"Empiricism may be defined as the assertion 'all synthetic knowledge is based on experience'."
(Russell, Bertrand.
Human Knowledge: Its Scope and Limits. 1948. Reprint, Abingdon: Routledge, 2009. p. 437)
"The stimulation of his sensory receptors is all the evidence anybody has had to go on, ultimately, in arriving at his picture of the world."
(Quine, W. V. "Epistemology Naturalized." In
Ontological Relativity and Other Essays, 69-90. New York: Columbia University Press, 1969. p. 75)
"From impacts on our sensory surfaces, we in our collective and cumulative creativity down the generations have projected our systematic theory of the external world."
(Quine, W. V.
Pursuit of Truth. Rev. ed. Cambridge, MA: Harvard University Press, 1992. p. 1)
First of all, there is no sharp boundary between theoretical science and philosophy.
"Metaphysics is the conjectural end of science. Its ontological claims must be tested by general scientific plausibility. Plausibility is largely a matter of maximal coherence of our beliefs in the light of often recalcitrant experience: in other words not only must theoretical beliefs cohere with one another but they must cohere with beliefs derived from observation and experiment."
(Smart, J. J. C. "Methodology and Ontology." In
Imre Lakatos and Theories of Scientific Change, edited by Kostas Gavroglu, Yorgos Goudaroulis, and Pantelis Nicolacopoulos, 47-57. Dordrecht: Kluwer Academic, 1989. p. 51)
"I regard metaphysics as continuous with science. Science gets metaphysical when it gets very general and controversial and relates itself also to humanistic and other non-typically scientific concerns. A criterion for metaphysical truth is plausibility in the light of total science."
(Smart, J. J. C. "Physicalism and Emergence." 1982. In
Essays Metaphysical and Moral: Selected Philosophical Papers, 246-255. Oxford: Blackwell, 1987. p. 248)
The epistemic foundation of empirical science are observations (sensory perceptions) and sentences describing these—observation sentences (Quine), protocol sentences (Neurath), basic sentences (Popper). The body of basic empirical knowledge is extended by means of logical inferences therefrom, there being three main sorts of inference:
"In a deductively valid inference, it is impossible for the premises to be true and the conclusion false. In an inductively strong inference, it is improbable (to some degree) that the conclusion is false given that the premises are true. In an abductively weighty inference, it is implausible that the premises are true and the conclusion is false. The abductive type of inference tends to be the weakest of the three kinds."
(Walton, Douglas N. "Abductive, Presumptive and Plausible Arguments."
Informal Logic 21/2 (2001): 141-169. p. 143)
Assertions, assumptions, or beliefs (
synthetic ones) are purely metaphysical or freely "metempirical" (
George Lewes' term—see below!) when there is no (actual or possible) empirical justification, no (actual or possible) empirical confirmation or disconfirmation (refutation) of them in terms of observational data or logical inferences therefrom. That is, (asserted or believed) propositions which aren't conclusions of any deductively valid, inductively strong, or abductively weighty argument with some empirical, observation-based premises are totally metaphysical or metempirical. What then remains is "anarchic" or "wild", i.e. empirically unconstrained and uncontrolled, philosophizing that is mere speculation or pure conjecture lacking scientific certainty, probability, or plausibility.
"Speculation is seeing with the mind's eye what is not present to Sense or to Intuition. It is ideal construction, and begins with conjecture,—too often, alas! ending where it began." (p. 27)
"…is it not obvious that he quits the ground of Experience to enter on that region where all sensible data and all verifiable inferences vanish? His conjectures on this point may be approximately right or absurdly wrong; no possible means of determining whether they are right or wrong exist." (p. 28)
"The speculative begins where the positive ends; and where the speculative quits the ground of Sense and Verification, the region of the metempirical begins. It is possible to move securely on the ground of Speculation so long as we carefully pick our way, and consider each position insecure till what was merely probable becomes proven. But in the metempirical region we have not even probability as a guide; it is a morass of uncertainty where all footing yields and all tests fail. In this region, conjectures, however fantastic, are as valid as conceptions which seem rational. They maintain their ascendency over the mind which has once admitted them, because being, by the nature of the case, incapable of proof, they are incapable of refutation; they never approach near enough to the truths of Experience for us to show how widely they diverge from or contradict it. Whenever a question is couched in terms that ignore Experience, reject known truths, and invoke inaccessible data,—i.e. data inaccessible through our present means, or through any conceivable extension of those means,—it is metempirical, and Philosophy can have nothing to do with it." (pp. 29-30)
"By way of preliminary I will ask permission to coin a term that will clearly designate the aspect of Metaphysics which renders the inquiry objectionable to scientific thinkers, no less than to ordinary minds, because it implies a disregard of experience; by isolating this aspect in a technical term we may rescue the other aspect which is acceptable to all. The word Metaphysics is a very old one, and in the course of its history has indicated many very different things. To the vulgar it now stands for whatever is speculative, subtle, abstract, remote from ordinary apprehension; and the pursuit of its inquiries is secretly regarded as an eccentricity, or even a mild form of insanity. To the cultivated it sometimes means Scholastic Ontology, sometimes Psychology, pursued independently of Biology, and sometimes, though more rarely, the highest generalizations of Physics. In spite of this laxity in its use, the term is so good a term, and has had godfathers so illustrious, that if possible it ought to be preserved. And it may be preserved if we separate it from its Method, and understand it in its primitive sense as ta meta ta physika, that which comes after Physics, and embraces the ultimate generalizations of Research. It thus becomes a term for the science of the most general conceptions. This is the Aristotelian view of it, adapted to modern thought. It is also in accordance with the scheme of Bacon, which represents Philosophy as a pyramid, having the history of Nature for its basis, an account of the powers and principles which operate in Nature (Physics) for its second stage, and an apex of formal and final causes (Metaphysics) for the third stage. Let us only modify the Baconian conception by substituting "the highest generalization of Research," in lieu of the "formal and final causes," and we have a grand province to bear the ancient name.
But what is implied in this arrangement? That since we are to rise to Metaphysics through Science, we must never forsake the Method of Science; and further that, if in conformity with inductive principles we are never to invoke aid from any higher source than Experience, we must perforce discard all inquiries whatever which transcend the ascertained or ascertainable data of Experience. Hence the necessity for a new word which will clearly designate this discarded remainder,—a word which must characterize the nature of the inquiries rejected. If then the Empirical designates the province we include within the range of Science, the province we exclude may fitly be styled the Metempirical.
The terms Empiricism, Empiricist, Empirical, although commonly employed by metaphysicians with contempt, to mark a mode of investigation which admits no higher source than Experience (by them often unwarrantably restricted to Sensation), may be accepted without demur, since even the flavor of contempt only serves to emphasize the distinction, There will perhaps be an equivalent contempt in the minds of positive thinkers attaching to the term Metempirical; but since this term is the exact correlative of Empirical, and designates whatever lies beyond the limits of possible Experience, it characterizes inquiries which one class regards as vain and futile, another as exalted above mere scientific procedure. Nor is this the only advantage of the term; it also detaches from Metaphysics a vast range of insoluble problems, leaving behind it only such as are soluble.
Thus whatever conceptions can be reached through logical extensions of experience, and can be shown to be conformable with it, are legitimate products, capable of being used as principles for further research. On the contrary, whatever lies beyond the limits of Experience, and claims another origin than that of Induction and Deduction from established data, is illegitimate. It can never become a principle of research, but only an object of infertile debate. The metempirical region is the void where Speculation roams unchecked, where Sense has no footing, where experiment can exercise no control and where Calculation ends in Impossible Quantities. In short, Physics and Metaphysics deal with things and their relations, as these are known to us, and as they are believed to exist in our universe; Metempirics sweeps out of this region in search of the otherness of things: seeking to behold things, not as they are in our universe,—not as they are to us,—it substitutes for the ideal constructions of Science the ideal constructions of Imagination." (pp. 14-6)
"Whether the object of research be Nature, Man, or Society in general, or some special group of their phenomena, we always find it presenting three aspects: 1, the positive or known; 2, the speculative or unknown though knowable; 3, the unknowable. The two first are empirical; the third is metempirical. The two first rest either, 1, on direct Sensation and verified Inference, or, 2, on Intuition and logical deductions from Intuition, which are verifiable by direct or indirect reduction to Sensation. The third rests on no such bases, and is therefore distinguishable from the two former in kind, not simply in degree." (pp. 26-7)
"There is then a rational and an irrational Ontology, and empirical and a metempirical Metaphysics. It is wholly a question of the manner in which the abstractions are formed, and not of the degree of abstractness." (p. 61)
"[W]e may say that understanding by Ontology the science of the abstract laws of Being, it is the science of those highest generalities which emerge from the study of Things, and there can be no difference between Science and Metaphysics except in the degree of generality. In other words, every science has its metaphysic; and our definition of empirical Metaphysics (we recognize no other) will be 'the science of the most general principles'." (p. 62)
(Lewes, George Henry.
Problems of Life and Mind: First Series; The Foundations of a Creed, Vol. I. Boston: J. R. Osgood & Co., 1874.)