I defend objective synthetic a priori truths instead of, like Kant, truths that are mentally imposed and do not apply to things in themselves. I observe that synthetic a priori truths are not, like analytic truths, based on linguistic stipulations. Then I argue among other things that mathematical truths are synthetic a priori instead of analytic and that there are synthetic a priori truths about the numerous similarities and differences of phenomenal space and time. I also make the more controversial claim that it is a synthetic a priori truth that the relation that unifies experiences diachronically does not require them to be qualitatively appropriate to one another. As I use the term something is metaphysically possible if it is not a synthetic a priori truth that it is impossible. I argue that while the notion of subsistence as timeless existence is incoherent, propositions may be accommodated as metaphysical possibilities of thoughts, universals as metaphysical possibilities of determinable qualities, and numbers as metaphysically possible properties that may be assigned to groups of objects determined by our interests in dividing the world. I grant that our apprehensions of synthetic a priori truths are not infallible, though we are less likely to be mistaken than we are about empirical questions.
It is certainly true that Kant coined the term “synthetic a priori”. However, Locke had already introduced the notion by the distinction between trivial and significant a priori truths, and still more important, unlike Kant, he regarded such truths as objective rather than mentally imposed and limited to phenomena. In addition, I shall say that p is metaphysically possible if it is not a synthetic a priori truth that p is impossible. For something to exist it must be logically possible, metaphysically possible, physically possible, and in accord with the actual state of the world.
We ascertain synthetic a priori truths by finding their denials logically possible but inconceivable. Finding something inconceivable is sufficient to show that it couldn’t exist as in the case of an unextended colour. If instead lack of familiarity keeps us from conceiving of something, it is, to coin a term, unconceivable rather than inconceivable, and it may or may not be metaphysically possible. First, I’ll add to the defence of such truths by providing two more examples whose sole interest is their epistemic status. Then I’ll turn to examples that do strike me as interesting.
A second simple example of the kind that is not interesting is the statement that everything with a shape must have a size. A third is Russell’s observation that it is logically possible but impossible a priori for a surface to be red all over and also green all over. I turn next to examples that strike me as interesting.
1. Propositions as timeless possibilities of thoughts instead of as subsistent thoughts
Propositions are sometimes rejected on the grounds that they are not ontologically acceptable. This objection would be justified if Frege were right in thinking that they would be subsistent thoughts since the notion of timeless existence is incoherent. Existence cannot be timeless: nothing can exist without having a temporal location, whether limited or eternal. Also, as Frege acknowledged, it is hard to see how we could grasp subsistent entities. Nevertheless, these objections to subsistence do not apply to propositions construed as timeless metaphysical possibilities of thoughts.
Furthermore, it is a major advantage of the view that propositions are timeless possibilities of thoughts that propositions can be true without being instantiated in actual thoughts. It enables us to justify among others the commonly accepted view that there were truths before there were creatures capable of apprehending them. Furthermore, propositions can be true even if, as Thomas Nagel has noted in regard to the nature of bats’ sensory experiences, it is physically impossible for us to apprehend them. We should, of course, limit our investigations to truths that we can apprehend, but we should also retain the distinction between truths in general and truths that we can apprehend instead of conflating the two notions. Otherwise, among other disadvantages, it would be contradictory to hold that there are truths that we cannot apprehend.
A further advantage of this account of propositions is that it supports our belief that whenever something happens it is true that it happens, that it will always be true that it happened, and that this even applies to such insignificant events as the movement of a single grain of sand.
2. Propositions and the defence of analyticity
Still another advantage of this account of propositions is that it can be used to defend analyticity against the objection to that sentences that seem to be analytic may be used in ways that do not make them analytic. For while this is true, it can be responded that we can either make it clear that we intend to use them in a way that makes them express analytic propositions, or else simply rely on conversational implicatur to do so.
3. The synthetic a priori and the defence of Euclidean geometry
The synthetic a priori can also be used to defend Euclidean geometry against the objection that there are no straight lines. For while there are ample grounds for holding that it is true that such lines do not exist, they are metaphysically possible, and there are synthetic a priori truths about them despite the fact that their physical impossibility prevents precise applications to the real world.
4. Universals as metaphysical possibilities of sets of determinable qualities
Universals can be accommodated as metaphysical possibilities of classes of qualities. Some philosophers accept universals as subsistent entities. Others see the incoherence of the notion of subsistence as timeless existence but accept them as a pragmatic fiction. Still others simply reject universals. Fortunately, this gives us an account of universals that is severed from these problems.
5. The ontological status of numbers
Numbers can be accommodated as metaphysical possibilities of numerical properties that can be assigned in terms of our interests in dividing the world into objects or events, and the same holds not only for our interest in numbers but our interests in other kinds of abstract entities. This avoids nominalists’ requirement for actual objects, intuitionists’ doctrine that abstract entities exist but only insofar as they are created by human concepts, the incoherent view that numbers are subsistent entities, and formalism the view that there are no numbers, so that while the use of numbers may be helpful number theory does not provide literal truths.
6. Mathematical truths as synthetic a priori instead of analytic
Numbers can, of course, be defined in a way that makes mathematical truths analytic, but construing them as analytic implies that they are only based on linguistic conventions, which leaves us free to pick and choose between different conventions. We should instead recognize that such truths as that 1+1 equals 2 are synthetic a priori and that it would be redundant to also make them analytic. Moreover, mathematical truths strike us as self-evident when we first learn them regardless of whether we have learned conventions that would make them analytic.
7. Synthetic a priori truths about the similarities of phenomenal space and time
Though there are also differences between phenomenal space and time in order to keep the paper short I only consider the similarities.
Please bare it in mind that I use a number of spatial terms including “location”, “distance” and “movement” metaphorically in ways that also apply to time and that, since I am concerned with phenomenal space and time, I omit “phenomenal.”
Phenomenal shared features
1. X is a location if it has the following features:
a. It is numerically distinct from other locations.
b. It can be occupied by objects and events.
c. It makes its occupants numerically distinct from other objects and events.
d. Its relation to other locations does not depend on their occupants. For instance, the relation of one time to another does not depend on what happens at those times.
e. Locations are distant rather than adjacent if there are intervening locations, in one case temporal, in the other spatial.
f. Both temporal and spatial locations may be at various distances from one another.
2. Movement in time, like movement in space, is from one location to another. Movement is away from a given location if it increases the distance from that location.
3. Neither spatial nor temporal locations move through a series of locations. Since an instant is itself a temporal location, this would require a location to have a location and lead to an infinite regress. The same holds for spatial locations. Both spatial and temporal locations are locations for events, not for locations.
4. Space and time cannot have boundaries. Time would not end if there ceased to be events, nor would there be an end to space where it ceased to have occupants. Suppose that all objects fell within a given space, say a sphere determined solely by the presence of objects within it. Instead of ending with the outermost objects there would still be space into which they could expand. If there are “boundaries” they are imposed by something—perhaps a central force—that prevents further expansion. But this would only mean that the expansion was physically impossible, not that there would be no space for expansion.
5. Neither time nor space requires changing occupants. Time is only contingently correlated with changes including the rate of change in clocks. We rely on the physically plausible assumption that their rate of change is constant, but it is metaphysically possible for there to be a sudden and systematic shift to a faster or slower rate of change that extends to the various devices we use as clocks.
Turning to physics, although it is impossible to determine that a pair of distant events are simultaneous, the factors that make it impossible to determine that they are simultaneous do not show that they cannot be simultaneous. Furthermore, the alternative to the acceptance of distant simultaneity is the astonishing view that every event is either before or after every other event in the universe.
And while time without events and space without occupants would, of course, be beyond its scope: physics requires measurement and measurement would be impossible. But ontological inferences based on the limits of measurement are to say the least questionable. Furthermore, even for physics it is difficult to account for an expanding universe without empty space for the expansion. And those who hold that space cannot extend beyond objects still need to account for space between objects, and it would be hard to do so without granting that it can extend beyond objects.
An alternative is to shift to the Kantian doctrine of noumena and hold that physical space is completely different from phenomenal space. But the shift would be ad hoc since, unlike Kant, physicists do not hold that there are no respects in which physical objects resemble our perceptual experiences of them.