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Logical and Spiritual REFLECTIONS

Book 3. In Defense of Aristotle’s Laws of Thought

Chapter 19. The status of conceptions

The concept of some thing(s), call it X, is the sum total of all observations, beliefs, thoughts, inductively or deductively proven items of knowledge, opinions, imaginations, we (as individuals or collectively) have accumulated across time relative to the thing(s) concerned – call these cognitive events or intentions: A, B, C, D, etc. Note well that the tag “X” refers to the objects X, intended by the concept of X, not to the mental apparatus or idea through which we know or think we know those objects.

Although we colloquially say that X “contains” A, B, C, D…, a concept is not to be thought of as a vessel containing a number of relevant mental entities, like a basket containing apples and oranges. It is best thought of as a collection of arrows pointing to various perceived phenomena, objects of intuitions, and related abstractions, which all together influence our overall idea of X. Our concept of X (an individual or kind) is our collection of beliefs about it.

The concept of X should not be thought of as equal specifically to its definition (as Kantians do), and still less to the name “X” (as Nominalists do). The name is just a physical or at least mental tag or label, allowing us to more easily focus on the concept, or more precisely on its contents (i.e. the objects intended by it). As for the definition, it is not the whole of X, but consists of some exclusive and universal characteristic(s) of X (say, A) among others (viz. B, C, D, etc., which may also be distinctive and always present, or not). One aspect is selected as defining, because it is helpful for complex thinking processes to do so. Definition is thus something both empirical and rational.

The definition “X is A” is therefore not a tautology, but holds information. Two propositions are involved in it: the predication that “X is A” and the claim that “A is the definition of X”. The latter is an additional proposition; it implies the former, but not vice versa. We may know that X is A, while not yet thinking or while wrongly thinking that A is the best definition of X. Our idea of X would be equal to A if all we knew or thought about X was A; this is clearly very unlikely a scenario, though such paucity of information is theoretically conceivable. In practice, our idea of X includes much more, viz. B, C, D, etc.

We do not get the concept of man through the definition “rational animal”, but through cumulative experience of men. The definition is only a later proposition, by means of which we try to find the essence of manhood – or at least, men. The proposed definition is itself a product of experience and not some a priori or arbitrary concoction. We may for a long time have a vague concept of X, without having found an adequate definition for it. When we do find a definition, it is not necessarily final. It is a hypothesis. It could turn out to be inadequate (for instance, if some rational animals were found on other planets), in which case some further differentia or some entirely new definition of man would need to be proposed.

Note in passing that tautology occurs when the predicate is already wholly explicitly mentioned in the subject, or the consequent in the antecedent. Thus, “X is X”, “XY is Y”, “if X, then X”, “if X + Y, then Y” are all tautologies. It does not follow that such propositions are considered by logic as necessarily true. Their truth depends on the actual existence of the subject or truth of the antecedent. For it is clear that the latter may be merely imaginary or hypothetical, as for example in “unicorns have one horn”. Thus, tautology is not proof of truth.

Clearly, too, a definition like “man is a rational animal” is not tautologous in the strict sense. Some nevertheless consider definition as an implicit sort of tautology, by extending the concept. Those who do so do so because they think that the concept defined is identical to its definition. This I of course do not agree with, for reasons already stated. Even so, note that if tautology is not proof of truth in the case of explicit tautologies, as just explained, the same follows all the more in the case of implicit ones.

Through definition, we try to identify the ‘essences’ of things. The essence of some concrete thing(s) is rarely if ever itself something concrete, i.e. empirically evident. In most or all cases, essences are abstractions. We cannot produce a single mental image or Platonic Idea of man that would represent or reflect all individual men. We just point in the general direction of the notion of manhood by defining men as rational animals, but we cannot concretize it. The constituent terms ‘rational’ and ‘animal’ are themselves in turn just as or more abstract. This important insight can best be seen with reference to geometrical concepts.

In the concept of triangle, all possible physical or imagined triangles are included, those already seen and those yet to be seen, and all their apparent properties and interrelationships. If I ask you what the essence of a triangle is, you are likely to imagine and draw a particular triangle. But this is not the essence; it is an example – a mere instance. There is no one concrete triangle that contains all possible triangles. The essence of triangularity does not concretely exist; it is just an abstraction, a verbal or intentional contraption. That is to say, we mean by the ‘essence’ of a triangle, “whatever happens to be distinctively in common to all triangles” – but we know we cannot mentally or physically produce such an entity.

The essence in such cases is thus just something pointed to in the foggy distance. We cannot actually produce it, but only at best a particular triangle. We can of course define the triangle in words as “a geometrical figure composed of three lines that meet at their extremities”, or the like. But such verbal definition still hides the concept of ‘line’, which in turn cannot be concretized except by example; it just passes the buck on. It reduces the problem (of triangular essence) to another problem (that of linear essence), but it does not really solve it. This is perhaps why many logicians and philosophers opt for Nominalism. But we should not allow it to lead us to skepticism.

Rational knowledge is built on the assumption that particulars that seem to us to have “something distinctively in common” do indeed have something distinctively in common. We extrapolate from appearance to reality, at least hypothetically – i.e. on the understanding that if ever we find some specific observation or logical reason that demands it, we will reclassify the appearance as an illusion instead. This practice is nothing other than an application of the principle of induction to the issue of conceptualization. It is logically impossible to argue against this principle without explicitly or implicitly relying on it, since all such argument is itself ultimately inductive. Likewise, being itself conceptual, any putative theory against our belief in abstracts is easily discredited and dismissed.

The essence of an individual is what is conceived as abiding in it through all possible changes; the essence of a kind is that which is conceived has shared by all its possible instances of it. Moreover, in either case, the essence must be found in that thing or kind of thing, and in no other. But though we cannot usually if ever empirically point to anything that fits this definition of essence, we assume each thing or kind to have such a core, because otherwise we could not recognize it as one and the same thing or kind. We rely for this assumption on our faculty of insight into similarities and differences. Through such insight, we ‘point towards’ an essence – though we do not actually experience such essence.

Since the similar things (the individual at different times or the scattered instances of the kind) seem to point in the same direction, we infer by extrapolation that they are pointing at something in common (the apparent essence). This constitutes a reification of sorts – not into something concrete, but into something “abstract”. There is thus some truth in what Buddhist philosophers say, namely that essences are “empty”. However, we should not like some of them draw the negative conclusion that essences “do not really exist” from this emptiness. For we can, as already mentioned, rely on the principle of induction to justify our inference. Provided we do not confuse abstract existence with concrete existence, we commit no error thereby.

We may call such cognition of essences conception or conceptual insight. This implies that just as we have cognitive faculties of perception of phenomenal concretes and intuition of non-phenomenal concretes, so we have a cognitive faculty of conception through which we ‘see’ the similarities and differences between objects. Such insight is not, note well, claimed to be always true – it may well be false sometimes, but it cannot be declared always false without self-contradiction. Its veracity in principle is verified by the principle of induction, in exactly the same way as the veracity of experience is in principle verified. That is to say, we may assume in any given case such conceptual insight true, until and unless it there is experiential or rational cause to regard it as false.

It is very important to understand all this, for all rational knowledge depends on it.

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