The Metaphysics of Reason
Now that we have solved the logocentric predicament and have understood that rational insight is in fact the way to have knowledge of logic. We must ask what metaphysics follows from our epistemology. What facts about reality can we immediately conclude from the fact that the laws of logic and various inference rules are true and justified?
So, let us first note that our a priori intuitions recognize the true and justified nature of certain inferential principles and logical principles as well. Let us recognize two of the latter and one of the former.
The principle of identity, or p = p, is the positive criterion of logic. All logical propositions adhere to it, and anything that comes into contradiction with it is illogical. This leads us to the principle of non-contradiction, or p ≠ ~p, the negative criterion of logic. Recognition of this principle allows us to understand that contradictory propositions are not logical propositions. Lastly, let us recognize that the positive and negative criteria of logic are notationally equal: (p = p) = (p = ~~p).
The inference rule of modus ponens, or p → q, p ⊢ q, is the most basic of inference rules because what it states is simply that if something entails another thing then if we have that thing then that thing it entails follows from it. Without this inference rule, conclusions about what follows from a certain proposition could have no inferential entitlement for their inference from p to q.
We know the epistemic status of all three of these principles, but what is their metaphysical status? Furthermore, are there metaphysical facts we can know a priori by way of rational insight? In response to the latter question, I believe the proposition “existence exists” is a proposition whose truth is easily intuitable. Simply, existence exists is saying existence is being itself, or p is p. It could be argued that it existing would be ping, so p is ping, but when we realize that all p is ping means is that p is being in the way of p, or p is being p, then it doesn’t really become problematic. The only reason that existence exists is a proposition about what is the case is because existence is what is the case.
So, what can we immediately deduce or have a rational insight of in regards to the nature of reality? “Existence exists.” “p is itself,” or “p is p.” We can know a priori that there is something rather than nothing and that this something is itself. Therefore, the structure and character of existence, and thus metaphysics, is logical. However, do we not suppose that existence is logical when we say that existence must necessarily exist? We know that the principle of identity and the principle of non-contradiction are both justified and true by way of a priori insight. We understand that existence is really something, by definition. Therefore, we are justified in believing that existence is itself not in virtue of existence but in virtue of the principle of identity and non-contradiction.
Do we not raise a larger question of why anything is logical? I think we do, thus, we must start not with other things such as the subject, the object, etc. but rather with logic itself, for logic is logical (assuming the logocentric predicament has been gotten around). It seems that all things can only be assumed to be logical. I must assume that existence operates according to the concepts of modality in order for me to conclude it is logical. This point was raised to me over a year ago by my friend Jeffery (though he goes by Neel). So, we must start with logic itself. If logic is more than just a proposition, and, for example, an abstract object, then we can begin to deduce a metaphysic for existence would be logical. Or, at least, that part of existence that those principles of logic and inferential principles “occupy” as abstract objects is logical, and if we can deduce any other entities from these abstract objects then we can characterize them as logical too.
However, it could be argued that “existence exists” does not assume existence is logical because no logical inference is employed but rather the non-inferential method of rational insight. “Existence exists” says “p is ping” which is equal to “p is p,” hence, if “p is p” is true then we have epistemic justification and thus epistemic entitlement to make the inference that “existence exists” is true, not because existence is logical, but because the proposition “existence exists” has a schema that is rationally intuitable. We can rationally intuit that the principle of identity is true, just like we can rationally intuit that modus ponens is true. Modus ponens tells us it is true simply by giving us the entitlement to make the inference, p ⊢ q, in its first premise, p → q. Similarly, the principle of identity gives us the epistemic entitlement to say p is p because it is really just saying p, if that makes sense. If we understand the logical connective of “=,” and we do, then we understand that nothing is really being stated other than p. The principle of non-contradiction can also be rationally intuited simply by way of understanding the logical connectives of “≠” and “~.” Thus, we can conclude that “existence exists.”
Now that we have concluded that existence exists is true. Can we also conclude that existence is logical?
: P1: The POI and PNC apply to all possible things (true; explanation: a possible thing is that which does not conceptually contain a contradiction, which is when the subject and predicate come into conflict with one another, and since identicality [semantic equality] must be maintained for contradiction not to arise, the POI and the PNC are being followed; example: a square triangle is not a possible thing because it is a contradiction in terms of a triangle has three sides yet this triangle must have four since it is square and is thus not a triangle even though it must, at the same time, be a triangle; see Christian Wolff’s definition of being for more on this).
P2: Existence is a possible thing (how do we justify this?).
C1: The POI and PNC apply to all possible things (from P1 and P2; true).
: P1: the propositional schema of p is ping is true. (true by way of rational intuition)
P2: the proposition “existence exists” has the propositional schema of p is ping. (true)
C1: the proposition “existence exists” is true. (true, by way of P1 and P2)
Note that this whole syllogism supposes that modus ponens is valid, but we can rationally intuit that modus ponens is a valid inference rule. It could be said that this syllogism also assumes that all propositions that have the propositional schema of p is ping are true, but that, I believe, is what the first premise states certainly in an implicit manner and maybe even in an explicit manner.