How ubiquitous, yet how strange, is sameness! A structure of reality so pervasive and fundamental that a world that did not exhibit it would be inconceivable.
How do I know that the tree I now see in my backyard is numerically the same as the one I saw there yesterday? Alvin Plantinga (Warrant and Proper Function, Oxford 1993, p. 124) says in a Reidian vein that one knows this "by induction." I take him to mean that the tree I now see resembles very closely the one I saw yesterday in the same place and that I therefore inductively infer that they are numerically the same. Thus the resemblance in respect of a very large number of properties provides overwhelming evidence of their identity.
But this answer seems open to objection. First of all, there is something instantaneous and immediate about my judgment of identity in a case like this: I don't compare the tree-perceived-yesterday, or my memory of the tree-perceived-yesterday, with the tree-perceived-today, property for property, to see how close they resemble in order to hazard the inference that they are identical. There is no 'hazarding' at all. Phenomenologically, there is no comparison and no inference. I just see that they are the same. But this 'seeing' is of course not with the eyes. For sameness is not an empirically detectable property or relation. I am just immediately aware -- not mediately via inference -- that they are the same. Greenness is empirically detectable, but sameness is not.
What is the nature of this awareness given that we do not come to it by inductive inference? And what exactly is the object of the awareness, identity itself?
A problem with Plantinga's answer is that it allows the possibility that the two objects are not strictly and numerically the same, but are merely exact duplicates or indiscernible twins. But I want to discuss this in terms of the problem of how we perceive or know or become aware of change. Change is linked to identity since for a thing to change is for one and the same thing to change.
Let's consider alterational (as opposed to existential) change. A thing alters iff it has incompatible properties at different times. Do we perceive alteration with the outer senses? A banana on my counter on Monday is yellow with a little green. On Wednesday the green is gone and the banana is wholly yellow. On Friday, a little brown is included in the color mix. We want to say that the banana, one and the same banana, has objectively changed in respect of color.
But what justifies our saying this? Do we literally see, see with the eyes, that the banana has changed in color? That literal seeing would seem to require that I literally see that it is the same thing that has altered property-wise over the time period. But how do I know that it is numerically the same banana present on Monday, Wednesday, and Friday? How do I know that someone hasn't arranged things so that there are three different bananas, indiscernible except for color, that I perceive on the three different days? On that extraordinary arrangement I could not be said to be perceiving alterational change. To perceive alterational change one must perceive identity over time. For there is change only if one and the same thing has different properties at different times. But I do not perceive the identity over time of the banana.
I perceive a banana on Monday and a banana on Wednesday; but I do not visually perceive that these are numerically the same banana. For it is consistent with what I perceive that there be two very similar bananas, call them the Monday banana and the Wednesday banana. I cannot tell from sense perception alone whether I am confronting numerically the same banana on two different occasions or two numerically different bananas on the two occasions. If you disagree with this, tell me what sameness looks like. Tell me how to empirically detect the property or relation of numerical sameness. Tell me what I have to look for.
Suppose I get wired up on methamphetamines and stare at the banana the whole week long. That still would not amount to the perception of alterational change. For it is consistent with what I sense-perceive that there be a series of momentary bananas coming in and out of existence so fast that I cannot tell that this is happening. (Think of what goes on when you go to the movies.) To perceive change, I must perceive diachronic identity, identity over time. I do not perceive the latter; so I do not perceive change. I don't know sameness by sense perception, and pace Plantinga I don't know it by induction. For no matter how close the resemblance between two objects, that is consistent with their being numerically distinct. And note that my judgment that the X I now perceive is the same as the X I perceived in the past has nothing tentative or shaky about it. I judge immediately and with assurance that it is the same tree, the same banana, the same car, the same woman. What then is the basis of this judgment? How do I know that this tree is the same as the one I saw in this spot yesterday? Or in the case of a moving object, how do I know that this girl who I now see on the street is the same as the one I saw a moment ago in the coffee house? Surely I don't know this by induction.
How then do I know it?