I suppose that the genesis of this post comes from one of my current study projects. Over the past several months, I’ve been slowly working my way through Harry Gensler’s really fine book ‘An Introduction to Logic’, 2nd edition. As is the case when I learn anything, I find that my mind automatically associates many things with many things. It seems to me a good strategy, because I remember the information much better and can apply it with greater ease. (This should be contrasted with the way I was taught or learned history – I still don’t know what the Battle of Hastings was, why I should care, and how it affects my life.)
Anyway, Chapter 3 of Gensler’s book deals with definitions and what is essentially epistemology, although I don’t believe that Gensler ever mentions that term explicitly. The most interesting part of that discussion is the presentation of the categories of definition attributed to Immanuel Kant and how they mesh with the two philosophical divisions of knowledge that are traditionally recognized.
Kant divides definitions into two categories:
Synthetic statements: Statements that are neither analytic nor are self-contradictory.
Traditionally, philosophers recognize two kinds of knowledge, which are defined as:
A priori knowledge: Rational knowledge based solely on intellect.
No doubt a few examples are in order to make these concepts clearer. The examples that Gensler provides (and which I believe an anonymous Wikipedia contributor lifted without attribution) tend to feature the noun ‘bachelor’.
Examples of analytic and synthetic statements are:
Daniel is a bachelor. (synthetic)
The first statement is analytic, since its subject ‘bachelors’ is synonymous with ‘unmarried’ (that is to say that its subject contains its predicate as an attribute), while the second statement is clearly synthetic, since the word ‘Daniel’ is not synonymous with ‘bachelor’, nor is it self-contradictory, as it would be if ‘Daniel’ were replaced by ‘Stacey’ (assuming the usual gender denotations of names).
The following statements are examples of a posteriori and a priori knowledge:
All bachelors are unmarried. (a priori)
The first piece of knowledge that ‘some bachelors are happy’ can only be obtained by us going out, meeting bachelors and determining (through whatever mechanism we like) that they are happy. The second bit of knowledge is based on our ability to see the essential definition of the word bachelor.
Obviously, there is an extremely close tie between a statement being analytic and a piece of knowledge being a priori. There is also a very close tie between a synthetic statement and a piece of a posteriori knowledge (but, I would argue, not as close as the association between analytic and a priori). Thus, there is a tendency in philosophy to equate the two terms in each case, and to say that all statements of a priori knowledge are analytic, and that all statements of a posteriori knowledge are synthetic.
This seems to be a natural conclusion, and one may dismiss the idea that some statements of a priori knowledge can be synthetic, or that some statements of a posteriori knowledge can be analytic. This dismissal is also supported, at least superficially, by the common notion that all of our mathematics is a priori knowledge and all of our science is based on a posteriori knowledge.
The problem arises when one starts to examine certain statements that, while not quite self-referential, fall into a category where they at least talk about each other, or, more precisely, they are statements that explicitly talk about the nature of knowledge.
As a possible example of an analytic statement of a posteriori knowledge, consider the sentence ‘the value of pi is about 3% larger than 3’. That there is a constant of proportionality between the diameter and the circumference of a circle is certainly an analytic statement of a priori knowledge, but the determination of the actual value (or some decimal approximation to it) is not. Okay, so maybe there is such a thing as an analytic statement of a posteriori knowledge, although Gensler leaves the door open for doubt when he says
But, apparently, the real drama in the philosophical world (I must admit I have fanciful images of Plato and Aristotle, dressed in wrestling tights, as squaring off in a steel-cage match) is over whether there is credible evidence to support the claim of a synthetic statement of a priori knowledge. Such a statement Q would be one such that Q is neither self-contradictory to affirm nor to deny, Q is true, and we know Q to be true only using our reason.
Trying to further explain where such a brain-twisting idea can arise, Gensler asks us to consider two types of philosophers: empiricists and rationalists. According to his discussion, the empiricist denies the possibility of synthetic a priori knowledge, while the rationalist admits such a possibility. The crux seems to come in the examination of the empiricist’s point of view. The first observation is that an empirical point of view seems to equate the experiences of the senses with the actualities of the world. An empiricist is inclined to say something like
Of course the empiricist seems to have no mechanism for embracing the idea that an object is actually red when it is perceived as red, except to resort to what seems to be synthetic a priori knowledge. It is synthetic because nothing in how the terms are defined requires an object that is perceived as red to actually be red. It is a priori because we use our reason to conclude that it is a tenable assumption that all objects perceived as red are, indeed, red.
Perhaps even more interesting is the position the empiricist takes on synthetic a priori knowledge in the first place. To say
seems to be an example of synthetic a priori knowledge, at least in-so-far as one is willing to agree that the statement, if true, is not true by virtue of the definition of the terms ‘synthetic’ and ‘a priori’, and is therefore synthetic, and that the statement, if true, cannot be determined to be so by our sense experiences, and so it must be a priori.
Okay, so what does any of this have to do with murder mysteries? Well, as I mentioned above, whenever I am learning something, I employ a personal strategy of associating things I understand with things I am trying to grasp. As I was reading Genler’s presentation, I couldn’t help but wonder how mystery writers employ these points to amuse, entertain, and sometimes baffle us.
So, next time, I will apply some of these concepts to some of the world’s most famous fictional detectives. We’ll have a chance to see if Sherlock Holmes is synthetic or analytic. We’ll ask how many of Hercule Poirot’s little gray cell depend on a priori versus a posteriori knowledge. We’ll examine whether Miss Marple’s understanding of human nature springs from analytic a posteriori knowledge. And we’ll explore how logic, reason, and epistemology figure into two of the twentieth century’s most philosophical writers, G.K. Chesteron and Umberto Eco, through their excellent characters of Father Brown and Brother William of Baskerville.