Demonstrative “Science”?

The “historiographical” notes on the history of philosophy I offer here from time to time are a sort of compromise. For much of my life, I’ve been very concerned with the fine grain of such history, and with casting a broad net encompassing many historical figures. Here, I made a strategic decision to focus instead on a mere handful of philosophers I consider most important.

Discussion of actualization in Hegel led to actualization in Aristotle, which led me to indulge my fascination with the Aristotelian commentary tradition. To the extent that it is possible to generalize about the historic readings discussed in the Greek, Arabic, Hebrew, and Latin commentaries, my own view of Aristotle is quite different on a number of key points, having more in common with some modern readings. Nonetheless, I am enormously impressed by the levels of sophistication shown by very many writers in this tradition.

I just mentioned al-Farabi again. As previously noted, al-Farabi (10th century CE) played a great historic role in the formulation of Arabic (and consequently, Hebrew and Latin) views of Aristotle. The Syrian Christians who did the majority of the translating of Aristotle to Arabic from Syriac had access to most of Aristotle’s works, but publicly only taught from the logical treatises. It was al-Farabi who initiated public teaching of the full range of Aristotelian philosophy in the Islamic world. He flourished during the so-called Islamic golden age, a time of tremendous interest in ancient learning not only by aristocrats but by many literate skilled crafts people. The political climate of the Islamic world at the time was much more embracing of secular learning than it came to be between the 13th and 19th centuries CE.

One unfortunate aspect of al-Farabi’s reading was a very strong privileging of a notion of demonstrative “science” over Aristotle’s own predominant use of dialectic in philosophical development. This was based on a reading of Aristotle’s Posterior Analytics as propounding a model of “science” as a deductive enterprise expected to result in certain knowledge, which is still dominant today, but which I (following a number of modern interpreters) think involves a misreading of the basic aims of Aristotelian demonstration.

The idea that Aristotle was fundamentally concerned to develop “sciences” yielding certain knowledge gave a more dogmatic cast to his whole work, which has been a contributing factor in common negative stereotypes of Aristotle. Many modern commentators who still accept this reading of Posterior Analytics have been puzzled by the huge gap between this and Aristotle’s actual practice throughout his works, which in fact is mainly dialectical. I think a careful reading of the Topics (on dialectic) and Posterior Analytics (on demonstration) with consultation of the Greek text on the originals of some key phrases yields a view that is far more consistent with Aristotle’s actual practice.

Demonstration is a pedagogical way of showing very clear reasons for certain kinds of conclusions. It works by assuming some premises are true, whereas dialectic makes no such assumption. Thus the only necessity that results from demonstration is the “hypothetical” one that if the premises are true, then the conclusion is also true. But the more important point in regard to the classic syllogistic form is that the common “middle term” that allows the major and minor premises to be both formally and materially composed together illuminates why we ought to consider it appropriate to assume the conclusion is true if we believe the premises are true.

Dialectic, as I have said, is cumulative, exploratory discursive reasoning about meanings in the absence of initial certainty. This is how Aristotle mainly approaches things. Dialectic implicitly relies on the same logical form of syllogistic argument explicitly used in demonstration, but Aristotle distinguishes dialectic and demonstration by whether premises are treated as hypotheses to be evaluated, or as hypothetically assumed “truths” to be interpreted.

It is also important to note that in the Latin scholastic tradition, the dogmatic trend resulting from wide acceptance of claims about demonstrative science was significantly mitigated by a strong counter-trend of evenhandedly analyzing arguments pro and con, which effectively revived a form of dialectic. (See also Foundations?; Fortunes of Aristotle; Scholastic Dialectic.)

Openness of Reason

In life, we most often do not really know what we are doing, but still, most of the time we find our way. This involves many small “leaps”, or actions on based on assumptions that we don’t actually know are true. These are unavoidable, they are “reasonable”, and most of the time they are harmless.

In forming views of the world, we need the maturity to distrust systematic unity or strong coherence as a supposed accomplishment, while still pursuing it as a goal. (See also One, Many; Unity of Apperception; Error; Foundations?; Interpretation.)

If we have a concept of Reason as something well distinguished but still fundamentally open in the last instance — which I find especially clear and well developed in Aristotle, Brandom, and Ricoeur — then we have no need ever for Kierkegaardian irrational “great leaps” or arbitrary founding decisions in the style of Badiou.


The last post suggests another nuance, having to do with how “total” and “totality” are said in many ways. This is particularly sensitive, because these terms have both genuinely innocent senses and other apparently innocent senses that turn out to implicitly induce evil in the form of a metaphorically “totalitarian” attitude.

Aiming for completeness as a goal is often a good thing.

There is a spectrum of relatively benign errors of over-optimism with respect to where we are in achieving such goals, which at one end begins to shade into a less innocent over-reach, and eventually into claims that are obviously arrogant, or even “totalitarian”.

Actual achievements of completeness are always limited in scope. They are also often somewhat fragile.

I’ll mention the following case mainly for its metaphorical value. Mathematical concepts of completeness are always in some sense domain-specific, and precisely defined. In particular, it is possible to design systems of domain-specific classification that are complete with respect to current “knowledge” or some definite body of such “knowledge”, where knowledge is taken not in a strong philosophical sense, but in some practical sense adequate for certain “real world” operations. The key to using this kind of mathematically complete classification in the real world is including a fallback case for anything that does not fit within the current scheme. Then optionally, the scheme itself can be updated. In less formal contexts, similar strategies can be applied.

There are also limited-scope, somewhat fragile practical achievements of completeness that are neither mathematical nor particularly ethical.

When it comes to ethics, completeness or totality is only something for which we should strive in certain contexts. About this we should be modest and careful.

Different yet again is the arguably trivial “totality” of preconceived wholes like individuals and societies. This is in a way opposite to the mathematical case, which worked by precise definition; here, any definition is implicitly suspended in favor of an assumed reference.

Another kind of implicit whole is a judgment resulting from deliberation. At some point, response to the world dictates that we cut short our in principle indefinitely extensible deliberations, and make a practical judgment call.


Ethical reason can potentially comprehend anything and it can influence things going forward, but it does not make everything or govern events. (See also Fragility of the Good.) Understanding comes late. Reason becomes free or autonomous only by a long, slow process. (See also Iterative Questioning.) Even so-called absolute knowledge — only “absolute” because it is free of the actually self-disruptive presumptions of the false freedom of Mastery — is just this freedom of reason.

There is after all a kind of negative freedom of reason at work here, but it is forever incomplete, and also has nothing to do with any negative freedom of a power, which is a fiction. We negatively free ourselves of unthinking assumptions while positively increasing our ability to make fine distinctions, our sensitivity to subtlety and nuance. This gives us new positive freedom in doing, with our still-finite power. (See also Ethical Reason, Interpretation.)


No one gets through life without making countless assumptions about things we cannot properly know. In routine cases, this is usually harmless. That does not remove our obligation to give someone a fair hearing if they initiate dialogue asking about our reasons for feeling committed to the assumption. Except in immediate emergencies, we should always be open to such questions, and on our own initiative we should raise such questions to ourselves in ambiguous situations. This means we also need to learn to be good at recognizing ambiguous situations, which involves lifelong care and active practice at doing it. (See also Epistemic Conscientiousness.)