Jacob, you seem to imply that physical mathematics exists within the Universe, and was recognized by H. Sapiens, whereas (metaphysical) Philosophy is entirely a creation of H. Sapiens. Could you elaborate?

Please allow me to reshape the question as follows:

"Are you implying that Mathematics is intrinsic to physical reality, while Philosophy is but a mental construct of H. sapiens?"

Indeed: The universe, meaning everything that exists in a tangible form of matter and energy, is imbued with mathematical formulas or principles that are integral part of it. There may be 'uncertainty principles,' but they will have to be understood within the context of our incapability to see 'blind' spots. I've written on the subject of the 'umbilicus,' a spot that separates us from the creator mother, and of the retina's blind spot where the optical nerve extends the brain as eye. Brain-mind has 'blind spots' being one of the motives for making us prone to fall pray of mystic musings serving no enlightening purpose.
H. sapiens has been 'discovering' those mathematical formulas and putting them in writing. And, as befitting an advanced successor of H. habilis, applying them for his own benefit.

Philosophy could not have been original, because it is not an integral part of the universe. When H. sapiens' curiosity, the motor behind his quest for learning --but mostly understanding-- cannot be satisfied by scientifical means, H. sapiens is lead to construe philosophical edifices. Both humans and animals express curiosity, but only man can wonder. Science and Philosophy are wonder's main results. There is also Poetry, because poetry reflects the whole Universe.

I pretend now to present to you a conundrum, which I believe is entirely new:
We 'know' what matter is, without the need of learning about atoms, because we see and touch objects that are so ubiquitous, as to become part of our reality, as much as our parents do. Not so, regarding energy. We are unpleasantly surprised when we fall and hurt, or are punished by a slap, or when we touch a hot object, or get an electric jolt. We will later learn that energy is defined as something that is capable of making work. Learn yes, but not truly understanding. Then we learn, and even understand, that there are several manifestations of energy, from the simple dynamic to the complex electric, where the energy is in the electrons.
And now to the conundrum: If energy must be manifested by means of the matter in which it is present, how can we conceive energy as an individuality?

Black Holes are obviously highly-condensed matter and energy. The primal object of the Big Bang is the highest expression of that condensate. Therefore, E=mc2, suggesting that matter can be converted into pure energy, does not make sense. Einstein reached that formula after several corrections. I wonder if he was entirely satisfied, and if he was not surprised at the way his formula was widely accepted. At any rate, I believe that the true formula ought to be something like M-->(qf)-->m , with tiny arrows in the opposite direction, where M is mass, q the quantum (subatomic) entities, f their interacting force, and m the new resulting matter. (qf) would represent the elusive moment of 'pure energy,' pristine energy avidly looking for matter to nest in. The definitive formula would be complex, where m=Hydrogen. In these musings, I consider f as the source of energy, and H, hydrogen, as the end result of complete fission.

To make my idea clearer: H is the first element created in the BB. Once a cloud of H2 is so large as to cause fusion, gluons are created, being the repositories of the gravitational force responsible for the new element. Liberating that force by fission, the sudden expansion is now dynamic energy. This example shows how force can transform into energy.
When hydrogen is fused into helium, a tiny portion of matter is transformed into "energy," which is the (qf), fastly creating a range of photons in whose guise that (qf) will now exist. Succesive developments, culminating in life, were possible because of that very exoenergetic phenomenon, not yet explained.
A mathematical formula to incorporate a reverse --endoenergetic-- process, in the case of complete fission, has not been offered. But here is the rub, DrZ: that formula exists! It is awaiting its discoverer...

DrZ, you well know that I am no physicist, while accepting that many laymen possess much information that was not available at Einstein's time. Even though I do not understand the latter's relativities, I feel no compunctions for writing on subjects appropriate to D-SP. Should I be threatened to chained for my hubris, I would avoid the liver-eating eagle by the clever delete maneuver.

Could you qualify the following propositions?

(1) Mathematical equations formulate physical events; for example, Cartesian geometry can show the slope between two specific points.

Examples, contrary to analogies, are the best means to convey the meaning of a complex proposition. Thus, I feel that I can comment on your question --as I understand it-- in a specific manner:

You are referring to Analytic Geometry, a representative example of Descartes' analytical mind. He attempted to apply Mathematics to the then prevalent Scholastic philosophy of the Church. I take that it was his "Cartesian Doubt" started as a rebellion against what he came to feel as a waste of his precious time. With good reason, he had to be careful in his writings, lest he suffer Galileo's fate.
But in mathematics Descartes was free of fear. He applied algebraic principles to geometry. It so happens that the Laws of Physics follow algebraic formulas, which are subsequently made arithmetical. Planets are configured following the algebraic formula that will finally be expressed specifically in diameters and volumes subjectible to arithmetic expressions.

(2) A philosophical proposition is descriptive of a reality, as understood by the author of the proposition.

Many such propositions have been accepted as correct, and consequently applied in the understanding of the world. Others have been accepted as desirable for the advancement of man and society. Their intended effect is partial, failing as society changes. Man's mind has not kept pace with the dizzying technological advances of the few last decades. This is a striking example of a 'chaotic' situation, which theoreticaly is amenable to be expressed in complex formulas, as befitting a complex societal situation.
New generations are rising, which feel at ease with the revolutionary technologies. Quite reasonable is to predict that they will be prepared to incorporate in their minds all possible new technological developments. The chaotic situation we are now watching will recede until it reaches a balance.

D-SP propositions are the result of their author's accretion of two sources:

a) The last decades' discoveries using the scientific method, with their validation through effective technological applications. b) A realm lying between Theology and Science, considered as the natural turf for Philosophical constructions.

D-SP is considered by its 'discoverer' and nurturer, as the one that can explain lucidly the world. None of its propositions, however, should be taken as an adumbrating of a better future, or as offering counsel.

(3) The logical processes (inductive and deductive) follow equal paths, whether applied to mathematics or to philosophy.

Syllogics is the deductive process, whether in the original, Aristotelian 'material' (concrete) frame, or in the modern, symbolic 'formal' (abstract) frame. Induction is the way to obtain the empirical (experiential) information to be subsequently applied to understand the world. Otherwise, any new observation would have to be studied anew from scratch. Every new thing would be taken as the manifestation of a capricious god. Logic is generalizing from well founded premises, which initially were empirical and now are almost always experimentally obtained. Empirical=experiential; Scientifical=experimental.
I am ignorant about Inductive Logic, which just cannot be. Induction is the basis for deduction; nowadays induction is the way of interpreting experimental results for the understanding of the world. While writing this, I realize that D-SP could we described as precisely attempting to do that... Your question is most relevant: D-SP is an HYPER-PHILOSOPHY. D-SP pretends to explain everything falling under the category of Philosophical subject, i.e., not Theological or Scientific. This hyperphilosophy could be created (discovered) only at the time it was, towards the end of the 20th century, the century that found the way to scientifically study the mind as a function of the brain. The more mathematics can be applied in this hyperphilosophy, the more exact it becomes.

Two more questions, Jacob:

(1) If the logical processes are the same, and the difference lies only in the mode of application, then wouldn't it be more correct to say that each one is a child of reason, rather than either one a child of the other?

To reason is to follow the correct way of thinking, either by applying known premises, or to finding new premises. The foundations for new premises are nowadays discovered by a new kin of thinkers, whether theoreticians or experimenters. Then comes the hyperphilosopher, looking for the interpreation of the findings as an added layer to the edifice of understanding the world. As another thread in the weawing of a tapestry, as another piece in the right place of a puzzle, as another stanza in the poem of the world. A sad poem, if strictly read in the light of H. sapiens' emotions.

(2) It would seem that mathematics, descriptive of the (physical) world as we know it, has raised (philosophical) questions, such as:

a) What exactly is responsible for the gravitational force? b) How does one account for the existence of quarks?

It would seem that until these questions are answered, the mathematics in question dangle from a very thin thread and over a very deep chasm.

a) Gravitational force: There is an answer, convertible into a mathematical formula. When the answer is found, still hyper-philosophy will have to place it in the context that explains the world. I have attempted above to condense the concepts of force and of energy. Let us use an example: a submarine reaches a depth where the weight of the water crushes it. Crushing is the result of 'work.' Therefore, the gravitational force acting on the water was converted into energy. Or perhaps the water contained potential mechanical energy. No matter, this is just a 'red herring.' Since nobody has offered an answer to your question, I'll profer mine: The primal matter-energy is made of proto-electrons and proto-positrons. The latter are the 'anti-particle' of the former, spinning in an opposite direction. At the BB, both are converted into the electrons and positrons that we know. But the positron is not exactly an 'inverse' electron. The latter is very robust, stable, while its counterpart is fragile. Following the Principle of the Triads, there is a third state: the electron-positron stable ('neutral') pair. Electrons are outside the nucleus because positrons would disintegrate (as neutrinos?). Electron-positron pairs inside the nucleus are responsible for the gravity force. Can you conceive those perpetual girations as a simple caprice, with no noticeable effect?

Having easily answered your first question, the second, on quarks, is now even easier. About 350 of ep pairs reach a critical point for the formation of a delimiting 'envelope', thus forming a quark. The three quarks are an obligatory result of the delimiting envelope's' interactions. Note that I do not use e+p-, but simply ep. The reason: avoiding confusion with electricity, where spin does not play a role. Positrons and electrons should be understood as just having opposite spins, not electric charges.
In electricity, the electrons are qualified as negatively charged, but what does this mean? Electrons are just the material medium used by the friction-created electric energy to vest itself. That frictional energy is the paradigm of energy. Negative and positive refer to the relative or absolute presence or absence of energetic electrons.

Since I know very litle of electricity, which I could sort of understand thanks to my musings, I am holding my fingers near the DELETE button...