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questions for a reductive materialist, the one and the many, numerical vs. formal identity

When I entertain the same belief at two different times, it seems that two acts are directed toward numerically one object.

If so, then how does it even seem to be the case that the two different acts are directed toward the same object?

Surely it cannot be through the formal identity of the two: that may (or may not) be a necessary condition, but it is not a sufficient one.  For example, I may do the following:

1. think the same thing twice without reflecting the second time on the fact that I have previously thought it.

In such a case, formal identity might suffice for the sameness of the object of two belief acts.  But something more seems to be going on in the situation that I describe below

2. think not only of the same sort of thought directed toward the same object twice, but also to note the sameness of these two thoughts.

The second case would seem to involve something more than formal identity of the second act with the first--otherwise there would be no difference between the two cases.

One may try to solve this problem by proposing that the something extra found in the case number two a representation of the first act.  But in response to this proposal I must ask, "how does one know that this representation is a representation of the first?

I don't think that one who relies upon inner representation can give a satisfactory answer to this question, for it leads to an infinite regress of representations.

My answer would be that there  must be some way in which we are non-representationally aware of the previous act as directed toward that same as that toward which we are presently directed.

I tend to think that the closer a theory of mind is to reductive materialism, the more it will be beset by the sorts of the problems just laid out.

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