Since no one can tell me what this non-physical stuff is even supposed to be, it would be ridiculous for me to claim to believe in it. So I'm left with believing the stuff I can observe and understand (the physical) and leaving the undefined something or other as an open question until we even know what it is we're talking about.
Uh huh. I think you're being a bit unfair. And, to be honest, I don't see anyone really trying that hard. Since neither of us is the OP, we can both say we haven't really made a claim. But, if someone is going to take a physicalist position, they need to define what "physical" is just as much as those taking the dualist position must define what "non-physical" is.
I've been reading some interesting papers on this recently ... all the more interesting in the way they parallel this conversation. It seems that even though all of us appear rather uneducated on the subject of physicalism, we're reinventing conversations from the professional literature in a rather admirable way.
First, there is a PhD thesis by Katalin Balog that does a very good job of dismantling all the dualist arguments. While that is the case, what remains when she is done (as she herself admits) is that even if dualists haven't proven the non-physical, neither have physicalists proven physicalism. Since the non-physical is conceivable, it remains possible.
In line with Balog there is an essay by Quine called
On What There Is. It's main purpose is to address a dualist argument that simply by saying "X does not exist" the physicalist admits X. I always thought that argument a bit silly, and Quine does away with it. But even more interesting, he goes on to argue things like: If a physicalist concedes, "That person has blue eyes," and "That house is blue," they have not admitted a metaphysical idea of "blueness." I can see his point, but his argument leaves me dissatisfied. To be honest, I find it a bit disingenuous. It smacks of a position that my opponent can agree with my conclusion (e.g. that a person has blue eyes) without revealing the path that led them to that conclusion such that I am not allowed to criticize them. IOW, it feels a bit like information hiding. Further, if you read Quine's definition of physical (in another essay called
Whither Physical Objects) it comes across to me as almost unintelligible.
With that said, having my instrumentalist view of science, I do sympathize with the types of arguments being made against the existence of number. I really like the argument made by Field in
Science Without Numbers that numbers provide a "conservative" account of science rather than explaining exactly what is.
All of this leads up to what I consider the masterpiece of this whole discussion - an essay by Markosian called
What are Physical Objects? In that essay he expresses my frustration that for all ink spilled on this subject, all the above authors never really define what they think physical is. Rather, they just seem to be playing games with language. Markosian gives 5 definitions of physical:
1) Spatial Location (which is the one Markosian defends)
2) Spatial Extension
3) Physical Theory
4) Sensational
5) Common Perception
The one most "physicalists" (if I can call you that) in this thread have been arguing is a combination of 3 and 4. His rejection of these positions is much the same as mine. #3 is circular and #4 is dependent on the individual.
He gives a long list of objections to #1 and tries to defend them. While it is an admirable job, I'm not sure he succeeds. What I like so much about his essay is the clarity he brings to the subject.
What I have been arguing is probably similar to #5. Markosian's objection to that position is that it is not precise enough, and I would agree. But after thinking about it, I believe it could be rescued by paring it down and integrating with #2.
Finally, with respect to number, I've been wrestling an idea that finally seems to be firming up. It always seemed to me that number must be a property in some sense, but I didn't have a good answer to arguments against that idea. At the same time, I've never liked the Platonist idea that number exists as an object - as a Form. So, briefly, I think what I would say is that number
is a property - a property of a set. In that sense, sentences like 1 + 1 = 2 are not statements about numbers, but statements about "thing" in the most general sense. The sentence would be "When a set of 1 thing is added to another set of 1 thing, it becomes a set of 2 things." My reaction to that is: surely someone has thought of that before. But if so, who? I'd like to know. If they have, there must be a problem with that idea that I'm not seeing because current philosophers of mathematics are off in the weeds talking other obtuse ideas about number.
Regardless, if we can satisfacorily move past this preamble, we can start to discuss some examples I have in mind for the non-physical to see what they might produce.