Of course, L. had not given me any thought-experiment akin to Galileo's that would make it intuitively clear -- would make it undeniable -- that what 1 + 1 (base 10) equals is relative to a belief or set of beliefs "strongly held" by a group of people. However, I did not pursue the lack-of-overwhelmingly conclusive thought experiment line of attack because L. did not seem to feel the force of it.
But he had given me a theory of truth which I could attack. He had reduced truth to belief. All I had to do now was find some wedge to pry truth away from belief.
L's theory of truth is naturally open to a number of other attacks. He had claimed that God does not exist. Is this supposed to be true in the 'the statement "no omniscient entity such as God exists is true if and only if no omniscient entity such as God exists' sense, or is it supposed to be true only relative to that reference frame provided by that group of people who strongly believe that God does not exist? Relatedly, is his claim that the truth of x consists in a group of people strongly believing that x itself relative?
My strong intuition is that L's theory of truth is vacuous, meaningless if it is itself relative. But I did not pursue this avenue with him because the idea 'vacuous, that is to say, meaningless' is a bit thin, a bit abstract. That L's theory of truth is meaningless if relative does not itself have the strikingly clear force of Galileo's thought experiment. One starts to enter the ozone layer; his head begins to swim a bit.
I could have attacked the 'that God does not exist is relative' claim by asking: suppose a group of nutcases strongly believed that you, L., do not exist? Would it be in any way shape or fashion true that you, L., do not exist?
But I envisaged L. coming back with something on the lines of: 'The concept of L. is highly abstract. L.'s existing is just a supervenient fact emerging from a collection of cells, each one of which is itself a collection of ancient bugs that had ended up associating with one another. Does anything as abstract as L. exist? Well, maybe one group of people strongly believe that it (he) does, and possibly another group of people might strongly believe that it (he) does not; and that is all one can say about the matter.'
So I envisage two things happening if I had launched that line of attack: First, L. would simply cheerfully say: Yes, of course that God does not exist is true for me (and the group of like-minded strong-believing people who agree with me) and false for the fundamentalist and his cohorts; of course that L. exists is true for those of us who strongly believe in personal identities and false for those who are more discriminating in what sorts of abstractions they will accept; of course that truth is relative is true for me (and the group of...etc.) and false for you (and the group of if-and-only-iffists who strongly agree with you). Second, I would beat my head helplessly against the table (either a restaurant table, most of these discussions taking place at lunch, or at the work table I shared with a number of other people) saying God (though I don't believe in You) have pity on me.
I chose a different line of attack.