Philosophy is a strange subject in that its name suggests that it isn't a subject at all, but rather an affection: the love of wisdom; and yet, philosophy is also viewed as the parent of all theoretical knowledge. What then is the relation between wisdom and knowledge? Perhaps it is right to insist that the wise distinguish what they know from what they do not know. Broadly, the purpose of this project is to explore this suggestion.
Socrates was the first Western thinker to maintain something like the view that philosophers can distinguish what they know from what they do not know. In Apology Socrates reports that he consulted one who had a reputation for his wisdom, but that "in the process of talking with him and examining him," Socrates was driven to the conclusion that his companion wasn't wise at all. In fact, Socrates congratulates himself, because although he thinks that he doesn't know anything much worth knowing, at least he doesn't think that he knows something worth knowing.
So, I left him, saying to myself as I went away: Well, although I do not suppose that either of us knows anything really worth knowing, I am at least wiser than this fellow--for he knows nothing, and thinks that he knows: I neither know nor think that I know. In this one little point, then, I seem to the advantage of over him. (1) (Plato/Jowett, Apology, 21df, p. 345)
Ironically, Socrates seems to imply that there is at least one thing worth knowing, and that is knowing that one doesn't know anything (else?) worth knowing. Irony is achieved by using a fragment of language to assert or designate the exact opposite of its literal meaning. I suppose, if anything is bad news, it is that no one really knows anything worth knowing.
The ironic response to Socrates' narrative surely is the current cliche: "Good to know."
The Socratic Paradox: On a Grand Scale
The above passage from Apology has given rise to a series of puzzles collectively designated as the "Socratic Paradoxes." Indeed, if one really knows nothing worth knowing (or perhaps doesn't know anything at all) but thinks that one knows, one must be seriously mistaken about what knowledge is or what it takes to get it. Imbedded is a crucial distinction between being aware of a given proposition and not knowing whether it is true and believing that there might (or even must be) some factor that is relevant to knowing that proposition, but not knowing what that factor is, or else what to make of it. Issues of this sort arise in epistemology and metaphysics, in natural science, in analysis of personal introspection and in the statistical analysis of significant empirical correlations.
Newton and his successors knew that the "wobble" in the precession of the perihelion of Mercury's orbit around the sun posed a threat to Newton's own unified account of terrestrial and celestial motion. One might attribute the deviation to some sort of intervention by God or perhaps to the gravitational attraction of a hitherto unobserved object (which was tentatively named "Vulcan." during the 19th century). Yet for over 200 years no one suspected or could have even conceived that the explanation for Mercury's misbehavior lay hidden in the presupposition of Newtonian science that space is "absolute." Unfortunately for Newton, Einstein demonstrated that the geometry of space depends upon the presence of mass. Although space emptied of all mass would be Euclidean, actual space is Riemannian, meaning that Euclid's Fifth Postulate is false of actual space, where straight lines within a plane do not have parallels. It is therefore the "deformation" of space due to the mass of the sun that accounts for the "wobble" in the precession in the perihelion of Mercury. (2)
Sometimes the impossibility of knowledge of specific facts is a consequence of scientific theory itself. For example, a consequence of the Special Theory of Relativity, which treats of non-accelerating inertial frames, is illustrated by Makowski's famous space-time diagram, which illustrates the fact that space and time are not independent and as a consequence much of the universe is inaccessible to us. (3) Another obvious example comes from Heisenberg, who demonstrated that it is impossible to determine the momentum and position of certain small entities, like electrons. (4) More recently Stephen Hawking suggested that despite evidence to the contrary, "information" apparently lost as events are gobbled up by black holes is nevertheless stored (somehow) at the event horizon itself. (5)
These examples are extremely important from a philosophical point of view because they show that even the most certain theories can turn out to be false. The most important of these cases mentioned above is Euclidean geometry. For two thousand years philosophers thought that Euclidean geometry was the paradigm of a successful theory of the structure of physical space. Descartes, for example, thought that any theory as certain as Euclidean geometry was surely beyond doubt. The fact that that the finest minds were mistaken about the structure of physical space ought to give us pause. We all believe the deliverances of the best minds of our time, but mightn't they be mistaken? Perhaps we do not have a reason now to doubt the great theories of our time, but that might be only because we are unaware of pertinent data. All this is to say that we cannot assess the epistemic importance of information that we do not have, and, by hypothesis, we do not know just what information that might be.
Worries about mathematical physics are troubling enough, but there are still grander questions. The questions of theoretical science do not challenge our capacity to know. Irony arises at this level as well, most explicitly and famously in Descartes, Pascal and Hume. Descartes wonders whether all putative knowledge is undermined by an evil force so that even the most certain of beliefs systematically mislead us about the world and even about ourselves. Only God, Descartes insists, can extricate us from systemic doubt. (6) Yet as most commentators have insisted, we can hardly know that God rescues us from doubt without knowing that God exists, and we can hardly know that God exists unless we already know that God has given us reliable tools that will rescue us from doubt about our powers to know.
One way in which Descartes was misled (indeed the most important way in my view), is that Descartes assumed that mathematics is the unshakeable foundation of physics. According to Descartes we clear and distinctly perceive the attribute of extension, which is the essence of matter, and therefore the mathematical truths about extension must describe the physical space in which matter is located. So, for Descartes, whatever is necessarily true of extension applies, mutatis mutandis, to matter and the space it occupies. Since we "know" that Euclidean geometry is necessarily true of extension, it must be necessarily true of physical space as well. As we have seen above, however, Einstein successfully argued that matter, (though extended) and the space that it occupies are not Euclidean, but rather are Riemannian--meaning that straight lines in the neighborhood of mass do not have parallels.
Pascal, who was reasonably threatened (intimidated?) by thoughts of the "infinite," accepts the idea that the grand questions of philosophy are imponderable.
Pascal claims that it is incomprehensible that God should exist, and incomprehensible that he should not; that the soul should exist in the body, that we should have no soul; that the world should be created, that it should not; that original sin should exist, and that it should not; etc. (7) Yet, Pascal concludes that one inescapably lives either on the basis of the existence of God or does not live on the basis of the existence of God. Arguing that the payoff for a correct bet on the existence of God is eternal bliss and that an incorrect bet against the existence of God is eternal damnation, Pascal concludes that the only wise course is to take a chance and go "all in" for God. (8)
There have been many objections to Pascal's line of reasoning about how to wager assuming that one "must" wager. Do we really know that the consequence of an incorrect choice is eternal damnation and of a correct choice eternal bliss? Isn't that very claim also open to open to Socratic doubt? Perhaps the right conclusion is that we just do not know how to choose. Perhaps Pascal concedes as much inasmuch as he insists that we "know" of God's existence only through faith. For many, however, that is just another way of saying that we really do not know at all; perhaps that is what Socrates would have said in response to Pascal.
Hume argues famously that our capacity to make simple predictions is flawed in that predictions presuppose that past and present are connected or related in a way that assures us that the future will continue to resemble the past. But knowledge that the future will resemble the past can be inferred from past successes only if we already know precisely what we do not know, which is that the future will continue to resemble the past. There is an additional and even deeper problem, which is that we cannot ever be certain that we have all the evidence that is pertinent to a given knowledge claim or even that what has counted as pertinent evidence in the past will continue to be counted as pertinent evidence in the future. To summarize: We do not and cannot know that we have all the pertinent evidence to support a claim about the future, but even if we did know that in the past we had all the pertinent evidence, we could not infer that what was then pertinent evidence is still pertinent nor could be infer that facts that were not pertinent in the past would not become pertinent. (9)
The Retreat to Probable Knowledge and Statistics
Perhaps all this goes to show only that our assertions need to be qualified in order to count as...