Dichotomous Knowledge

Dichotomous Knowledge

There is a long tradition of recognizing two distinct categories of knowledge: knowledge of logic, meaning, and mathematics, on the one hand, and knowledge of geography, history, and chemistry, on the other (these lists are not exhaustive). We might name these “A-type knowledge” and “B-type Knowledge”, so as to be neutral about the nature of the distinction. It is not obvious what the difference actually consists in. Looking for something more descriptive, philosophers have hit on a pair of Latin terms that seem vaguely evocative and have stuck, namely “a priori” and “a posteriori” (usually italicized to mark their somewhat esoteric meaning). If we try to dig into them, we do not return with conceptual gold: they translate as “prior” and “posterior”, as in “before” and “after”. The OED gives us “existing or coming before in time, order, or importance” and “coming after in time or order; later”, respectively. Before or after what, we ask. Not breakfast or lunch, presumably; no, before or after something called experience. That notion is not pellucid or theory-independent; it is usually specialized to sense experience, i.e., the five human senses. Here things start to get controversial; also, the reference to temporal order is questionable—does A-type knowledge always precede B-type knowledge in time? The original distinction is not so much clarified as immersed in definitional murkiness. Does this form of definition really capture what we intuitively recognize in the examples cited? Isn’t it more of a place-holder than a theory? Not surprisingly, other concepts have been invoked in order to hit off the distinction: experiential vs. non-experiential, analytic vs. synthetic, intuitive vs. observational, innate vs. acquired, abstract vs. concrete, causal vs. non-causal, rational vs. sensory. These all have their merits and demerits, which have been amply discussed; I think they are all lacking in one crucial respect—they don’t tell us about the internal structure of the two types of knowledge. They focus on the means of acquiring the types not their constitutive anatomy. They don’t say anything much, if anything, about the inner cognitive architecture of knowledge of A-type truths or B-type truths. They tell us about etiology but not about form—causation not constitution. We are trying to articulate epistemic natural kinds and to do that we have to look at the internal structure of the two types of knowledge. How do they operate, and what kind of structure permits that operation? To answer these questions is going to take some fresh thinking.[1]

B-type knowledge proceeds as follows: first, observations of particular states of affairs take place; then, inferences to generalizations are made. General knowledge is inductively inferred from perceptual knowledge of instances of the putative generalization. Singular instances precede general truths. The particular is anterior to the general: the former justifies the latter, while being itself justified by experience. That is the basic structure of what we call a posteriori knowledge. Notice that the singular premises are separate and distinct—one observation does not entail another. We may think of these as the atoms of this kind of knowledge, its ultimate constituents or building-blocks. B-type knowledge is thus atomistic and inductive (or abductive). I know that the Sun will rise tomorrow because I have seen it rise many times in the past, each of these a separate act of knowing. If we were to draw a diagram of this kind of knowledge, it would have an array of points on one side, corresponding to the totality of singular observations, and a bunch of arrows pointing right to the general truth thereby justified. The cognitive structure has this kind of shape and it operates by the depicted procedure; we might call it the singular-to-general structure, or the “sing-gen” structure. Experience is the medium in which this occurs, its enabling format. But A-type knowledge is not like that; in fact, it inverts this order of reasoning. Logic is the paradigm: we don’t know that modus ponens or the law of non-contradiction is logically true by inductive inference from individual instances; instead, we know the general principle directly and then deduce its instances. The order of justification is reversed. If we were to draw a diagram, it would have a general principle on the left with arrows pointing to individual instances on the right: it would have a general-to-singular structure, or a “gen-sing” structure. What we call reason or intellect is the medium in which this occurs. First, we know the generalization by what we call “intuition”, then we move deductively to its logical consequences. It is the same with mathematical and semantic knowledge: we don’t infer that every number has a successor from individual instances by induction, or that bachelors are unmarried by observing that similar propositions have always been true in the past (e.g., the proposition that spinsters are unmarried). We grasp a general principle and know it to be true, and then we deduce its particular instances. This implies that such knowledge has a holistic character in that the consequences are united by a general principle and are not known separately from each other. You can’t know that 4 has a successor but not know that 6 does, or that sisters are female without knowing that brothers are male (given that you have the concept). You know a general property of numbers and of meanings (that semantic containment generates analytic truths). The general is epistemically prior to the singular, whereas with B-type knowledge the singular is prior to the general. In addition, B-type knowledge takes the form of a bundle while A-type knowledge takes the form of a unified whole. The form of what we designate as a priori knowledge is aptly captured by a system of general axioms and theorems; but the form of a posteriori knowledge consists of a collection of singular instances linked inductively to a general proposition. The fundamental unit of empirical knowledge is the singular proposition, but the fundamental unit of a priori knowledge is the universal proposition. A-type knowledge is principle-based and holistic, while B-type knowledge is particular-based and atomistic. So-called a prioriknowledge is systematic and organized (“logical”); so-called a posteriori knowledge is fragmentary and haphazard, dependent upon the knower’s location and sensory acuity (“accidental”). We could say that the latter type of knowledge pertains to a totality of particular facts, while the former concerns a body of general principles. The two types of knowledge move in different “spaces”, proceeding by different methods. The cognitive apparatus is different in the two cases, differently structured.

The two types of knowledge are therefore opposites of each other. The faculties involved have contrasting forms. The process of knowledge formation accordingly varies in the two cases. It isn’t just that they have different types of causation—one is caused by experience and one isn’t—they have a different inner structure. The rest is extrinsic. Moreover, all varieties of the two types are unified in their structure: all a priori knowledge fits the “gen-sing” form and all a posteriori knowledge fits the “sing-gen” form. Thus, we can include metaphysics (and philosophy in general) and ethics in the category to which logic, mathematics, and semantics belong; and we can include knowledge of mind in the category to which geography and chemistry belong. For example, knowing the nature of identity belongs to the A-type category and so does knowing that cruelty is wrong; and my knowledge that I am in pain or that people have an unconscious belongs in the B-type category. There really are two large and distinct types of knowledge—two basic epistemic natural kinds. This is a philosophical discovery of the first importance. Trying to discredit is a fool’s errand. And it is an interestingdiscovery: we have two very different modes of knowing co-existing (and interacting) in our head—it’s surprising we have a single word (and concept) for both of them. Knowledge is deeply dichotomous. Some knowledge is constructed from separate pieces picked up by the senses—it is compositional, aggregative; but some knowledge is based on general principles that are recognized by the intellect and imply many (infinitely many) individual truths. They are polar opposites, yet both qualify as types of knowledge. Memory of particular facts is the hallmark of one, but not of the other (we don’t remember that 4 is even or that every number has a successor). Memory is atomistic and selective; reason is holistic and inclusive. If anything, we have underestimated the differences between the two types of knowledge, as if they only differ in their origins and not in their intrinsic character—innate versus acquired, derived from experience or the result of intuition, based on the senses or the intellect. But actually, they differ in their fundamental modus operandi and internal logic (induction or deduction, derivational structure). It’s not a matter of what comes first but of the deep nature of what comes.[2]

[1] I published my first paper on this subject nearly fifty years ago: “A Priori and A Posteriori Knowledge” (1976). I am still thinking about it.

[2] This paper is quite programmatic; a more thorough treatment would require looking in detail at specific areas of knowledge and teasing out the role of the singular and general within them. The kinship between the senses and the singular, on the one hand, and that between the ratiocinative and the universal, on the other, is however quite intuitive and traditional (see Plato). Just consider the contrast between the propositions of pure geometry and ascriptions of shape to particular objects. Generality is at the heart of the a priori, while the a posteriori has trouble escaping the bonds of the particular (witness the problem of induction).