The Presup Challenge:
Define a formal logic, complete with syntax, semantics, a deductive system, and a meta-theory. Then we can talk about whether it’s absolute or not.
UPDATE: The Beginner Presup Challenge
Complete this logic practice quiz:
Which of the following are well-formed formulas:
2. (¬P ↔Q ⊃ R)
3. (Q v (P ↔R))
4. (P ∧ Q ∧ R)
5. (P ∨ Q)
Construct truth tables for the following:
Conduct a Moorean Shift on the following:
(P ∨ Q) ⊃R
∴ (P ∨ Q)
This is a verbatim personal correspondence I had with Sye Ten Bruggencate via email dated 28 April 2012, regarding my blog post found here. Honestly, after this I’m so frustrated by the inanity of it all that I’m not going to debate logic with someone unless they’ve at least read an introduction to logic text. I don’t have the time or the patience for stuff like this.
I’ve recently written a critique of the presuppositionalist analysis of logic on my blog that you may be interested in. You’re welcome to respond here: https://dubitodeus.wordpress.com/2012/04/23/logic-math-and-presuppositionalism/
Sye: Sorry, but I had to stop at “logic is conventional.”
Me: Umm…what? Are you telling me that you’re not even going to finish reading my response to the core of your apologetic strategy?
Sye: Nah, when you said that logic was conventional, I lost all interest. You see, I could just make a convention that everything you wrote is illogical, and be done with it.
Me: See, if you had read my article, you would understand why what you said is completely irrelevant to the topic. But since you don’t seem to have an interest in actually discussing what I wrote, let’s play this game your way:
How do you account for elliptic geometry?
Sye: With Friday motballs under the twice. (I just made a new convention of logic 🙂
Me: Ok Sye, I have to ask…are you interested in a conversation, or just in being obtuse and contrary?
Sye: I am simply answering a fool according to his folly (Proverbs 26:5). If logic is conventional, you can have no problem with my response,but you do, exposing the fallacy of your view.
Me: “If logic is conventional, you can have no problem with my response”. See, once again, you completely misunderstand conventionalism with regard to logic. What you just said is like responding to a question said in French with, “That doesn’t mean anything. If language is conventional, you can have no problem with my response.”
Just because logics are a convention, doesn’t mean that you can arbitrarily say silly things and then declare that everyone must accept them as not silly. You can create a new convention, but you still have to define rules for that convention. Just like languages – you can create a new language, but you still have to define a grammar. Just like board games – you can create a new board game, but you still have to write down the rules for your game.
But once again, if you read my article, you would already know this. I’d recommend that you read a logic textbook, but if you can’t even read a few hundred words on the subject without deciding to be obtuse, I guess there’s not much hope for that. It’s obvious that you don’t understand logic, but I’m starting to suspect that you don’t want to understand it.
Sye: //”Just like languages – you can create a new language, but you still have to define a grammar.”//
Not according to my new convention.
Me: This is pointless. My blog post renders everything you’ve said irrelevant, and brings up huge problems for your account of logic, yet you refuse to read it. So, do you mind if I post this conversation publicly, so everyone can decide for themselves who “won”?
Sye: Please do.
Theists who employ what is known as “presuppositional apologetics”, and more specifically, the transcendental argument for God, often make confused claims about logic. John Frame claims that logic is based on the nature of God, and Matt Slick says that the laws of logic are absolute and independent of the human mind. There are others who use such argumentation in slightly different ways (such as Eric Hovind and Sye Tenbruggenate), but the general view seems to be that theism, and specifically Christianity, is needed in order to justify one’s use of logic.
But this view of logic is sorely mistaken. The so-called “laws of logic” are merely conventions that exist within a man-made, formal system. To see why, we merely have to look at “logic” for what it really is – an entire field dedicated to the study of inference and relation. In the past century, many methods of doing this have appeared. Graham Priest writes:
Despite this, many of the most interesting developments in logic in the last forty years, especially in philosophy, have occurred in quite different areas: intuitionism, conditional logics, relevant logics, paraconsistent logics, free logics, quantum logics, fuzzy logics, and so on. These are all logics which are intended either to supplement classical logic, or else to replace it where it goes wrong.
Relevant logic, for example, differs from classical logic in that it attempts to solve the paradox of material implication. The paradox of material implication is the observation that “If the moon is made of cheese, then 2+2=4” is true, even though the antecedent is in no way related to the consequent. Material implication just does not capture what we really mean by “if…then” – yet it is classically valid. Relevant logic attempts to solve this by saying that andecedents must be “relevant” to consequents.
This seems to make sense, but it leads to an interesting feature of relevant logic. Relevant logic is not explosive, which means that unlike classical logic, you can sometimes have contradictions which do not entail the trivial truth of every proposition. Thus, “~(A & ~A)”(the so-called “law of non-contradiction”) is not a theorem of relevant logic (while it is a theorem of classical logic).
This is important because it shows that the unchanging, transcendent view of logic that presuppositionalists talk about just isn’t the case. These logical and mathematic systems are just models we invent to examine different ideas. We can and have changed them, or even thrown them out and started over with different “laws”, many times in the past. Relevant logic is just one example. Some other logics even change the definition of truth. Four-valued logics (often used in computing and electronics) don’t have “P v ~P” as a theorem; and fuzzy logics even have an infinite range f truth values. Intuitionist logics aren’t even concerned with truth, but justification. And these all have real-world applications.
Even mathematics does this. In elliptic geometry, for example, the sum of the angles of a triangle is more than 180 degrees; and Euclid’s parallel postulate is false – there are no parallel lines in elliptic geometry. Now, one might object by saying, “well, that’s just a thought experiment, and doesn’t obtain in reality”. The problem with this is that neither does Euclidean geometry. When’s the last time you saw a triangle? You haven’t. You never have. The only thing that exists in reality is an approximation of a triangle. A “real” triangle would have to have infinitely thin sides in order to have angles that add up to exactly 180 degrees; and would also have to be infinitely flat. We live in a 3-dimensional (at least) universe, and triangles exist in 2 dimensions. A triangle is just a concept, a thought experiment.
All this points to a simple fact: logic and mathematics are made up. We invented them to describe what we see, and they are only approximations.
 Priest, Graham. An Introduction to Non-Classical Logic. 2nd ed. New York: Cambridge University Press, 2008. xvii.