Albert Einstein, who was struck by the astonishing organization of the cosmos, said:
“The most incomprehensible thing about the universe is that it is comprehensible” and asked “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”
I have to deduce that Einstein hadn’t an understanding of traditional metaphysics. Otherwise he would neither have spoken about the comprehensibility of the universe as “the most incomprehensible thing” or a “miracle”, nor he would have been surprised that math is so “appropriate to the objects of reality”. In fact metaphysics postulates “universal intelligibility” (nothing is unknowable in principle). The comprehensibility of the world is only a limited by-product of universal intelligibility, which is far more extended than that. Moreover, logic and math, which – when are correctly related to truth – are not mere “products of human thought”, are so effective and appropriate to describe the world only because of the power of the metaphysical principles which they derive from.
How does metaphysics explain the comprehensibility of the world? See this picture:
A camera c “sees” an object – say – an apple a by its lens but has not comprehension of it. A man m sees the apple with his eyes and, in addition, has comprehension of it. What gives man the comprehension, which the camera has not and cannot have? Materialists answer: “Man has the brain”. But the brain is only a physical tool, like the eyes. The brain per se doesn’t explain the deep meaning of comprehension. Furthermore, the brain itself, and its origin, has to be explained, and materialism is unable to do that.
In the figure you see that the apple (and all manifested things) is “connected” by a line R-a to the metaphysical Reality, which contains its principle (or archetype) and gives the apple all its reality. This is really a key point. What has the higher degree of reality is not the apple a, rather the apple in R! Who wants to grasp metaphysics, as first step, must understand that the entire cosmos has a lower reality respecting R. This lower relative reality of anything in the cosmos is fully due to a higher absolute and causative counterpart in R.
Man is connected to the Reality, which is the total Knowledge, by the line R-m, which gives him too all his reality, his being, and in the same time allows his mind to get comprehension of the apple (and anything else). Therefore existence and comprehension are direct participations to the Being and to the total Knowledge. No being, no knowledge is possible without this participation connecting man to the ultimate Being/Knower. This explains why Aristotle defined the highest knowledge as identification, and why Plato said that any real knowledge is remembering, reminiscence. In the picture the line R-m symbolically represents the ontological derivation of man from his principle and also the remembering-identification of his power of knowledge. The line R-a represents the beam connecting the higher apple to the lower apple, like in the Plato’s cave the Ideas/Forms are connected by light beams to their images in the cave, where humans see them.
In the language of Scholasticism this remembering is a sharing of essence/quality. In the language of modern algebra, this remembering is an isomorphism between the Reality and the knowledge of man. (An isomorphism between two things means that they share a common structure.) Without this triangular isomorphism (the lines R-a, R-m, m-a) man could have no comprehension at all of the physical apple a (also if his eyes see the apple along the line m-a). Without it man would be like a camera, an unintelligent receptor of light only.
Since Reality is also the Truth, the divine Intellect, the line R-m is called the universal intellect, which illuminates all intelligent beings. For this reason Thomists defined knowledge as adequatio rei et intellectus, i.e. the isomorphism between the material thing, its image in the human intellect, and finally its Form in the ultimate Source of all, the divine Intellect.
Since logic and mathematics are universal truths they are in the Truth-Reality R. When a scientist, by means of logic and math, is able to understand something about the working of the cosmos or one of its objects, like a, it is via the line R-m that pass downward, the logic, the math and all other stuff needed by m to know the object a, via the line m-a.
Now let’s apply the above explanation to the case when the comprehension of the natural object involves design inference. A design inference, at least partially, is always a reverse-engineering. Reverse-engineering is always, at least partially, isomorphic to the original direct engineering. Thus, also design inference involves the triangular isomorphism of knowledge, with the difference that in this case the Reality is seen as a Designer. The IDer doing the inference somehow remembers what the designer did, and even, at some lower relative level, identifies with him.
Materialists deny the metaphysical Reality R and its connections R-a and R-m. For them, knowledge and comprehension are physical states of the brain only. At the very end, for materialists, also knowledge is matter. This is nonsense of course, how can matter comprehend matter? Materialism absurdly conflates agent and object, knower and known, who sees and what is seen, who understands and what is understood. Consequently, materialism is entirely incapable to explain knowledge and comprehension of anything. So, for materialism, the Einstein’s question remains unanswered. Logic and math (that is fully based on logic), to be so effective, must be universal truths. If they are only states of the brain of one or more individuals – as materialists maintain – they cannot be universal at all. Universal truths must be objective and absolute, not just subjective and relative. Only this way they can be shared among all intelligent beings.
Knowledge of a by m, to be what really is, needs an absolute reference, which is a reference to the absolute. This absolute reference cannot be other than the source of the reality of the object a in R. This is the reason why both a-R and m-R necessarily converge to R, the final source of all: objects and knowledge of objects, the world and comprehensibility of the world.
Bottom line: without an absolute Truth, no logic, no mathematics, no beings, no knowledge by beings, no science, no comprehensibility of the world whatsoever.