Back to first principles

Way back in the 1960s when I was in high school we had different levels at which you could learn maths. There was 2S for second level Short, 2F for second level Full and 1st level, on which you went right back to first principles for grounding the foundations upon which the rest of the maths on top rested. In a way you could say that those studying the 2nd level courses were being short-changed in favour of learning by rote methods for solving mathematical problems that worked, without really knowing why.

Much later I learned that going back to first principles was something practised already by Aristotle, one of the West's deepest thinkers, whose concepts, despite vehement denial by  modern science, maintain their hold on our mind to the present day. Thinking deeply amounts to going backwards, not forwards. Thinking forwards amounts to continuing along the tracks laid down by ancient foundations that today are hardly visible any more.

At university I did a year of physics, continuing on from the 1st level physics I did at high school. I was not satisfied with the way physicists played fast and loose with the maths they needed to present their theories. All they needed was maths that worked for the theoretical explanations of the physical phenomena in question. The equations they came up with only had to be experimentally tested to 'prove', in terms of scientific method, that they were correct and hence true, that is. unless some other physical phenomena were discovered generating empirical data that did not verify the predictions generated by the theoretical model. This was called falsification. If enough instances of falsification were found, or maybe just one black swan, the physical model was in trouble and physicists proposed new models with modified equations. The empiricist scientific methodology was never put into question, and isn't even today. Especially in physics, whether it be quantum theory or cosmology or what have you, scientists demand that theoretical models be conjectured that can be tested empirically by generating predictions. Extremely elaborate and expensive apparatuses may be necessary to generate the data necessary for the empirical testing. Like most modern scientists today, physicists, too, have to compete for funding. Think of what it costs to detect a gravitational wave, as predicted from the theoretical model for the phenomenon of gravitation!

Being dissatisfied with physicists' treatment of maths in their mathematical models, and motivated by the urge to get to the bottom of things, I concentrated my university studies on the three types of maths offered at the time: applied maths, mathematical statistics and pure maths, the last of which seemed to me most promising in my quest for going back to first principles. Unsurprisingly in retrospect, I ended up being deeply attracted by a still fresh branch of mathematics at the time, category theory, in which I earned a Master's degree. Mathematical category theory seeks higher levels of abstraction on which it can investigate in one fell swoop several kinds of mathematical entities sharing the same structure. It thus strives for a kind of universal knowledge of mathematical entities.

After finishing my mathematical studies,  I returned to philosophy, having felt the need for more existential grit in my thinking. This landed me very quickly in German philosophy, for the analytic philosophy taught at Sydney University at the time (and even today) was, to put it succinctly, too dry. In retrospect I would also say that today's hegemonic Anglophone philosophy not only does not go back to first principles, but positively represses any attempt to do so. It has adapted very well to a positivist world in which facts are supposed to be the final arbiter of truth.

The category theory I studied in the final years of my pure maths bears the distinctive name, 'categories', redolent of Aristotle's foundational thinking on categories. Back in the 1970s I had no notion what category theory had to do with Aristotelean categories. Today I do. It is not merely fortuitous that I was immediately attracted in 1976 to a reading of Marx's Critique of Political Economy critically grounded in Hegel's dialectical conceptual system. Hegel's insistence upon systematically developing concepts to grasp the phenomena in question, and that in a proper order, also goes back to Aristotle. A concept can never stand alone, but only has sense and standing through its dialectical interconnections with other concepts that are either systematically prior or posterior. As far as I can make out, conceptual thinking is hardly taught today in universities.

Aristotelean categories are the most primitive, elementary concepts that come first of all. To grasp what a category is, your thinking first has to pass through the ontological difference encapsulated in the Aristotelean formula "the being qua being" (τὸ ὂν ᾖ ὄν). This famous formula is incomprehensible today, since the ontological difference has been forcibly closed down by the rise of positivist thinking, in tandem with the march of triumph of the 'hard' mathematized sciences. led by physics, in the mid 19th century. The second "being" in the Aristotelean formula is best interpreted as the present continuous participle of the Greek verb εἶναι, 'to be'. This allows us to hear it as a movement (of presencing for the mind: cf. my On Human Temporality), rather than as something 'standing', 'static', whereas "the being" in the first half of the formula says something that has come to a stand and is therefore static.

The first of the famous Aristotelean categories are 'what', 'how', 'how much' and 'in relation to'. Asking the question what something is (τί ἐστιν;) leads to the investigation of its whatness, its essence or quiddity. A something (τόδε τι, Etwas) has its whatness (οὐσία) in which it stands as a 'sight' (εἶδος) of what it is. These sights are seen and understood by the mind.

There is a simple phenomenological seeing exercise for learning to see the category of 'something'. Think of a potato with your mind's understanding. You will presumably agree that you see the potato as (or qua) 'something'. Now think of a chair. You will presumably also agree that you see the chair, too, as (or qua) 'something', albeit as a different something. The category of 'something' is available to our mind, through which we can understand anything at all as something. It is given to understanding prior to our seeing anything at all, no matter whether it be through sense perception or through our imagining mind. 

I say 'our' mind because we share this category that enables us to understand anything as something. 'Something' is a universal category available to our understanding prior to anything given by empirical experience. We understand a potato, a chair, etc. as something, and this 'as' is the mind's interpretation of it. Hence it is called the hermeneutic As. Anything we experience ontically, i.e. simply as being, whether it be through sense perception or mental imagination. is always already interpreted by the primitive category of 'something', which is different from anything in particular. This difference is called the ontological difference that is held open by the hermeneutic As that interprets the ontically given 'fact' ontologically, i.e. in its mode of being (understood as a continuing present participle indicating the movement of mental presencing).

The categories laid out by Aristotle address the things (πράγματα) encountered in the everyday world, thus constituting a kind of ontological scaffolding for understanding, in the first place, the world of physical, extended things (called Vorhandenes by Heidegger). One can say that the categories are examples of what is uncovered by going back to first principles (πρῶται ἀρχαί), at least with respect to physical things. In their primitive simplicity, they cannot be taken back (or re-duced, 'led back') any further. As simply discovered for the mind, they are true (ἀληθές). They are deployed by Aristotle in his Physics, which is an ontology of physical things that can be moved (κινούμενα), hence an ontology of physical movement.

By contrast, modern physics is a science (ἐπιστήμη) of the movement of physical entities based on an epistemology of empirically verifiable or falsifiable hypothetical models into which ontic facts, or data, are fed. It skips over the ontological preconceptions tacitly already assumed (and thus 'baked in'), prior to constructing or modifying any theoretical model. In this sense, it does not go back to first principles, and cannot do so since the ontological difference has been closed off to modern science, which pretends that it has rid itself of 'metaphysics'. It does not know that it is caught in the Aristotelean ontology of just one kind of movement: efficient productive movement.

Going back to first principles differs from the Da Capo I propose. The latter entails not just going back to first, elementary, primitive principles, but re-examining, revising and recasting them. Although it can be said that the Aristotelean categories retain their truth in hermeneutic phenomenology with regard to the ontological interpretation of physical things, Aristotle's ontology of movement is restricted to the efficient-causal movement of physical things, as if that were the only kind of movement we encounter through our openness to the world. Aristotle at least allowed phenomena that were fortuitous (τύχῃ) and accidental (κατὰ συμβεβηκός), but placed them beyond the grasp of science. This has led historically to a narrowing of the view of phenomena of movement in the bloody-minded attempt to force all kinds of movement into the corset of efficient-causal movement. 

The conception of efficient causality goes hand in hand with the concept of one-dimensional, linear time developed by Aristotle, no matter whether it be a straight, circular, elliptical or curved line. Straight here refers to Newtonian inertial movement; circular and elliptical to movement of the celestial bodies; curved to cosmological movement in general-relativistic space-time. Wherever efficient causality or a weaker modification thereof (e.g. probabilistic) is taken as axiomatic, the absolute will to power over all kinds of movement is the secret driving force. The tyranny of this absolute will to power must lead, and has led, to the denial of free movement that can be seen most blatantly in neuroscience, in which there is an intense focus on trying to 'causally explain' the generation of consciousness by movements in the material brain. The onslaught on human freedom by neuroscience is complemented by the progressive algorithmization of movement that goes so far as to interpret even human intelligence itself as algorithmic. As a mathematician, I have, of course, published on the cyberworld and its digital ontological cast.

Further reading: On Human Temporality: Recasting Whoness Da Capo De Gruyter, Berlin 2024.

Movement and Time in the Cyberworld: Questioning the Digital Cast of Being De Gruyter, Berlin 2019.