“Hoping for a big tent in which it is understood that disagreement is the price to be paid for exploring important ideas.”
The Procrustean Bed of Logic.—Since the bulk of the problem of logic is not in the process of deduction itself, but rather lies in the formalization of the problem that precedes deduction, almost any deductive framework will serve equally well. Whether we employ Aristotelian syllogisms, Stoic propositional logic, medieval terminist logic, or contemporary mathematical logic, is largely indifferent. While our modern logic is more advanced in virtue of having incorporated into itself the logical discoveries of the past twenty-five hundred years, it is not the be-all and end-all of logic. The formalization of a problem to the point at which it can be made to fit the Procrustean bed of logic is instead where we should seek the embodiment of human reason, but that would be formalization seemingly unmoored to logic, and that would deliver us over to a kind of rational vertigo—a disequilibrium of the reason, apparently without a handhold to steady ourselves. But not quite. We formalize a body of knowledge with an eye to how exactly it can be funneled into the strictures of logic, so our choice of logic for our deduction is not indifferent in this sense. The logic we employ governs the formalization we employ, so it is our choice of logic that ought to be attended by a rational vertigo, but here we have the spirit of seriousness to guide us, which, in the case of logic, is not the self-deception of ready-made values, but rather the self-deception of ready-made calculi. Given the calculus, our problem has been preemptively defined for us, as has its formalization; we have already surrendered our logical autonomy in our implied consent to the mode of formalization entailed by our chosen logic.
The Problem of Formalization.—The bulk of the problem of logic is not the process of deduction, but the formalization of the problem that precedes deduction. It is how the problem is set up for deduction rather than the deduction itself in which the art of logic lies. And here we must take the “art” of logic seriously, for that part of logic not yet reduced to mechanical derivation remains an art and not a science and cannot be mechanized in the manner of fully formalized proof procedures. How exactly we shoehorn ordinary thought into the strictures of logic so that anything at all can be derived is the real problem of logic, and this is the problem of formalization. This problem of formalization has many dimensions, all of which bear upon the result, but each of which can be taken up separately. How we break down the problem of formalization into discrete parts is itself a part of logic, or, rather, transcendental logic. Ancient axiomatics distinguished between axioms and postulates: axioms are common to all the sciences, while postulates were specific to a particular body of knowledge. We could still break down formalization in this way, but the distinction between axioms and postulates is now regarded as archaic. While the distinction remains valid, it passes over in silence specifying the choice of logic employed in derivation, unless we consider this a tacit function of the axioms. Twentieth century axiomatics distinguished between formation rules and transformation rules: formation rules govern what can be a well-formed formula (WFF), while transformation rules govern transforming one WFF into another WFF. This conceptualization has the virtue of making reasoning (transformation) explicit, but it does not explicitly thematize the elements that may be employed in a WFF (what we could call the ontology of a calculus), which is taken for granted, as the ancient conception took the univocity of reasoning for granted.
Historical Rigor.—In the early twentieth century, logical empiricism appeared to provide a template for the formalization of heretofore unformalized bodies of knowledge, by leaving undefined terms that can take any value within a generic logical calculus—i.e., hypothetico-deductivism. The undefined terms become receptacles for intuition, while the generic logical calculus embodies the formal structure through which the intuitions are related to each other. All concerted efforts at rigorous thought involve a tension between intuition and formalization, and so it must be with a rigorous formulation of history—there will be a tension between historical intuition and historical formalization. We seek a resolution to this epistemic tension by gravitating either toward intuition or formalization. As a consequence, there will be formulations that leave greater scope for intuition, and other formulations more closely bound by the formalism. That is to say, there will be a range of possible formalizations of historical knowledge, with each degree of formalization representing a distinct form of abstraction with a distinct utility in our thought. This logical empiricist method was not brought to bear upon history, but this missed opportunity of the past century is our opportunity today. When a rigorous science of history is at last available, historical sciences conceived to date in naive positivity (as Husserl called it) will be, for the first time, possible to express with formal precision.
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The Permanent Possibility of Formalization.—Even if most reasoning is not fully formalized, knowing that reasoning can be formalized, and reasoning within the parameters of the possibility of formalization, exercises a formal regulatory function over reason. There is much that can go wrong, however, if we adopt this attitude too casually. We may imagine that, as we extrapolate our reasoning into unfamiliar theoretical territory that we are all the time reasoning within the parameters of the possibility of formalization even as we incrementally depart from these parameters. Thus it becomes necessary to regularly recur to full formalization under the changed and changing conditions of our reasoning. It is not enough to clarify the foundations of reasoning a single time, and then to move on to further constructions on this foundation. One must return to the foundations time and again to see how they are bearing up under the superstructure that is being erected upon them.
A paper of mine has just appeared in the Journal of Big History special issue on complexity. This paper isn’t specifically about philosophy of history, but it does touch on some philosophical problems, so I will consider some of these problems in the context of philosophy of history. In particular, I will discuss definitions and the use of scientific measurement in the increasing formalization of knowledge and what this could portend for history.
Nielsen, J. N. (2024). A Complexity Ladder for Big History. Journal of Big History, VII(2); 1-8.
DOI | https://doi.org/10.22339/jbh.v7i2.7202
Paper: https://jbh.journals.villanova.edu/index.php/JBH/article/view/2976/2780
Quora: https://philosophyofhistory.quora.com/
Discord: https://discord.gg/r3dudQvGxD
Links: https://jnnielsen.carrd.co/
Newsletter: http://eepurl.com/dMh0_-/
Video: https://youtu.be/DzQcJtZ8zTc
Text post: https://geopolicraticus.substack.com/p/a-complexity-ladder-for-big-history