Are there indexical facts?

My review of Bill Vallicella's articles on constituent ontology has led me to his category facts, and in particular to  Are There Indexical Facts? Are They a Threat to Materialism?   Here Bill retells Ernst Mach's account of stepping onto an omnibus after a tiring rail journey and catching sight of another man, who looks to Mach like a 'shabby pedagogue', doing just the same.  Moments later Mach realises that he sees his own reflection in a large mirror in the bus.

Here is what Bill says about this:
When Mach got on the bus he saw himself, but not as himself. His first thought was one expressible by 'The man who just boarded is a shabby pedagogue.' 'The man who just boarded' referred to Mach. Only later did Mach realize that he was referring to himself, a thought that he might have expressed by saying, 'I am a shabby pedagogue.'

Clearly, the thought expressed by 'The man who just boarded is shabby' is distinct from the thought expressed by 'I am shabby.' After all, Mach had the first thought but not the second. So they can't be the same thought. And this despite the fact that the very same property is ascribed to the very same person by both sentences. The difference emerges quite clearly if we alter the example slightly. Suppose Mach sees that the man who has just got on the bus has his fly open. He thinks to himself: The man who has just boarded has his fly open, a thought that leads to no action on Mach's part. But from the thought, I have my fly open, behavioral consequences ensue: Mach buttons his fly. Since the two thoughts have different behavioral consequences, they cannot be the same thought, despite the fact that they attribute the very same property to the very same person.

But if they attribute the same property to the same person, what exactly is the difference between the two thoughts?
He goes on to develop an argument roughly as follows:

There is a category of  first-person (indexical) thoughts that is distinct from third-person (non-indexical) thoughts.  These indexical thoughts are underpinned by indexical facts such the fact of DB's being me.  These facts are irreducibly real but not physically real.  Hence materialism, which claims that reality is exhausted by non-indexical physical facts, must be false.

I say roughly above  as  I find Bill's argument rather unclear;  readers will see that I have merely transcribed Bill's final paragraph.  But I would like to make the following comment.

Bill uses Mach's story to drive a wedge between indexical and non-indexical thoughts.   I am a shabby pedagogue is a distinct thought from The man who has just got on the bus is a shabby pedagogue.  Yet, Bill says, I and the man who has just got on the bus refer to the same individual and attribute the same property to that individual.  How then can they be distinct thoughts unless they are underpinned by distinct indexical and non-indexical facts? We have a number of ways open to us to reject this.  I think the simplest and most convincing is to deny that  I and the man who has just got on the bus refer to the same individual.  It's clear from Mach's account that he initially believed that two men got on the bus, himself at one end and another man at the other end.  If Mach spoke his thoughts out loud he would say something like this:  There are two men getting on the bus.  Myself, Ernst Mach, at one end and a second man at the other end.  The second man looks a shabby pedagogue.  This is a perfectly consistent story that could have been told by a third person (forgetting the myself) and that could have been true.  In it, the second man clearly does not refer to Ernst Mach.  If it were to do so the story-teller would be telling us that Mach was in two well-separated places at the one time.  But this is not a piece of magic realism fiction.  It's just a common or garden perceptual mistake with which we are all familiar.  Now one could argue that Mach really is seeing himself and therefore the other man must refer to Mach.  But this would suppose a causal connection between object and speech that was not mediated by belief and left no room for error, and it's clear that Mach believes there to be two men involved.  This belief is supported by Mach's prevailing belief that he is not a shabby pedagogue, whereas the other man is.  Sadly, this belief turns out to be false also.

In conclusion, this line of thought undermines the premise of Bill's anti-materialist argument that there is a distinct category of irreducibly indexical facts.   Bill's piece seems to have another argument for indexical facts which I'm not clear about yet.  So for the time being I will stop here.  More in another post perhaps.

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