Facts and Incomplete Information

A modern notion of hard-nosed common sense is to appeal exclusively to positive facts. This is also a major basis of simplistic notions of empirical science. Serious scientific methodologies are more indirect, and quite a bit more involved.

From a broadly Kantian point of view that I think Plato and Aristotle would also endorse, all putative facts are really just assertions of facts, made by people. The validity of the corresponding assertions depends on the soundness of the reasons that lead us to believe them. Thus, regardless of whether our concern is ethical or scientific, it is always the quality of reasons that matters in assessing the validity of assertions.

The notion of a fair and objective weighing of evidence for or against an assertion presupposes that we symmetrically consider the pro and con, as Plato emphasized in his discussions of “dialectic”. But the simplistic bias for positive facts results in an inherently asymmetrical treatment any time we have to deal with incomplete information, because what putative facts we currently have in our possession is in part a matter of sheer chance.

In a fact-biased approach, if there happen to be insufficient facts in our possession to adequately support a hypothesis, the hypothesis is likely to be be dismissed out of hand as “speculation”, regardless of how inherently plausible it might otherwise be. We end up assuming something is not true merely because we cannot empirically prove it is true. This is independent of any other prejudice that may also enter into situations involving human judgment.

Once again, I want to recommend a prudent suspension or qualification of belief in cases of incomplete information, rather than active disbelief. (See also Debate on Prehistory.)

Three Logical Moments

The “Logic Defined & Divided” chapter of Hegel’s Encyclopedia Logic contains some brilliant, relatively popular aphorisms from his lectures, and provides a nice introduction to his views. Having recently treated with approval Kant’s denunciation of speculation in the usual sense, I’m turning to this now because among other riches, it contains Hegel’s recovery of an alternative, much more positive sense for “speculation”. As Aristotle would remind us, things are said in many ways, and it is wise to give heed to the differences.

Hegel says that every notion and truth involves three moments that are all essential and cannot really be separated from one another: Understanding, Dialectic, and Speculation.

In other places, Hegel frequently polemicizes against the narrowness and rigidity of mere Understanding. Here, he rounds out the picture, noting that “apart from Understanding there is no fixity or accuracy in the region of theory or of practice” and that knowledge begins “by apprehending existing objects in their specific differences”. He cites examples of how Understanding contributes to science, mathematics, law, practical life, art, religion, and philosophy.

Preparing the transition to dialectic, he notes “It is the fashion of youth to dash about in abstractions — but the man who has learnt to know life steers clear of the abstract ‘either-or’, and keeps to the concrete”. Dialectic for Hegel if viewed separately is the moment of “negative” Reason or criticism. He says that dialectic subordinated to Understanding’s mode of thought leads to skepticism, but dialectic freed from this subordination builds on distinctions developed by the Understanding, even while “the one-sidedness and limitation of the predicates of understanding is seen in its true light”. Dialectic studies things “in their own being and movement”. He goes on to expound Plato’s use of dialectic, and its difference from sophistry. (See also Contradiction vs Polarity; Aristotelian and Hegelian Dialectic.)

Speculation in Hegel’s special sense is the “positive” moment of Reason, which if considered separately begins from a kind of faith in reasonableness in the world. He implicitly connects it with a charitable reading of the long religious tradition of faith seeking understanding, construed in such a way as to be not incompatible with a charitable version of Enlightenment criticism. He notes that “the true reason-world, so far from being the exclusive property of philosophy, is the right of every human being [of] whatever grade of culture or mental growth”, adding that “experience first makes us aware of the reasonable order of things… by accepted and unreasoned belief”. Once this rational order becomes an object of thought rather than mere belief, we have speculative Reason proper.

Speculative Reason builds on both Understanding and dialectic. “A one-sided proposition… can never even give expression to a speculative truth.” He notes a connection between this and basic intuitive fairness. Starting from a simple faith in the reasonableness of the world and advancing through various stages of criticism, speculative Reason ultimately realizes substance as subject, and overcomes the dichotomy of subject and object.

Dialectic undid the abstract, atomistic, foundationalist, “either-or” tendencies of isolated Understanding. Speculative Reason in Hegel’s sense turns this into a new affirmation. In many places, Hegel talks about Reason or dialectic in ways that subsume both the dialectical and the speculative moment described here.

I read Hegelian speculative Reason — or dialectic incorporating the speculative moment — as just ordinary reason moving forward without the crutches of foundationalism and dogmatic claims of certainty. Reason without foundationalism is concerned with the very same open-ended work of interpretation I have attributed to Aristotle. Ultimately, Hegelian Reason is defeasible rational interpretation of experience, optimistically doing the best we can with the resources we have, and always on the lookout for something better. Thus, it too can be reconciled with Kantian discipline. (See also “Absolute” Knowledge?)

Likely Stories

Plato had his characters engage in a good deal of speculation, but generally was very conscientious about explicitly identifying it as such. Larger speculations are often explicitly couched as myth or poetic invention. All such things are explicitly considered no more than “likely stories”. On a smaller scale, verbal cues generally abound to tell us when things are intended in a more tentative way.

Plato and Aristotle were generally — each in their own way — extraordinarily good at this sort of thing. However, the much more “dogmatic” style of the Stoic school set a new default tone for the later tradition, all the way to the time of Kant. It became standard to present what was actually speculation as if it were a simple report on the truth, or a certainty grounded in a strong kind of knowledge. (See also The Epistemic Modesty of Plato and Aristotle; Kantian Discipline.)

Kantian Discipline

The Discipline of Pure Reason chapter in Kant’s Critique of Pure Reason makes a number of important points, using the relation between reason and intuition introduced in the Transcendental Analytic. It ends up effectively advocating a form of discursive reasoning as essential to a Critical approach.

If we take a simple empirical concept like gold, no amount of analysis will tell us anything new about it, but he says we can take the matter of the corresponding perceptual intuition and initiate new perceptions of it that may tell us something new.

If we take a mathematical concept like a triangle, we can use it to rigorously construct an object in pure intuition, so that the object is nothing but our construction, with no other aspect.

However, he says, if we take a “transcendental” concept of a reality, substance, force, etc., it refers neither to an empirical nor to a pure intuition, but rather to a synthesis of empirical intuitions that is not itself an empirical intuition, and cannot be used to generate a pure intuition. This is related to Kant’s rejection of “intellectual” intuition. We are constantly tempted to act as if our preconscious syntheses of such abstractions referred to objects in the way that empirical and mathematical concepts do, each in their own way, but according to Kant’s analysis, they do not, because they are neither perceptual nor rigorously constructive.

All questions of what are in effect higher-order expressive classifications of syntheses of empirical intuitions belong to “rational cognition from concepts, which is called philosophical” (Cambridge edition, p.636, emphasis in original). This is again related to his rejection of the apparent simplicity and actual arbitrariness of intellectual intuition and its analogues like supposedly self-evident truth. It opens into the territory I have been calling semantic, and associating with a work of open-ended interpretation. (See also Discursive; Copernican; Dogmatism and Strife; Things In Themselves.)

I am more optimistic than Kant that something valuable — indeed priceless — can come from this sort of open-ended work of interpretation. Its open-endedness means no achieved result is ever beyond question, but I think we implicitly engage in this sort of “philosophical” interpretation every day of our lives, and have no choice in the matter. I also think serious ethical deliberation necessarily makes use of such interpretation, and again we have no choice in the matter. So, pragmatically speaking, defeasible interpretation is indispensable.

Kant goes on to polemicize against attempts to import a mathematical style of reasoning into philosophy, like Spinoza tried to do. Spinoza’s large-scale experiment with this in the Ethics I find fascinating, but ultimately artificial. It does make the inferential structure of his argument more explicit, and Pierre Macherey used this to great advantage in his five-volume French commentary on the Ethics. But there is a big difference between a pure mathematical construction — which can be interpreted without remainder by something like formal structural-operational semantics in the theory of programming languages, and so requires no defeasible interpretation of the sort mentioned above, on the one hand — and work involving concepts that can only be fully explicated by that sort of interpretation, on the other. Big parts of life — and all philosophy — are of the latter sort. So it seems Kant is ultimately right on this.

Kant points out that definition only has precise meaning in mathematics, and prefers to use a different word in other contexts. I make similar well-intentioned but admittedly opinionated recommendations about vocabulary, but what is most important is the conceptual difference. As long as we are clear about that, we can use the same word in more than one sense. As Aristotle would remind us, multiple senses of words are an inescapable feature of natural language.

Kant says that unlike the case of mathematics, in philosophy we should not put definitions first, except perhaps as a mere experiment. Again, he probably has Spinoza in mind, and again — personal fondness for Spinoza notwithstanding — I have to agree. (Macherey in his reading of Spinoza actually often goes in the reverse direction, interpreting the meaning of each part in terms of what it is used to “prove”, but the order of Spinoza’s own presentation most obviously suggests the kind of thing to which Kant is properly objecting.) More than anything else, meanings are what we seek in philosophical inquiry, so they cannot be just given at the start. We can certainly discuss or dialectically analyze stipulated meanings, but that is strictly secondary and subordinate to a larger interpretive work.

Following conventional practice, Kant allows for axioms in mathematics, but says they have no place in philosophy. He has in mind the older notion of axioms as supposedly self-evident truths. Contemporary mathematics has vastly multiplied alternative systems, and effectively treats axioms like stipulative definitions instead. If we have in mind axioms as self-evident truths, Kant’s point holds. If we have in mind axioms as stipulative definitions, then his point about stipulative definitions in philosophy applies to axioms as well.

A similar pattern holds for demonstration or proof. Mathematics for Kant always has to do with strict constructions, which do not apply in philosophy, where there is always matter for interpretation. (From the later 19th century, mathematicians began increasingly to invent theories that seemed to require nonconstructive assumptions — transfinite numbers, standard set theories, and so on. This is currently in flux again. Contrary to what was thought at an earlier time, it now appears that all valid “classical” mathematics, including transfinite numbers, can be expressed in a higher-order constructive formalism. Arguments are still raging about which style is better, but I am sympathetic to the constructive side.) Philosophical arguments are informally reasoned interpretations, not proofs.

Kant says that speculative thought in general, because it does not abide by these guidelines, unfortunately ends up full of what he does not hesitate to call dishonesty and hypocrisy. (When I occasionally ascribe honesty or dishonesty to a philosopher, it is with similar criteria in mind — especially the presence or absence of frank identification of speculation as such when it occurs. See also Likely Stories.)

The kind of philosophy I am recommending is concerned with explication of meanings, not a supposed generation of truths, so it is not speculative in Kant’s sense. What may not be obvious is just how large and vital the field of this sort of interpretation really is in life. The most common and compact form by which such interpretations are expressed in the small looks syntactically like ordinary assertion, and in ordinary social interaction, mistaking one for the other has little effect on communication. When the focus is not on practical communication but on improving our understanding, we have to step back and look at the larger context, in order to tell what is a speculative assertion and what is an interpretation expressed in the form of assertion. (See also Pure Reason, Metaphysics?; Three Logical Moments.)

(In the present endeavor, the great majority of what look like simple assertions are actually compact expressions of interpretations!)