Let us take the major points one by one:
(1) The first point is as follows:BIBLIOGRAPHY“Lord Keynes tries to undermine Kant’s notion of the synthetic a priori by use of empirical evidence. This will not do. The synthetic a priori, as Kant formulates it, is a category of knowledge by which we come to understand synthetic claims (claims about the real world) by means of aprioristic reasoning (logical deduction). Pointing to an empirical event as falsifying or refuting a claim about a methodology misses the mark entirely. Kant’s ideas on the synthetic a priori may well be wrong or mistaken, but one must prove so by means of showing where the logical error lies. It is simply poor philosophy to argue that an empirical event can refute epistemic claims. This is a category mistake. Epistemic claims — claims of how we understand knowledge — are of an altogether different category than claims of knowledge themselves.”The idea that one cannot refute the claim that some particular knowledge x is synthetic a priori is a bizarre assertion, and entails that modern science did not refute the rationalist claim that Euclidean geometry was a universal theory of space known as necessarily true a priori. Is that what Mattheus von Guttenberg thinks?
Kant’s synthetic a priori knowledge is known with necessary truth, and known without appeal to empirical evidence. Yet, as we will see below, it was precisely the collapse of most imagined synthetic a priori knowledge via the empirical evidence from modern science that credibly refuted the existence of this type of knowledge. Other remaining kinds of synthetic a priori knowledge, such as mathematics, have been shown logically to be analytic a priori statements deduced from axioms, and ultimately non-informative in an empirical sense.
(2) The next claim is this:“In the second place, Kant’s musings on pre-Einsteinian geometry are fascinating, but hardly foundational for the synthetic a priori paradigm.”On the contrary! Euclidean geometry was the most fundamental kind of knowledge that Rationalists down through the centuries have relied on to support their claim that there was synthetic a priori knowledge.
Euclidean geometry was the very paradigm of alleged synthetic a priori truth (Salmon 2010: 393; Musgrave 1993: 245–246).
(3) Next, we have this:“Just because Kant did not, or could not, imagine non-Euclidean geometric theorems does not invalidate his notions on the category of the synthetic a priori in general.”As it happens, the collapse of Euclidean geometry as a universal theory of space known a priori deprived Kant of his major example of alleged synthetic a priori knowledge, but, fundamentally, all of Kant’s alleged synthetic a priori knowledge has also collapsed in the light of modern science and philosophy of mathematics, whether it is Euclidean geometry, time, deterministic causality, mathematics, and so on.
For example, the very belief that we can know a priori that time passes objectively and unidirectionally towards the future is disputed by many physicists on the basis of general relativity, and it is the Eternalist/Block Universe theory of time that is adopted by numerous physicists today. This Eternalist theory actually entails that the perception of the passing of time is an illusion. Although there is a rival theory called Presentism, we cannot know which theory is correct a priori, and the question will be determined empirically.
Moreover, quantum mechanics destroyed the idea of universal deterministic causality known a priori.
Even logical truths like the Law of Excluded Middle, when regarded as universally true a priori, is possibly refuted by quantum mechanics, as Willard Van Orman Quine noted long ago, though he was even more radical in that he denied any strict distinction between even analytic and synthetic truth:“Furthermore it becomes folly to seek a boundary between synthetic statements, which hold contingently on experience, and analytic statements which hold come what may. Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in ... [sc. our web of belief]. Even a statement very close to the periphery can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws. Conversely, by the same token, no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?” (Quine 1951: 40).(4) Then this passage from Hoppe is quoted:“Since the discovery of non-Euclidean geometries and in particular since Einstein’s relativistic theory of gravitation, the prevailing position regarding geometry is once again empiricist and formalist. It conceives of geometry as either being part of empirical, aposteriori physics, or as being empirically meaningless formalisms. Yet that geometry is either mere play, or forever subject to empirical testing seems to be irreconcilable with the fact that Euclidean geometry is the foundation of engineering and construction, and that nobody there ever thinks of such propositions as only hypothetically true.”The final sentence in this passage is a non sequitur.
Yes, Euclidean geometry is a highly useful system in a limited domain. But how can we justify that it is useful in this limited domain? The answer is: empirically.
We have a great deal of empirical evidence over a long time that Euclidean geometry is useful in a certain domain. Yet its truth as a physical theory of space in that domain is only ever extremely probable and known a posteriori.
Contrary to Hoppe, that fact that “nobody [sc. in engineering and construction] … ever thinks of such propositions as only hypothetically true” is irrelevant! Hoppe has committed a crude informal logical fallacy called the appeal to (invalid) authority (and it may also imply an equally fallacious argumentum ad populum). People who work in engineering and construction most probably do not understand the evidence and arguments from modern science and philosophy of science, so their opinion on this question cannot prove Hoppe’s point, because they are invalid authority. (And even our belief in the probable truth of modern scientific theories ultimately does not come from any consensus of scientists, but from the strength of the arguments and evidence for, and the empirical testing and predictive power of, scientific theories.)
In modern philosophy of science, all scientific theories and geometries (asserted as true theories of real space) are only ever highly probable, fallible, but not certain. Even the scientific theory that the earth revolves around the sun is ultimately an extremely probable theory that has been confirmed by a vast amount of evidence, but could in theory be false.
For example, can we know a priori that Euclidean geometry is a necessarily true theory of all space in our universe? That is what the advocate of classical synthetic a priori knowledge is claiming, and yet the belief that Euclidean geometry was a universally true theory known a priori is precisely what was discredited when general relativity and non-Euclidean geometry received overwhelming empirical support.
(5) Furthermore, as a matter of fact, von Guttenberg’s claim that I only think that there are two forms of knowledge – analytic a priori or synthetic a posteriori – is false, since I happen to think that Kripke’s necessary a posteriori knowledge is a defensible third type (though I find Kripke’s concept of the contingent a priori unconvincing). But Kripkean necessary a posteriori propositions are epistemologically different from synthetic a priori ones, and seem of little value to modern Rationalists, since they apply to identity statements using proper names, definite descriptions, or scientific statements of the essence of natural kind terms, and are also only known by empirical evidence (that is, a posteriori).
(6) Finally, von Guttenberg offers these remarks on causality:“Even making empirical observations requires that the observer understand a causal framework, simply in order to make sense of his observations. The understanding of causality is thus inherent and irrefutable within every action. This renders causality to the status of the synthetic a priori and—that every event is interconnected with other events and causes—is both true logically, because every action demonstrates the actor must know this, and it also gives us usable and important information about the real world.”No, making empirical observations presupposes some metaphysical assumptions, such as the validity of induction, the universality of the laws of nature in space and time, the existence of an external world, and so on.
But these are not known a priori: they are defended with probable inductive arguments (some better than others), and the justification of these metaphysical assumptions is not certain: modern science has long since abandoned apodictic certainty, or any belief that mere human intuition gives necessary truth.
Take causality: the Kantian idea of necessary, deterministic causation as a universal truth known a priori is untrue given the idea of probable but not necessary causation in modern quantum physics (Melnick 2006: 229; Anscombe 1993), which now also separates the notions of causation and determinism (Weinert 2004: 260).
An even more shocking possibility can be given. Kant apparently thought that the principle of the uniformity of nature was a synthetic a priori statement. But a few years ago some remarkable evidence was reported that the “fine structure constant” (or what is called “alpha”) – a fundamental law of nature – may not be constant throughout the universe:“Laws of Physics Vary Throughout the Universe, New Study Suggests,” Sciencedaily.com, 9 September, 2010.If even fundamental laws of nature as established by modern science can be empirically falsifiable, there is little hope for the rest of Kant’s synthetic a priori knowledge.
Michael Brooks, “Laws of Physics may change across the Universe,” New Scientist, 8 September 2010.
Anscombe, G. E. M. 1993. “Causality and Determination,” in Ernest Sosa and Michael Tooley (eds.), Causation. Oxford University Press, Oxford.
Melnick, Arthur. 2006. “Kant’s Proof of Substance and Causation,” in Paul Guyer (ed.), The Cambridge Companion to Kant and Modern Philosophy. Cambridge University Press, Cambridge. 203–237.
Musgrave, Alan. 1993. Common Sense, Science and Scepticism: Historical Introduction to the Theory of Knowledge. Cambridge University Press, Cambridge.
Quine, W. V. 1951. “Two Dogmas of Empiricism,” Philosophical Review 60: 20–43.
Salmon, W. C. 2010. “Geometry,” in Jonathan Dancy, Ernest Sosa, and Matthias Steup (eds.), A Companion to Epistemology (2nd edn.). Wiley-Blackwell, Chichester, UK and Malden, MA. 393–395.
Weinert, Friedel. 2004. The Scientist as Philosopher: Philosophical Consequences of Great Scientific Discoveries. Springer, Berlin and London.