By Robert Hanna
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The Axiocentric Predicament, And What To Do About It
According to the classical hard problem in philosophical logic known as the logocentric predicament, as formulated in 1926 by Harry Sheffer,
[i]n order to give an account of logic, we must presuppose and employ logic. (Sheffer, 1926: p. 228)
It follows directly from the logocentric predicament that any attempt to explain or justify logic must presuppose and use logic.
So, due to that inherent circularity, apparently or prima facie, logic is inexplicable and unjustifiable.
But, exactly analogously to the logocentric predicament, there’s also another hard problem that I’ll call the axiocentric predicament.
I’ve created the neologism “axiocentric” by using the Greek root axios, meaning “worthy,” which is also the root of the term “axiology,” meaning of course “the theory of value.”
The axiocentric predicament focuses on normativity.
By normativity, I mean the following irreducible two-part fact (i) that all rational human animals or real persons have aims, commitments, ends, goals, ideals, and values, aka norms, and (ii) that these rational human animals naturally treat their aims, commitments, ends, goals, ideals, and values — or norms, (iia) as rules or principles for guiding theoretical inquiry, especially including explanation, and also for guiding practical enterprises, especially including deliberation and choice, (iib) as reasons for justifying beliefs and intentional actions, and also (iic) as standards for critical evaluation and judgment.
Furthermore, normativity in this sense can be either (i) instrumental, that is, conditional, hypothetical, desired for the sake of some further desired end, pragmatic, prudential, or consequence-based, or (ii) non-instrumental, that is, unconditional, non-hypothetical, desired for its own sake as an end-in-itself, non-pragmatic, non-prudential, and obtaining no-matter-what-the-consequences.
Here, then, is the axiocentric predicament: in order to evaluate, explain, or justify any kind of normativity, normativity must be presupposed and used: for obviously, evaluation, explanation, and justification are, paradigmatically, normative activities.
So, due to that inherent circularity, apparently or prima facie, normativity is unevaluable, inexplicable, and unjustifiable.
And it gets even worse (or actually, even better) than that.
For it’s demonstrable that there exists a categorical normativity or a highest value.
By “a categorical normativity” or “a highest value” I mean a value that’s a transfinite cardinal quantity in relation to all denumerable or countable, economic, or otherwise instrumental kinds of value, for example psychological pleasure or preference-satisfaction.
It seems clear that however we measure such things, whether in terms of market value or monetary price, degrees of psychological pleasure, degrees of preference-satisfaction, degrees of betting behavior, etc., or comparative rankings of such things, nevertheless every actual or possible economic or otherwise instrumental value is expressible as some rational number quantity or another, including denumerably infinite rational number quantities.
Then, by essentially the same method that Georg Cantor used to show the existence of transfinite numbers (Cantor, 1891, 2019), at least in principle, we can create a vertical and denumerably infinite list of every actual or possible economic or otherwise instrumental value, then draw a diagonal across it, and discover another value that’s essentially higher than any economic or otherwise instrumental value.
Or, equivalently, we can take the complete denumerably infinite set of every actual or possible economic or otherwise instrumental value, then form its power set (i.e., the set of all its subsets), and thereby find a transfinite value quantity that’s essentially higher than any economic or otherwise instrumental value.
So this transfinite value quantity is the prime example of what — following Cantor’s alternative term for transfinite numbers, transcendental numbers — I’ve called transcendental normativity (Hanna, 2015a).
Correspondingly, it’s what I’ll call transcendental value, by which I mean either a single transcendental value or else a unified system of several distinct but essentially complementary or interlocking transcendental values.
Kant called the unified system of all transcendental values the highest good (Kant, 1996: pp. 228–236, Ak 5: 110–119), and for the purposes of this essay, I will too.
Then, what I’ll call the supercharged axiocentric predicament says this: in order to evaluate, explain, or justify any kind of normativity, the highest good must be presupposed and used; so, due to that inherent circularity, apparently or prima facie, the highest good itself is unevaluable, inexplicable, and unjustifiable.
The supercharged axiocentric predicament, in turn, is closely related to G.E. Moore’s famous argument in Principia Ethica against the naturalistic fallacy —i.e., the failed reduction of “ought” to “is,” which is David Hume’s version (Hume, 1978: pp. 469–470, book I, part I, section I), or equivalently, in Moore’s own formulation, the failed analytic reduction of The Good to any fact or property that’s purely natural — the open question argument:
[T]he naturalistic fallacy … [is] the fallacy which consists in identifying the simple notion which we mean by “good” with some other notion. (Moore, 1903: p. 58)
[The naturalistic] fallacy, I explained, consists in the contention that good means nothing but some simple or complex notion, that can defined in terms of natural qualities. (Moore, 1903: p. 73)
The hypothesis that disagreement about the meaning of good is disagreement with regard to the correct analysis of a given whole, may be most plainly seen to be incorrect by consideration of the fact that, whatever definition be offered, it may always be asked, with significance, of the complex so defined, whether it is itself good. (Moore, 1903: p. 15)
We must not, therefore, be frightened by the assertion that a thing is natural into the admission that it is good: good does not, by definition, mean anything that is natural; and it is always an open question whether what is natural is good. (Moore, 1903: p. 44)
Rationally reconstructed for my purposes here, Moore’s open question argument is as follows:
1. Consider any reductive analysis of the form: “The Good is identical to the natural fact or property XYZ.”
2. For any such reductive analysis, it can always be self-consistently and intelligibly asked: But is XYZ itself good, or not?, hence XYZ is possibly not good, and therefore XYZ cannot be identical to The Good.
3. Therefore, The Good is an irreducible, primitive, and unanalyzable fact or property, and it’s always viciously circular and self-undermining to attempt to give a reductive analysis of it.
Now, it’s well known that there are some important problems in Moore’s own formulation of the open question argument, so in my 2018 book, Kantian Ethics and Human Existence (Hanna, 2018b: section 1.5), and more recently in a companion-piece to this essay (Hanna, 2022b), I’ve worked out a cleaned-up and explicitly modal metaphysical version of Moore’s argument, as the failure of any and all attempts to show the logical or nomological strong supervenience of The Good on some or another natural supervenience base.
In any case, again for my purposes here, we can identify Moore’s fact or property of The Good with what I’ve been calling “the highest good,” and thereby recognize that Moore was at least implicitly aware of the supercharged axiocentric predicament.
Moreover, there’s at least one other logically distinct argument for the existence of the highest good — indeed, this one is an argument-by-cases, hence it doesn’t have maximum rational demonstrative force, even though it’s fairly compelling and philosophically quite illuminating — from the standard exposition of any normative ethical or moral theory.
So, for example, how does one give the standard exposition of utilitarianism?
Utilitarianism says that the highest good is happiness, hence we all ought to choose and act in such a way as always to bring about as much happiness as possible for as many people as possible.
Or, the standard exposition of hedonism?
Hedonism says that the highest good is pleasurable experiences, so we all ought to choose and act in such a way as always to experience as much pleasure as humanly possible.
Or, the standard exposition of egoism?
Egoism says that the highest good is the pursuit and satisfaction of individual self-interest, hence we all ought to choose and act in such a way as always to pursue and satisfy our individual self-interest.
And so-on, through all the actual and possible normative ethical or moral theories — although of course, precisely how one is able to close the set of all such cases, is an inherent challenge for any argument-by-cases, which I won’t attempt for the purposes of this essay.
Nevertheless, assuming that such a closure is somehow really possible, then we can conclude that the highest good is also presupposed and used in the standard exposition of every normative ethical or moral theory.
So, for all those reasons, the supercharged axiocentric predicament stands.
Now, supposing all that to be the case, then what is to be done?
In my 2006 book Rationality and Logic, in an article from the same year called “Rationality and the Ethics of Logic,” and in my 2015 book, Cognition, Content, and the A Priori, I argued that every actual and possible logic is cognitively constructed by rational (human) animals, and that logic itself is the set of categorically normative, innately specified first principles of human theoretical rationality — a universal a priori minimally non-contradictory proto-logic — when taken together with all the supplementary humanly-constructed ceteris paribus principles of an open-ended plurality of logical systems, just as morality is the set of categorically normative, innately specified first principles of human practical rationality — a universal a priori dignitarian proto-morality — when taken together with all the supplementary humanly-constructed ceteris paribus principles of an open-ended plurality of moral systems (Hanna, 2006a, 2006b, 2015b: ch. 5).
Let’s call this the morality-of-logic thesis.
So, using the morality-of-logic thesis, my proposed way out of the logocentric predicament is to postulate the existence of an innately-specified universal a priori proto-logic in all rational human animals — featuring the strictly universal and a priori minimal principle of non-contradiction (see also Putnam, 1983) — that we presuppose and use in order to construct any actual or possible logic, by using various different axioms, operators, inference-rules, and so-on.
Or in short, and more colloquially put, I’ve proposed that the way out of the logocentric predicament is to recognize that the inherent circularity of logic, which apparently or prima facie presents us with a hard problem about the nature of logic, is in reality nothing more and nothing less than a rationally benign and rationally enlightening circularity, since it simply shows us precisely how logic is built into the rational human condition from the get-go.
And, again in view of the morality-of-logic thesis, which postulates an exact analogy between the nature of logic and the nature of morality, then we can find a rational segue to an exactly analogous way out of the axiocentric predicament and the supercharged axiocentric predicament alike.
More precisely, I want to postulate the existence of an innately specified universal a priori proto-morality, featuring a capacity for essentially non-conceptual awareness of the highest good, and also a further capacity for generating the higher-order desire for moral self-transcendence — i.e., the higher-order desire to be moved by all and only first-order desires that are non-utilitarian, non-hedonistic, non-egoistic, etc. (see Hanna, 2018a: ch. 3, 2021a) — which is inherently guided by and for the sake of the highest good, that we presuppose and use in order to construct every actual and possible normative ethical or moral theory, by using various different, and perhaps culturally and historically specific, axiomatic assumptions about human nature and what should count as the highest good, and so-on (see Hanna, 2018b: ch. 2).
Moreover, and perhaps most importantly, direct evidence for the existence of this essentially non-conceptual awareness of the highest good, and for the existence of the higher-order desire for moral self-transcendence, which is inherently guided by and for the sake of the highest good, is to be found in (i) the experience of the moral emotion of respect for human dignity (Hanna, 2021a, 2021b), (ii) existential-spiritual experience, including religious experience (Hanna, 2018c: part 1), and (iii) the phenomenological aesthetics of the sublime, as directed to what I call the the proto-dignity of the natural cosmos (Hanna, 2022: section 4.5).
So in other and more colloquial words, I’m proposing that the way out of the axiocentric and supercharged axiocentric predicaments alike is to recognize that the inherent circularities of normativity and of the highest good, which apparently or prima facie present us with respectively hard and superhard problems about the nature of normativity, are, just like the inherent circularity of logic, nothing more and nothing less than rationally benign and rationally enlightening circularities, since they simply show us precisely how, just like logic, normativity and the highest good are built into the rational human condition from the get-go.
Moreover, it follows directly from this way out of the axiocentric predicament, that the all-too-familiar naturalistic thesis that normativity can be explained in terms of essentially non-normative — for example, purely material, physical or otherwise natural — facts or properties, is not only false but also viciously circular and self-undermining.
For if normativity and the highest good are inherent in human rationality itself, then it’s clearly self-stultifying to assert, as rational human animals inherently capable of asserting or denying such things, that we can somehow take up an explanatory standpoint outside normativity in order to explain it in terms of something else.[i]
[i] I’m grateful to Scott Heftler for thought-provoking conversations on and around the topics of this essay.
(Cantor, 1891). Cantor, G. “Ueber eine elementare Frage der Mannigfaltigkeitslehre.” Jahresbericht der Deutschen Mathematiker-Vereinigung 1: 75–78.
(Cantor, 2019). Cantor, G. “A Translation of G. Cantor’s ‘Ueber eine elementare Frage der Mannigfaltigkeitslehre’.” Trans. P.P. Jones et al. 23 August. Available online at URL = <https://www.researchgate.net/publication/335364685_A_Translation_of_G_Cantor%27s_Ueber_eine_elementare_Frage_der_Mannigfaltigkeitslehre>.
(Hanna, 2006a). Hanna, R. Rationality and Logic. Cambridge: MIT Press. Also available online in preview HERE.
(Hanna, 2006b). Hanna, R. “Rationality and the Ethics of Logic.” Journal of Philosophy 103: 67–100. 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. Also available online in preview HERE.
(Hanna, 2018a). Hanna, R. Deep Freedom and Real Persons: A Study in Metaphysics. THE RATIONAL HUMAN CONDITION, Vol. 2. New York: Nova Science. Also available online in preview HERE.
(Hanna, 2018b). Hanna, R. Kantian Ethics and Human Existence. THE RATIONAL HUMAN CONDITION, Vol. 3. New York: Nova Science. Also available online in preview HERE.
(Hanna, 2018c). Hanna, R., Kant, Agnosticism, and Anarchism: A Theological-Political Treatise. THE RATIONAL HUMAN CONDITION, Vol. 4. New York: Nova Science. Also available online in preview HERE.
(Hanna, 2021a). Hanna, R. “Sensibility First: How to Interpret Kant’s Theoretical and Practical Philosophy.” Estudos Kantianos 9: 97–120. Available online at URL = <https://revistas.marilia.unesp.br/index.php/ek/article/view/12288>.
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(Hanna, 2022a). Hanna, R. The Philosophy of the Future: Uniscience and the Modern World. Unpublished MS. Available online at URL = <https://www.academia.edu/62653411/THE_PHILOSOPHY_OF_THE_FUTURE_Uniscience_and_the_Modern_World_2022_version_>.
(Hanna, 2022b). Hanna, R. “G.E. Moore’s Open Question Argument Against The Naturalistic Fallacy Revised, Updated, and Redefended.” Unpublished MS. Available online at URL = <https://www.academia.edu/74336725/G_E_Moores_Open_Question_Argument_Against_The_Naturalistic_Fallacy_Revised_Updated_and_Redefended_March_2022_version_>.
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(Moore, 1903). Moore, G.E. Principia Ethica. Cambridge: Cambridge Univ. Press.
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