After some intense discussion in my philosophy group. A user by the name of Pete Finch has convinced me of the following flaws in my reasoning. I have conceded to him that the concept of the three classical laws of logic do not exist. In my time beginning to learn philosophy I adopted this concept debating theologians. These theological doctrines are included in mostly presuppositional apologist arguments with the presumption of logical absolutes being the foundation. Absolute truth here is used as a pretext for the justification of a God existing. Apologist will often employ outdated classical terms in logic to ramrod assertions in an ill-attempt to salvage their outdated theology. You will hear me refer to the three classical laws by several names “laws of logic, laws of thought, and the three classical principles.” I will use these terms interchangeably. Although, the theological tenants of the ‘three classical laws’ may not fit with Aristotle’s original treatment. I wont clarify the distinction here. The purpose of this thesis is to show that the original supposition of the three classical laws can be falsified by using modern ideological principles of philosophy.
1) Where the laws of logic come from? The etymology of the three classical laws pre-dates Christianity during the 4th century B.C.. The Greek-Athenian philosophers Plato and his young student Aristotle were the first to describe these concepts as laws of thought. It was early Christian theologians like Thomas Aquinas who first refereed to them as absolute laws (Summa Theologica) What the three laws are are classical forms of first order logic/propositional logic. The classical three principles were based on the principle of bivalence in which there are only two-valued instances of (true or false) conclusions a statement can have.
- The law of identity, which states that a thing is identical with itself.
- The law of non-contradiction, which states that two contradictory statements cannot be true at the same time.
- The law of excluded middle, which states that, for any proposition, either the proposition is true or its negation is true.
2) Can contradictions be used meaningfully? St. Anselm tried to conclude with this line of reasoning in his now infamous Ontological argument. “If God is the greatest being conceivable then a being that exist in reality is greater than a being that exists only in the mind alone. God must exist because this would otherwise be a contradiction”. To counter this claim one only need point out that contradictions can and do exist conceptually. Humans can conceptualize contradictions and performative contradictions. Karl Marx in expounding upon his idea of ‘dialectical materialism’ spoke of wealth & poverty as an existing contradiction that co-occurs as a consequence of capitalism. St. Thomas Aquinas rejected this argument, pointing out the categorical error that to exist in the mind is not the same as to exist in reality. The idea that contradictions do not exist comes from Aristotle’s classical axioms. With the idea being that if a contradiction could exist then anything follows (principle of explosion).
3) The concept of the laws of logic are not valid in the modernity of academia. We must face the fact that modern logic has turned to mathematics. This was repeatedly pointed out in my conversations with Finch. However this isn’t true as its still applicable to propositional logic. Yes, you may find these principles repudiated in English literature, debate, and some courses in philosophy. Its not wrong to use them. It’s just not equipped for advanced studies of logic. The classical definitions are too vague to have much meaning in mathematical terms. This fact should weaken anyone’s confidence for the three classical laws. Just know that I’m rooting for you but you’re still wrong.
4) The classical system of propositional logic has been largely replaced by propositional calculus. With propositional calculus we delve into not just (true or false) statements but the degree of true statements. Fuzzy logic can semantically and mathematically demonstrate the inclusivity of seemingly contradictory terms. Dialetheism/paraconsistent logic refutes the orthodoxy of the classical ‘principle of explosion’ and deals with contradictions in a non-trivial manner. Consider the fact that some truths are logically equivalent. If I observed a simple phenomenon that had a 50% chance of happening then both P and ¬P are logically equivalent. This violates the 2nd of the three classical principles (i.e. the law of non-contradiction.) Paraconsistency could be thought of as belonging to the property of a consequence or relation between two contradictory premises.
5) “If there are no absolute truths then is such a statement absolutely true?” I’ve come across this half-witted response many times in my experience arguing with theologians. It’s anything but a play-on-words. It could easily be dismissed if you don’t accept the presupposition. The glaring fallacy here is committed by asserting in the initial premise that ‘truth’ is absolute, its another question begging statement. If you wanted to argue the supposition without initially dismissing it you could also comment that something does not have to be absolute to be true.
What the classical three laws are are simply recursive definitions that have been repeatedly re-purposed for there practicality and explanatory power. It may be true that most arguments are propositional, which can be satisfied by referring to these three classical laws. But just because the three classical laws are reliable in many justifiable circumstances doesn’t give them the quality of being absolute nor universal.
Smith, Robin, “Aristotle’s Logic”, The Stanford Encyclopedia of Philosophy (Summer 2019 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/sum2019/entries/aristotle-logic/>.
Cintula, Petr, Fermüller, Christian G. and Noguera, Carles, “Fuzzy Logic”, The Stanford Encyclopedia of Philosophy (Fall 2017 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/fall2017/entries/logic-fuzzy/>.
Priest, Graham, Berto, Francesco and Weber, Zach, “Dialetheism”, The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/fall2018/entries/dialetheism/>.