Dec 102017

Back to the riddle.

We have seen where the word Science comes from: scire means to cut, split (as in scissors), separate, decide true from false. We, like other living creatures, do so on the basis of evidence – what we see there is. We use evidence to update our beliefs. We are all Bayesian.

Despite Kant’s grand attempt to salvage some of it, there is no such thing as a priori knowledge. What may appear to us as transcendent knowledge, emanating from pure reason independent of evidence, is and can only be based on notions – concepts, principles, axioms – that we regard as self-evident.

Such notions are the subject of Metaphysics. The word came about, apparently, to denote the collection of Aristotle’s treaties that his late editors arranged to place after (meta) his Physics. Whereas Aristotle himself had not called them Metaphysics, actually referring to them as ‘first philosophy’, dealing with concepts that came before Physics in importance and generality.

Be as it may, we can think of metaphysics as the area we enter once we start running out of answers to our Why questions. Answers are local explanations built on our own hard evidence or, most often, on soft evidence emanating from trusted sources. We learn to accept local explanations and live with them, but every answer begets new questions, in a seemingly endless why-chain whose infinity we find impossible to accept. Explanations cannot go on forever. At some point, even the cleverest dad succumbs to the urge to end his child’s relentless barrage of whys with a resounding last answer: ‘because that’s the way it is!’

But to the undaunted child dad’s last answer turns into the ultimate question: What is the way it is? Once we set out to answer this question we have entered the land of metaphysics. Metaphysics is mankind’s effort to establish the absolute, unquestionable and irrefutable episteme that stands firm above Physics. Episteme is knowledge that does not need evidence because it is self-evident, certain without experiment and secure from the perils of experience.

How can we achieve such knowledge? Clearly, we can’t reach it from the side of experience, whence we can only expect an infinite regress of explanations. So it must come from the other side. But what’s on the other side? Clearly, we know nothing about it – if we did, we would have already gone past the answer we are looking for. As Immanuel Kant put it, noumena are on the other side – things-in-themselves, absolutely unknowable and irremediably inaccessible to our mind. All we can know are phenomena – things as they appear to us in the light of evidence.

Metaphysics is the boundary between phenomena and noumena – a boundary that mankind would love to cross but can only push forward, unfolding and accumulating new and better physical explanations of natural phenomena. Such is the love at the root of philosophy – the ever-burning, insatiable desire for sophia, the supreme wisdom in whose full light we would finally be able to contemplate the way it is. But the light of philosophy is the same light that illuminates phenomena. Metaphysics is and can only be on the side of phenomena – the side of experience and evidence. In the words of Arthur Schopenhauer:

Metaphysics thus remains immanent, and does not become transcendent; for it never tears itself entirely from experience, but remains the mere interpretation and explanation thereof, as it never speaks of the thing-in-itself otherwise than in its relation to the phenomenon. (Will, Volume II, p. 183).

Metaphysics is not and cannot be a priori knowledge, independent of evidence. Its value does not rest on its being beyond evidence, but on being based on notions that we regard as self-evident. Like mathematics and geometry, metaphysics is an axiomatic system – true insofar as its axioms are true. An axiom is that which is thought worthy, weighty, and thus bears authority – a concept interestingly close to the original meaning of probability. Axioms are statements assumed to be self-evidently true, thus requiring no proof or demonstration. Given the axioms, the theorems built on them using truth-preserving rules of inference are demonstrably true.

As such, the validity of an axiomatic system depends on the weight of its axioms. The more precise, clear, obvious, intuitive, indubitable the axioms, the stronger the system. Take Euclid’s Elements, which, as we know, is built on five axioms (or postulates). As we have seen, one can argue about the fifth. But not about the first: A straight line can be drawn joining any two points. Or the second: A finite straight segment can be extended indefinitely into a straight line. The third: From any straight segment a circle can be drawn having the segment as radius and one endpoint as centre. And the fourth: all right angles are equal. A geometry in which any of these four axioms is untrue is even hard to imagine. They are glaringly, unquestionably self-evident.

Now let’s compare it to Spinoza’s Ethics, which he explicitly wrote along the lines of Euclid’s Elements.

Here is its first axiom: ‘Everything which exists, exists either in itself or in something else’. The second: ‘That which cannot be conceived through anything else must be conceived through itself’. And the third, which we have encountered as the Principle of Sufficient Reason: ‘From a given definite cause an effect necessarily follows; and, on the other hand, if no definite cause be granted, it is impossible that an effect can follow’. And so on. One may or may not agree with any of these statements – provided that he truly understand what they mean. But it would be at least preposterous to regard them as self-evident.

And what about Definitions, which in Elements as well as in Ethics precede the Axioms? Let’s take the first three. In Elements they are: 1) ‘A point is that which has no part’. 2) ‘A line is breathless length’. 3) ‘The ends of lines are points’. Hard to disagree. But in Ethics: 1) ‘By that which is self-caused, I mean that of which the essence involves existence, or that of which the nature is only conceivable as existent’. 2) ‘A thing is called finite after its kind, when it can be limited by another thing of the same nature; for instance, a body is called finite because we always conceive another greater body. So, also, a thought is limited by another thought, but a body is not limited by thought, nor a thought by body’. 3) (we have seen this one) ‘By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception’.

Whaaat? Definitions and axioms can only be as clear as the terms that compose them. We all know and agree on what a point, a straight line and a circle are. But what about essence and existence, cause and substance? They are much more complex, vaguer and harder concepts to define and comprehend. It’s no wonder, then, that all the ensuing Propositions in Ethics are, let’s say, less cogent than Pythagoras’s theorem. Take, for instance, Proposition XI, Part I:

God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists.

Here is the proof:

If this be denied, conceive, if possible, that God does not exist: then his essence does not involve existence. But this (Prop. VII) is absurd. Therefore God necessarily exists. Q.E.D.

Uhm. And what is Proposition VII?

Existence belongs to the nature of substances.

and its proof:

Substance cannot be produced by anything external (Corollary, Prop. VI), it must, therefore, be its own cause – that is, its essence necessarily involves existence, or existence belongs to its nature. Q.E.D.

Oh well. I spare you Proposition VI and its Corollary. Spinoza was a great philosopher and an admirable man, and his Ethics is a trove of powerful thoughts and ideas. But its metaphysical value can only be as compelling as its murky foundations.

This is metaphysics’ typical pitfall. While usually conceived as the product of pure reason, standing above physics and unrestrained by experience, metaphysics can’t really be nothing else than a more or less coherent inferential system which is in fact so entwined with evidence as to be entirely based on supposedly self-evident foundations.

The trouble is that self-evidence is in the eye of the beholder. And – as we have seen repeatedly throughout this blog – it is amazing what different people, from the dimmest to the supremely intelligent, come to regard as self-evident. Once one is satisfied that he has made all the way through why-chains to answering the ultimate question, and that he finally knows the way it is, it is tempting to invert direction and reinterpret reality in the light of his newfound metaphysical principles.

This, as we shall see, is a recipe for disaster.

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