instrumental practical standpoint on logic must be rationally internal to logic itself.
15. Because Analytic philosophy, whether classical (pre-1950) or post-classical (post-1950), is either platonistic or empiricistic, but in any case scientistic and logic-valorizing, it’s not only thoroughly ensnared by the fully generalized and strengthened logocentric predicament, but also self-refuted by it (Hanna, 2006a: esp. chs. 1 and 3, 2015b: esp. chs. 4 and 5, 2021a: esp. chs. I and XVI-XVII).
16. Because Postmodernist philosophy is either relativistic, skeptical, or both, but in any case anti-science and logic-hating, ironically enough just like Analytic philosophy, but in an equal and opposite way, it’s also not only thoroughly ensnared by the fully generalized and strengthened logocentric predicament, but also self-refuted by it (Hanna, 2006a: esp. chs. 1, 7, 2021a: esp. chs. I and XVI).
17. In fact, there is one and only one adequate solution to the fully generalized and strengthened logocentric predicament:
logic is nothing more and nothing less than a strictly a priori, universal, and non-instrumentally practical, innately-specified structure of the human capacity for theoretical and practical rationality, in the Ur-format of a proto-logic that’s presupposed and used in the construction of every other other logic whatsoever, every scientific or non-scientific theory whatsoever, every justification whatsoever, and every explanation whatsoever (Hanna, 2006a, 2006b, 2015b: esp. ch. 5).
18. This unique adequate solution to the fully generalized and strengthened logocentric predicament, in turn, is committed to the metaphysical and ontological thesis of weak transcendental idealism, which says that
(i) necessarily, the basic metaphysical and ontological structures of the manifestly real world conform to the basic innate structures of our rational human cognitive and practical capacities, especially including our sensible capacities for first-order consciousness, affect or emotion (including desire, feeling, and passion), sense-perception, memory, and imagination, and also our discursive capacities for conceptualization, thinking, self-consciousness, theoretical rationality, and practical rationality,
(ii) necessarily, if the manifestly real world exists, then if sensible, discursive, conscious, and self-conscious rational human cognizers were to exist, they would be able to cognize that world veridically to some salient extent, which in turn is fully consistent with sensible, discursive, conscious, and self-conscious rational human cognizers not actually existing at any given time, and
(iii) the existence of the manifestly real world necessitates the real possibility of sensible, discursive, conscious, and self-conscious rational human cognizers, but not their actual existence at any given time (Hanna, 2015b: section 7.3).
19. In short—and now in the format of a three-word slogan that approvingly and indeed wholeheartedly echoes Wittgenstein’s Tractatus, as per the second epigraph of this essay—the unique adequate solution of the fully generalized and strengthened logocentric predicament is that logic is transcendental.[i]
NOTE
[i] Of course, the logic-is-transcendental solution to the fully generalized and strengthened logocentric predicament is also broadly Kantian (Hanna, 2021b). In any case, I’m grateful to Evan Jack and Scott Heftler for thought-provoking conversations or correspendence on and around the topics of this essay.
REFERENCES
(Carroll, 1895). Carroll, L. “What the Tortoise Said to Achilles.” Mind 4: 278-280.
(Dummett, 1973/1978). Dummett, M. “The Justification of Deduction.” In M. Dummett, Truth and Other Enigmas. London: Duckworth. Pp. 290-318.
(Haack, 1976). Haack, S. “The Justification of Deduction.” Mind 85: 112-119.
(Hanna, 2006a). Hanna, R. Rationality and Logic. Cambridge: MIT Press. Available online in preview at URL = <https://www.academia.edu/21202624/Rationality_and_Logic>.
(Hanna, 2006b). Hanna, R. “Rationality and the Ethics of Logic.” Journal of Philosophy 103: 67-100. Available online in preview HERE.
(Hanna, 2008). ) “Husserl’s Arguments against Logical Psychologism: Prolegomena §§ 17-61.” In V. Mayer (ed.), Husserls Logische Untersuchungen. Munich: Akademie Verlag. Pp. 27-42. Also available online in preview HERE.
(Hanna, 2015a). Hanna, R. “Transcendental Normativity and the Avatars of Psychologism.” In A. Stati (ed.), Husserl’s Ideas I: New Commentaries and Interpretations Berlin: De Gruyter. Pp. 51-67. Also available online in preview HERE.
(Hanna, 2015b). Hanna, R. Cognition, Content, and the A Priori: A Study in the Philosophy of Mind and Knowledge . THE RATIONAL HUMAN CONDITION, Vol. 5. Oxford: Oxford Univ. Press. Available online in preview HERE.
(Hanna, 2021a). Hanna, R., The Fate of Analysis: Analytic Philosophy From Frege to The Ash-Heap of History. New York: Mad Duck Coalition. Affordably available in hardcover, softcover, and Epub at URL = <https://themadduckcoalition.org/product/the-fate-of-analysis/>.
(Hanna, 2021b). Hanna, R. “Jäsche Logic.” In J. Wuerth (ed.), Cambridge Kant Lexicon. Cambridge: Cambridge Univ. Press. Pp. 707-711. Also available online in preview HERE.
(Quine, 1976). Quine, W.V.O. “Truth by Convention.” In W.V.O. Quine, The Ways of Paradox. 2nd edn., Cambridge, MA: MIT Press. Pp. 77-106.
(Sheffer, 1926). Sheffer, H.M. “Review of Principia Mathematica, Volume I, second edition.” Isis 8: 226-231.
(Wittgenstein, 1979). Wittgenstein, L. “Notes on Logic.” In L. Wittgenstein, Notebooks 1914-1916. Trans. G.E.M. Anscombe. 2nd edn., Chicago, IL: Univ. of Chicago Press. Appendix I. Pp. 93-107.
(Wittgenstein, 1981). Wittgenstein, L. Tractatus Logico-Philosophicus. Trans. C.K. Ogden. London: Routledge & Kegan Paul.
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