A recent post on Dubito Deus critiques a popular argument from presuppositionalists called the Transcendental Argument (TAG). The TAG is known for arguing from necessary principles like logic to the conclusion that God is a necessary precondition for such principles . In other words, if you deny God’s existence, you deny logic and thereby commit yourself to mental absurdity. I am not a supporter of presuppostionalism as a complete methodology, but I do appreciate some of the insights it offers. In this particular instance though, I only want to defend classical logic in its metaphysical form as opposed to a more conventional form that modern philosophy has reduced it to. Formal systems of reasoning is a powerful tool for successive precision in one’s thinking but its limited to a particular set of rules, syntax, or symbols that form a set pattern for the structure of our arguments. In some cases however, I find these “non-classical” logics to be a rather superfluous (and meaningless) attempt at solving obscure problems that is best reserved for those who like technical mind games. I realize it may provide benefits in helping us formulate certain propositions more precisely but it tells us no more about reality than a programming language does.
There are multiple programming language (e.g, C , BASIC, Java, Objective-C, etc) that offer certain solutions to different operations within a computer. However, these varying means of preforming a function do not tell us about the function itself as much as it tells us how we actualize that function. Each language can do so in different ways, but the nature of that function should remain the same. For example, one language could use “PRINT ”Hello World!”“ and another could use ”printf( “hello worldn” );“ but each one should ultimately do the same thing – namely, output the words ”Hello World!“ into a window. One language could be simpler and another could be more complex in order to provide more precise control over things. You can debate all day over which one of these is better but it all depends on the kind of applications you want to develop. BASIC may be better suited for developing simple programs like calculators but C could be superior for gaming. However, just because these languages use different syntaxes does not make the function itself conventional. A language could even create a contradictory syntax and strangely arrive at some ”coherent” function but at that point, it just gets ridiculous.
If that’s all “conditional logics, relevant logics, paraconsistent logics, free logics, quantum logics, fuzzy logics” do then I think they’re useless in telling us what reality is. They’re useful for other purposes, to be sure, and can provide the kind of distinction between ideas that we need but without a metaphysical foundation, such things are simply absurd. Paraconsistent logic, for example, is said to allow for contradictions by removing the disjunctive syllogism and “proof of LNC” rules of inference . At this point, I cannot help but think this is simply semantic sophistry. If you want to avoid some linguistic problem (such as liar paradoxes) by creating an ad hoc system of logic then be my guest, but this is not what classical logic is about. Logicians have separated themselves from metaphysics today, but sometimes, when discussing the law of non-contradiction for example, their “conventional” understanding of logic is used to dismiss it or worse, is used to tell us that contradictory essences can exist in reality. Classical logic, on the other hand, is a metaphysical discipline of the intellect that is directed toward grasping the essences of things through the proper distinctions and the proper reasonings in a structural form. The means by which we understand these essences must itself be in response to a metaphysical understanding of reality, not as a trivial response to a linguistic problem.
Language itself ought to reflect essences and is itself a form of logic as far as it communicates our thoughts about things into a conventional form. Nonetheless, it is not the language itself by which we understand the essences of things, it is simply a creation of words and sounds that provide reference to the objects or actions in question. Insofar as language is understood in this manner, I think our attempts in being precise and distinct is good but not if it comes at the expense of our metaphysical foundation. Arguably, you could change “cat” to mean “jdfodo” just as the law of non-contradiction can be rendered meaningless in paraconsistent logic, but doing so does not removes how things are. For Aristotle, a denial of the law of non-contradiction amounts to the denial of essentialism . It’s like saying essence x and essence y are both the same and not the same in the same sense and at the same time. Either x is y or it is not. This conclusion is not dependent on some abstract rules of the elite, it just depends on whether it corresponds to reality and how well it coheres with our intellect or common sense .
Whatever is true of a proposition must be true to the degree by which the intellect truly grasps a universal, essence, or thing. Each instance of a kind will participate in that kind to varying degrees, depending on how perfectly that instance instantiates that kind. For instance, if we compare a poorly drawn triangle to a carefully drawn triangle, we’ll immediately notice that one is more “true” to how a triangle ought to be than the other . The intellect is capable of extrapolating a more perfect understanding of a thing by understanding its kind without necessarily seeing the perfect triangle. I may not be able to imagine a 1000 sided polygon, for example, but that by no means implies that I do not understand the concept. The same applies here. Even approximations are instances of a triangle and as such, provide the immediate basis from which our intellect extrapolates a universal to the conceptualization of a perfect triangle. This may be physically impossible to actualize, but it is not impossible for our intellect. Having said all of this, I think any rejection of classical logic must explicitly deny essentialism and thereby commit itself to utter stupidity. No metaphysical construct can hope to rescue any sort of logic that claims contradictions are metaphysically possible. You can redefine logic to refer to something else, but I’ll stick with a more classical approach because it is metaphysically relevant, rational, sophisticated, and in accord with common sense.
- http://en.wikipedia.org/wiki/Transcendental_argument_for_the_existence_of_God#The_argument ↩
- http://plato.stanford.edu/entries/logic-paraconsistent/ ↩
- http://plato.stanford.edu/entries/aristotle-noncontradiction/#5 ↩
- http://edwardfeser.blogspot.com/2012/04/fine-on-metaphysics-and-common-sense.html ↩
- Feser, Edward. Aquinas: A Beginner’s Guide. Oxford: Oneworld, 2009. pg 33. ↩