You have to remember that all of these thinkers predated evolution and so it did seem marvellous to them that there was such a mapping of the apparent laws of intellect and the laws of nature. This no longer seems surprising to us. 

That said, I am not sure what your second last paragraph means. Can you clarify?

Certainly, your whole question seems to point towards a very busy and hotly debated area of cognitive science and neuroscience. I imagine that you could spend many happy hours looking at the current experimental literature in the area. I certainly waste a lot of time on the FrontiersIn journals site : http://www.frontiersin.org

Am I right in reading, especially in your post's final sentence, that the coherence we find in Nature arises directly and only from the coherence we find in our own thinking?

@Ronan Michael, if I have understood correctly your request of clarification, the problem  Kant sought to resolve….., the foundation of our knowledge is not in the nature but (in)the activity itself of the subject. In this regard even David Hume, before Kant, had pointed out that the characteristics of necessity and universality that we attribute to the natural laws are actually a product of the subject, but in doing so he had destroyed their claim to objectivity, ending up only to judge them as arbitrary and totally subjective. It seems to me that the decisive step of the reflection of Kant consists in recognizing the objectivity in the heart of subjectivity. In fact, an object is such only in relation to a person, that is, only if it is thought, say, by me. It is the consciousness that I have of myself as a thinking subject that allows me to have representations of the world, as the simple  consciousness of "I think" can not ignore the critical, active consciousness of own interiority("I think that I think ").

The “I think” must be able to accompany all my representations; because otherwise it would be represented in me something that could not be thought at all. It then means precisely that the representation either would be impossible, or at least for me, it would not be, whatsoever. That representation, which can be given before any thought, is called ‘intuition’. I call it pure apperception, to distinguish it from empirical or even original apperception, since it is precisely that self-consciousness - as it produces the representation 'I think' - that must accompany all the others, and it is in each consciousness one and the same - it can no longer be accompanied by any other.

For instance, becoming aware that a given object is a product of my thought is to place it within the unitary framework of all my representations: to know means in fact connect, unite, make a synthesis.

The “I think”, is precisely the activity that performs this function, which is carried out when the bond that the “ I” put between two phenomena, expressed by the copula "and", has a value necessary and objective, different from the case in which two perceptions, which for example are given successively in time, appear linked by a connection purely arbitrary and variable. In fact, in the first case, differently from the second one, the “I think” intervenes to provide objective basis for that connection.

 I sincerely hope that what I have tried to express may be clear enough.

@Gianrocco           In your question introduction I am reminded of Parmenides...'the road is unknowable".....'whatever is dreamt must exist',  'nothing is ever brought into existence, nothing leaves existence', a void does not exist.  And I compare the non-existence of void with the void of the Greek philosopher Democrites within which occurs recombination that produces variety. Then later with Aristotle who makes the plane the species of the surface rather than as Euclid the surface of the sphere the species of the surface.

    Laying in the 'void' between Parmenides and Aristotle is the question of existence, induction as a means of knowledge, the statistical method of modern science...if it is a void that traverses Parmenides and Aristotle it contradicts Parmenides claim that a void does not exist, and if Parmenides is correct and a 'void' does not exist, the existences of modern science become but abstracted myth and refer to the class of existences of thought only and not to material substance that it claims witness. 

    This is where I place my understanding of Kant, the 'void' of science, empty spaces within the atom turn out not to be a 'void' at all but Kants' 'I think'....it is not sound or coherent in (scientific) claims to speak of what is unconditionally unwitnessible, e.g. electrons, atoms, or distant places too far to ever reach for witness.  It follows that it is also illogical to believe that the thought process can be captured scientifically, the "I think" precedes science, refers to the exact abstracted objects intended to capture it or consciousness...i.e. introspection is not able to capture the thought process to either material or transcendental aspects,  "I think" underlines all, is (the only possible) universal, to refer beyond "I think" in abstraction is to refer beyond existence and  its' witness. I would add to (clarify) Parmenides assertion that all mental content exists, ..  content cannot exceed what is experience based, path based, possibility for the transcendental object. Though...'are there unicorns anywhere?',  for the human the transcendental is all that exists,  only humans can make claim to thought, to their own existence.

   I am addressing this topic because think it is important to take issue; -scientific discovery is not the same as the discovery that precedes the evolution of new concepts, science is but a concept.  Machines were discovered before the ways of their functioning was questioned and investigated. There is lot of confusion historically about the potential of science. Science is captive to a paradox of Judio-Christian ethics, is but a physical tool not unlike a spear or hammer, and has only human suffering and a simple morality of right and wrong rather than nature to refer to regarding ethics and survival.  There must be something inherent to the transcendental so that one can claim:

          "the transcendental"  if and only if "existence".

@Marvin some few ideas and recollections at the edge of your intervention. For the scientist the universe is spherical and finite, made of a space turned in on itself; a sphere is not closed, because of being out of infinite space and there can be nothing but tending to close indefinitely. Note how in Parmenides the “being” is an absolute size, which permeates even the same philosophy (it is the same thing “being” and thinking). Since “being” coincides with thought, the latter is not able to objectify, because to do so it should get out, but this is impossible, because outside of “being” there is nothing. Thus Parmenides does not say what is the “being”; he hands it over there without a predicate: “being” is, and nothing else.

Now, a second consideration concerning the void. While the philosopher Benedetto Croce, referring to Augustinian speculation, puts the issue of ‘nothing’ in morality, negating any theoretical validity to this kind of conjecture, Heidegger considers a metaphysical central argument inspired by the meaning of anything like nothing, "no body". Nothing in fact should not be intended as a negative entity but rather as the revelation of the nullity of the entity and therefore of all the entities that have this feature as a determinant of their being. Through the experience of '' distress - Kierkegaard type” it shows the insignificance of ‘beings’ as well as of our existence in the balance between ‘being’ and nothingness.

Sartre resumes this latter theme in the work ‘Being and Nothingness’ where nothing is defined as '' being-for-itself ", which coincides with our conscience that acts freely and implements reality that in their entities is nothing . The entities of the world instead are "being-in-itself" as in their essence without determinations identify ‘being’, very well.

I conclude, briefly: “Form and content, transcendent and immanent, a synthesis before the creation of reality (self-consciousness) and simultaneously coinciding with it (self-creation)”.

@Gianrocco  After Einstein, though he disagreed through his death, it is accepted that world is expanding; things are  seen in space growing apart.  Unless it is stipulated that parts of the world can expand at different rates it would not be possible to witness expansion.  It may also depend on what is described to expand; depanding on whether it is radius, circumference, that expands, relative volume changes are different and depend on proximity to the center-so witness of expansion would be possible in the situation of an ever expanding sphere.   My question regarding this involves the coherency of correspondences made/ there seems to be a lot of jumping of levels occuring.  For instance, to claim a congruence of men and world, men expanding at a different rate than world, men are also attributed to be like world so that different parts of the body must expand at different rates. When Einsteins relation  E=mc^2   is applied there is a different change in energy depending on whether the foot, toe, arms, head move separately or together, so that all that can be seen is a consumption of energy for metabolism that is different depending on different parts and their relative motion...the knee has so much energy, the head, arms etc...distances between parts are not fixed; it becomes evident if association to another moving individual is made that a part, a toe for instance, must be fixed in position if any parts of the body are willed to move together as one.....if a constant velocity of light is asserted different relative times of motion of body parts in all instants of the whole (body) becomes a necessary assumption though one can imagine the instance arm bones or thigh and calf to move as one, as the whole  body moves. Then in  accounting, biochemical energy, relative size of parts, time must be given a plastic distribution within the whole.  In cartoon form this could look quite comical.   Lots of like trouble with correspondences  so to  look as if "voids" (e.g. gaps in explanation) are filled with voids so that all is assembled from and rests on a single premise (with a unique time and place over the course of history), e.g. a growing (expanding) continuous line(closed) exists that can be logically considered to be both discontinuous (open...eternally filled) (per Parmenides) and closed (not filled but with sterile places where a unique number of finite elements recombine to produce variety (per Democrites) simultaneously. The view seems to follow through until modern times; raises to question where and if sterility/pureness exists.  I think it sterility/pureness refers rather than to full or completeness, to void, but in a medical sense consistently to sterility/contaimination (vis Medeaval philosophies that ordinary life was dirty and purity found only at world extremes) (vis Neitzsches' diagnosis of a medical cause to the behavior/expression "men have conquered themselves") (an attitude that men can create as nature creates, are congruent/equal/expanding circles).

Paints a picture of disease, of men and space though it is evident men do not have to comply...hence they are free to be released from bondage depending on knowledge constructed exclusively from the transcendental.

Crucial towards positive action is whether  "logical positivism" is logically coherent , can physical measurement support the validity of a philosophy or theory in any instance/multitude of instances?  Vis...the expansion argument presented above or an idea supported by some that answer to philosophical questions can come from scientific exploration...is obvious the acquired answer will say "not sterile". 

    Philosophy is paramount, beyond science.  The mind nourishes the body, longest life time(even in the presence of a (species) life shortening pathology), most fertile fields, the hands of the farmer are immanent to it.

Philosophers of knowledge, the epistemologists, should carefully study the works by Jean Piaget on how consciousness, knowledge, intellect, rationality, etc. develops from babyhood on to adolescence, in order to avoid sterile, unworldly views on epistemology. An evolutionary point of view, realizing that knowing arose because of its adaptive value, may also contribute to this avoidance (see Dr. Conroy's comment).

@Peter       I think we are addressing two slightly different things though possibly overlap, parallel questions about nature are entailed.

    Piaget points to phenomenon that suggest a hard wiring that  is related to genetics of a species. Can genes explain it all, explain evolution (there are inherited factors that seem to come from other directions; e.g. the arrangement of cells in the womb, or in the distinction between clones ( a physical line of the transmission of traits) and clads (the simple sharing of traits that does not seem to have ties to gene flow from parent to off spring).  The epistemologist can question whether instinct is a property of nature that includes and extends beyond topics of genes. 

   In the balance is a dark area hardly addressed that entails both.  For instance in the history of ideas Socrates stated "if a man knows the truth he will act accordingly".  Aristotle, Socrates student, thought that a truth was not always possible or available to know, a based  his interpretation on a world that demonstrates a variety of dispositions.  Some men will committ immoral acts because they have (for whatever cause, upbringing, other personal experience or genetic) different dispostions.  The world, behavior of men is not so easily divided according to who knows the truth.  Todays world mostly ensues from Aristotles views, Aristotle was also probably the first scientist-studied the species, anatomy systematically.  I believe that a bridge exists to connect Socrates and Aristotles philosophies and perspectives (Aristotle was a third person perspective adherer, scientific, whereas Socrates might be called a first person adherer).  I interpret the same dilemma, paradox, to surface in Nietzsches' writing where he suggests that though a unifying basis might be found for thought, consciousness, cognition, that introspection would be ineffective in arriving at a physiological basis  of brain function related to cognition, possibly was not one accessible to the rational mind by scientific method. 

 Again I see the same paradox in Einsteins mathematics verses his philosophy, or verses the philosophy of those who followed from him that almost to the letter dissent with him.     Is the world expanding? how would one measure it if he is a part of the world?  Einstein put obstruction factors in his equation because he did not have an answer in scientific rational language.  From my view this is where the world stands today, in the wake of a paradox that is possibly dismissed as no coherent resolution possible.

   In the above question, rationality is addressed, the meaning of "universe", the aperception of unity, oneness from which knowledge is organized. Not all notions are rational or expressible in scientific language, but communicate understanding that is not divisible into information or data as a scientist would describe, depends on commonality, familarity, that is setting related.  Piaget, as most scientists, is a third person adherer, but as discussed there remains still a broader question.  On the topic of ethics, yes it might be claimed that humans have some moral sense from the first association with the level horizon, must be genetic.

What then of the A-bomb, the instantaneous destruction of millions of persons at a time, works very pettily by preventing water from escaping the bombs enclosure to cause critical mass and detonation not found naturally....pretty devious, a product of the rational mind, statistical, Aristotlian in basis.  Though the glue of the atom is the glue of the atom, may be just a single unique entity and not something that each atom has individually.  Perhaps using the bomb, malicious intent (intention is 90 percent of the law) has shortened human lifetime in two ways, damaging both nature and humanity.  Tell me that a world come to be dominated by Atomic power, looking as if inevitable, "all roads lead to where I stand" is a hardwiring phenomenon or a matter of freewill whose range becomes naturally reduced, (beyond awareness?, measureability?)... . radioactive decay, the opposite of development that acquires rather than reduces space.  A smaller and faster moving world that looks as if some facility is misssing from the rationale has come about; is justified by rationalization  entailing notions as "modernity",  ideas about the progression of mankind, or from science fiction.  

   Perhaps Piagets theorizations  are observational and have good usefullness, but they do not have universal capability, other questions that  are more rudimentary are possible. Bertrand Russell, about the time of Einstein, I think was hot on the trail in his discussions of logic and language,  particularly with his philosophical deduction that form rather than observation and measurement, or constants or absolutes,  was paramount to the understanding of nature.  Disparity, ratio, comparison may be all that exists within a sea that is directionally trended but relativistic in a non mathematical way, of which rationality, scientific method,  is but a single facet of the defining bounds of knowing inherent to the mind 

   In the balance if "all roads lead to where I stand", they lead there in retrospect, after and not before, from where I once stood,  mind, rather than by rational method,  is naturally bounded by "universe",  Einstein is known to have reiterated that the imagination, not detail or scientific mathematical proof,  is the most vital facility. 

  If interested I am attaching "Determining the Determined: A sizing of size from aside/the amassing of mass by a mass"...relates science method, mind and matter, universe, to a shape evolved with a three dimensional grapher.

Article Determining the Determined State : A Sizing of Size from Asi...

The decisive step of the reflection of Kant, to which he arduously arrived by his own admission, is then to recognize the objectivity in the heart of subjectivity. In fact, an object is such only in relation to a person, that is, only if it is thought by me. It is the consciousness that I have of myself as a thinking subject that allows me to have representations of the world, for the simple consciousness of external datum ("I think") can not ignore the critical consciousness, active, of his own inwardness ("I think that I think "). [and there was no apperception of me, that is I am always the same as myself in representing to me the changing nature and the variety of phenomena, inside me there would not be thinking of anything, because they would not  be a" mine "representation, and therefore I could not have consciousness.

Kant uses the expression "I think" to indicate the apperception, which he understood as 'transcendental' apperception, suited to the manifold, in the sense that is activated only when it receives data to be processed. It is located at the top of critical knowledge, because it unifies and gives meaning to the representations of the world. Knowledge, in fact, derives not only from the sensations felt: on the basis of these an objects is "given", but with the apperception it is "thought", through the use of twelve mental categories, without which everything would be dark .

"The unification is therefore not in the objects, and can not be considered as something drawn by them by way of perception, and thereby assumed primarily in the intellect; but it is only a function of the intellect, which is nothing but the ability to unify a priori, and to refer to the unit of apperception the manifold of given representations; and this is the supreme principle of all human knowledge. »

Being formal, apperception can not be reduced to a simple objective "datum", because it operates only in relation to an object: we can not know in itself but only when it goes with our representations. In other words, it is not a simple empirical-factual knowledge of the inner reality of the individual, but it is the formal condition of all knowledge, the container of consciousness, not a content. It is an activity of thought that belongs to all people but not to any of them in particular, structurally identical in all. It is distinct from the empirical ‘I’ or empirical apperception, which is rather the conscience of each individual based on the personal sensitivity and such to belong only to ourselves individually.

In your original question, you invoke the idea of freedom. Keep in mind that for Kant (the possibility of) freedom from nature occurs at the level of reason. (So it would involve the relation of propositions to one another, as reason always does in Kant.) Apperception, as discussed in the Transcendental Analytic, concerns cognitive acts that relate concepts merely to each other (analytically) or to intuitions (synthetically). These acts Kant considers acts of understanding (rather than reason), and they involve the formation of propositional content. I don't see where he associates the idea of freedom with the latter, nor does it seem intuitive to do so. After all, we do not seem to be free to perceive or experience the world as we choose.