Being & Analogy
My book Geometry & the Interior Life: On Gottfried Leibniz’s Situational Analysis is now available for purchase.
The human being is created in order to inquire into & discover the proper causes of things, and hence, explanations of things. In discovering the sequence of explanations, those explanations cannot go on forever — because that would mean that nothing at all is explained.
In order for anything at all to be explained, the sequence of explanations must terminate in something that is self-explanatory or self-evident – this is common sense. Thus, common sense is the necessary beginning of a shared understanding of explanation and causality. The science of self-evidence is the science of causality. The principle of identity [A = A] is the normal expression of what is self-evident. But how does what is necessary (or eternal) fit together with what is contingent (temporal, transitory)?
Theorem: the three fundamental laws of thought— the law of identity (A = A), the law of non-contradiction (A ≠ ~A) , the law of excluded middle (A or ~A) — are mutually equivalent to and mutually imply one another, and already contain implicit transitive analogy relations (A → B → C, therefore A → C), within themselves. Transitive analogy relations are derived from (are a direct consequence of) the mutual equivalence and mutual implication. This demonstration is taken to suggest some insight about the intrinsic relationship between necessity (or eternity) and contingency (or time).
We begin with the simple axiom of identity, or “being” is what it is.
(1.A) Being is what it is, [A = A], therefore,
(1.B) [A = A] is irreducible, therefore,
(1.C) [A = A] is unknowable in advance, therefore,
Scholium: Being (1.A) expresses the law of identity. Irreducibility (1.B) and unknowability in advance (1.C) are contingent implications of this law, rather than positive definitions of the law itself.
Scholium: Irreducibility (1.B) implies that being (1.A) is the simplest, most self-evident definition. Being cannot be defined more simply. In accordance with Shannon, Solomonoff, & Chaitin’s algorithmic information theory, the definition of random is a string of symbols that is exactly what it is — the string has not sufficient repetition that it could be compressed in a more concise pattern that would reproduce the original string. Being or identity is the most concise mathematical pattern of existence. But it cannot simply be characterized by the concept of randomness alone, because true randomness is is not possible, only pseudo-random; any appearance of randomness or attempt to create randomness in human reason, is actually rationality of a higher order.
Scholium: Since being (1.A) is irreducible and “random” by this definition (1.B), it is therefore unknowable in advance (1.C) -- it cannot be predicted in advance by a model. Being can be known by experience, a posteriori, not a priori. That does not mean that it has no formal model, only that its empirical experience is simultaneous with its formal model. Thus, being is hylomorphic-- a combination of matter and form, both, and not one or the other.
(2.A) Being (1.A) implies irreducibility (1.B) implies unknowability in advance (1.C), can be reduced to the representation:
(2.B) [A = A] ➞ B ➞ C, therefore,
Scholium: In so reducing the expression (2.A), we reduce the implication of irreducibility (1.B) — which is the middle term — this does not reduce being itself (1.A) or even irreducibility itself (1.B), but only reduces their contingent implications. It excludes the middle term:
(2.C) [A = A] ➞ C, therefore,
Scholium: This (2.C) is an expression of the law of excluded middle (A or ~A), which demonstrates how the law of excluded middle begets transitive analogy relations, and how the law of excluded middle is derived from being or identity (A = A) (1.A).
(3.A) [A = A] ≠ C, therefore,
Scholium: This expresses the law of non-contradiction; A is not equal to not A. And thus it shows that:
(3.B) Equivalence is not equivalent to implication, therefore,
(3.C) Equivalence implies implication.
Scholium: equivalence implies implication, by necessity. There are no pure equivalence relations or pure implicit relations, but equivalence and implicit relations always co-exist. This is the reason for Leibniz’s term congruence or the contemporary term isomorphism.
Triune being (1.A) is shown in the three axes of: necessary equivalence, contingent implication, and analogically equivalent implication.
The axis of necessary equivalence ( = ) runs horizontally:
1.A = 2.A = 3.A
1.B = 2.B = 3.B
1.C = 2.C = 3.C
The axis of contingent implication ( → ) runs vertically:
1.A → 1.B → 1.C
2.A → 2.B → 2.C
3.A → 3.B → 3.C
Therefore, the axis of analogically equivalent implication ( =→ ) runs diagonally (there are other diagonals as well):
1.A =→ 2.B =→ 3.C
2.A =→ 3.B =→ 1.C
3.A =→ 1.B =→ 2.C
Conclusion: It is thereby shown that law of identity, the law of excluded middle & the law of non-contradiction, are mutually equivalent to and mutually imply, one another, and that these properties are what derive the laws of transitive analogy relations. Quod erat demonstrandum.
Thus, it is demonstrated that, how, and why necessary being reduces its own contingent implications (or representations) by transitive analogy relations, without reducing itself. Being is the free reduction of its own implications, that does not reduce itself. Transitive analogy relations converge on being. Contingent implications are in proportional (or superpositional) relationship with one another. This relation is not merely quantitative but also implicit or qualitative. The relation of proportionality is the relation of two contingent implications to an implicit criterion of equivalence. And thus, any of the terms can mutually take on the significance of the equivalent criterion of measure in relation to the other two.
Thus, it is also shown that being has a triple significance – equivalence, implication, and equivalent implication. In the final step (3.C), the proportionality between two contingent implications is the negative measure of equivalence. And thus, proportionality between two implications is the proportionality between two implications and their suggested equivalence and differentiation. This proportionality converges to what is self-evident or self-explanatory or equivalent, without reaching finality. It is a kind of magnifying lens (like a telescope or microscope) of experience, in which the truth of reality is made clear, against the background of noise.
And thus, being is what reduces its own contingent implications without reducing itself. And thus, being is what chooses & allows things to converge in itself, even as they remain distinct, in its own perfected harmony.