Rodrigues is, I guess, a mathematician or philosopher. I also guess, though more certainly, that he is blinded and confused by his faith. That's not too surprising. Faith is a thing that bogs down the mind with pretending to know things that aren't known and that leads to irrational responses when challenged epistemically.
G. Rodrigues, addressing and then quoting me:
@James Lindsay:It seems like a good time to put this here, since Tom Gilson and crew are so fond of definitions.
Axioms are statements taken to be self-evidently true. Establishing the soundness of an axiom really means establishing that we have good reasons to call such a thing self-evident.(1) Stop using words of which you quite obviously do not know the meaning of. Only deductions are valid or sound, not statements and certainly not axioms.
|Axiom: n. 1. a statement or proposition that is regarded as being established, accepted, or self-evidently true|
(2) Axioms can be argued for dialectically, but they are not proved, at least not in the usual sense of the word.Sigh. No joke. See the definition. They can also be utter nonsense, but that doesn't make them worth using. It seems that he's saying that we have no way to judge these things, though, and that seems positively weird.
(3) A minor quibble, but in the technical sense, no, an axiom is not a statement “taken to be self-evidently true”."Taken" as in "treated as if." So, yes, it is. See the definition.
(4) If a statement is self-evident, then there is nothing to establish. That is kinda the point of the “self-evident” qualifier…Sigh. No joke. "Taken" as in "treated as if," as in I didn't say that they're self-evident.
(5) And no, “establishing an axiom” does not mean “establishing that we have good reasons to call such a thing self-evident”. First, there are axioms which are accepted and are far from being self-evident. Second, a statement may be deemed “self-evident”, but if someone disputes its self-evident status what this usually means is that said someone is really disputing is the truth of said statement. But in that case, it does nothing to advance the discussion to establish “that we have good reasons to call such a thing self-evident”; it accomplishes exactly nothing.See below.
IOW, what the heck are you talking about?
G. Rodrigues (initially quoting me):
I actually agree. It's probably not a hypothesis. It's more than likely an axiom. That means it, meaning God here, is abstract. That's a gigantic point of my book Dot, Dot, Dot. What does it assume? Everything you think is true about God. That's how the axiom works. The superfluous stuff is everything that used to be God's province (usually for giving explanations) that can now be explained without a God. "I have no need for that hypothesis," or something like that.The God hypothesis simply assumes a lot of stuff (much of which has been shown to be superfluous) and thus really teeters on the far side of being self-evident.Huh? The existence of God is not an “hypothesis”, certainly not in the sense of a scientific hypothesis. And assumes a lot of stuff? What does it assume? What superfluous “stuff”? How does an *hypothesis* *assume* anything other than what it purports to explain? And since what is in discussion is precisely whether God exists or not, who the heck is claiming anything about “self-evident”? In God’s name, from where are you pulling this much crap?
Speaking of hypotheses, God's existence can be treated like a hypothesis, though, if one doesn't accept the theological axiom that "God exists" (more on this below). Such a treatment isn't favorable to his beliefs, so he's better off keeping it as an axiom, except that that shows that his God is abstract. Yikes (for him).
G. Rodrigues (initially quoting me):
Fascinating. People are truly fascinating.Why, by the way, do you assume that proving God exists must be different than proving something physical, say a keyboard, exists?Hmmm, I don’t know. Maybe because God, if He exists, is not “physical”, and thus the method of proof employed is necessarily different from that of proving the existence of physical things? Just a random thought. But hey, we are the ones pretending to know what we do not know, so what do we know about proving what we pretend to know what we do not know? For all I know (and I am just pretending), we are pretending all the way down, even to the level of pretending we are pretending.
Can Rodrigues prove God isn't physical, or is this part of his axiomatic construction of him? There are lots of questions here, actually, like: what does all of this non-physical stuff even mean, apart from God being an abstraction? Note, by the way, that everything else we call non-physical and eternal is an abstraction (the universe, even if eternal, is not exactly non-physical). There are also the usual suspects like: how would such a God interface with the physical if he is strictly non-physical, or, as an abstraction does God just not do that kind of thing? Slightly less random thoughts, I suppose.
I lament his sarcasm in his admission about pretending to know, as he is indeed pretending to know things he doesn't know. I don't really know a lot about what he pretends to know but does not, or at least I wouldn't, but these guys talk about and write about it a lot, so I have some inkling as to what kinds of things they think they know but do not. We could start with God, but that's their bag.
I will say, though, that he has given us an interesting take on the nuclear option--"pretending all the way down." (This can be identified with what philosopher Stephen Law called Going Nuclear in that it could be used to level all arguments to the level of pretending to know.) It might be true, in the strict philosophical sense, but it's stupid, useless, and offered in poor faith. Rodrigues almost surely doesn't write, act, or think as if he believes it's true, so let's just pretend he didn't say it to spare him that embarrassment.
G. Rodrigues (initially quoting me):
I wonder: can he prove that God necessarily must be immaterial and nonphysical? Can he do it without exposing God as an axiomatic abstraction, like every other immaterial and nonphysical thing? Good luck to him.Is it because you’ve taken on faith that God is immaterial and nonphysical?It is not taken on “faith”, (if you are using “faith” in the same disingenuous, intellectually dishonest sense Boghossian is) but follows logically by what God necessarily is if He exists.
G. Rodrigues (initially quoting me):
See below.If so, I’ve already covered that issue: it’s not possible to conclude that God exists because, at best, the prior plausibility for the hypothesis is indeterminable.Of course you did (smile). But if you actually did that (giggle), what you did was establish that “it is not possible to establish that God exists”, not anything about whether He is immaterial, which He must be if He exists. And if you did that (laugh), please enlighten us, what are the prior probabilities of the *assumptions* you used in the proof? And if you actually did that (laugh out loud), why do you think we should be worried by it? Since the best arguments for God’s existence are *deductive* arguments, whether or not you have established that the prior probability is “at best” (??) “indeterminable” (roll on the floor laughing) is absolutely irrelevant.
This is too ridiculous for words.Indeed, but I think he has misidentified the antecedent of "this."
Below, which is to be seen, a la "see below":
Of course there are axioms that are used but aren't actually self-evident. And they're argued about, particularly with regard to their soundness, or, if we want to be more precise and careful, their grounding, i.e. whether or not we should take them seriously or use them for anything.
As an expert in these things, Rodrigues is no doubt familiar with the Axiom of Infinity, for instance, which is certainly not self-evidently true, but for the purposes of doing certain kinds of mathematics is taken to be "self-evidently true" (without requiring outside justification) in practice. To do mathematics that requires it, we have to assume it, and for math, that's good enough justification to be getting on with. Of course, math--even by its own admission--isn't exactly tethered to making only salient claims about reality. (NB: We might expect it is sort of "evident" because, for instance, the Peano Axioms of number theory suggest that it might be something important, though they certainly don't establish its truth--see Dot, Dot, Dot for more information.)
The core theological axiom (really axioms, plural, because it's unlikely that any two believers agree on what theirs mean, at bottom, in all the details) is that God exists. It's a philosophical axiom, not a mathematical one, of course. It carries with it all kinds of interesting premises like that this "God" is a "necessary agent cause of contingent reality" or that "God is the source of objective morality" or that "God is an omnipotent, omniscient, omnibenevolent, perfect entity." None of this is self-evident. It's just the definitions (often apparently made ad hoc after less abstract and more mundane conceptions of God get thrashed) that theologians employ in their God-axiom, largely to win enough debates to get to keep talking about this nonsense, so far as I can tell, though impressing the credulous seems to be a part of it as well.
But before we get too far afield, let's come back to the Axiom of Infinity. Note that there are some people (finitists) who reject that axiom, saying it's insufficiently grounded (because we cannot complete the construction of an infinite set) to use in mathematics. These people have done more than complain too! They've gone through the substantial trouble of proving a huge swath of the important theorems of mathematics without it--which in many cases can be identified with doing math in Hard Mode. (They argue essentially all of mathematics that isn't directly about infinity and much of what is can be done without accepting the Axiom of Infinity.)
Maybe the finitists are right--perhaps math can be better captured without requiring an axiomatic acceptance of the actually infinite. Similarly, maybe the axiom(s) that God exists are also superfluous--here, perhaps the fundamental nature of reality is better captured without requiring the axiomatic acceptance of some "necessary agent cause of contingent reality," who happens to be multiply omni-able and the source of objective moral values and ultimate teleology and available to have a personal relationship with everyone who wants it. Just maybe. What with all this inability to establish God outside of believing in God first (that challenge/invitation remains open), God smells awfully axiomatic, but I'm open to solid evidence of the kind Rodrigues says doesn't exist that proves me wrong about that.
Some of us don't treat "God exists" as a valid axiom. Because God is said to interact with the world, that renders the matter salient enough to treat "God exists" as a hypothesis instead of an axiom. Doing so allows us to analyze the question differently. In one way, we can analyze such a hypothesis in a Bayesian manner, which has stood up extremely well in practice when we want to properly assess how confident we can be in a particular claim or claims.
But how would someone assess the plausibility that a God hypothesis is true? The only evidence we have for God quite plainly requires us to look at the evidence via acceptance of the beliefs first! This is really a case where if we wished to do a Bayesian analysis, we have no salient starting point (see chapters 12 and 13 of Dot, Dot, Dot, again).
So, we can either pick some prior willy-nilly or we can admit that when treated as a hypothesis, one cannot be assigned. In the willy-nilly case, there is no way to justify any choice of prior.
(Only almost certainty in one direction or the other can be defended, both values rejected in strict Bayesian analysis. Also, there are very good reasons why almost certain existence is a bad choice--as it could then apply to any fictional thing as well. I argue in Dot, Dot, Dot that almost sure non-existence isn't an automatic death-knell for a hypothesis too because almost sure evidence could potentially overcome it in an application of Bayes's Theorem. Note also that we usually take the position that having to produce almost sure evidence of non-existence, which we would require if we chose almost sure existence instead is on the wrong side of the burden of proof for any existence claim.)
In both cases, the growing body of evidence--slowly chipping away at that which God has traditionally been necessarily responsible for--suggests that such a hypothesis is unnecessary. In fact, this has been a universally one-way street. No scientific explanation has ever been replaced by a theological one, but theological ones have been replaced every time science has touched them (when they're falsifiable). That means in both cases, a Bayesian assessment of God's existence as a hypothesis renders a negligibly low plausibility for accepting it as true.
Rodrigues's way out of this is (a) to mock me and (b) to double-down on the axiomatic conception--God is non-physical, beyond time, beyond space, outside the universe, and so on. Okay, fine. Whatever. He can have it his way. God is an axiomatic, thus abstract, construction. Thanks for doing the heavy lifting for me. Nice abstraction he's got there.
Of course, that Bayesian assessment I mentioned, though, still casts serious doubt on the groundedness of that axiom if we want to say it pertains to the real world. This turns out also to be true of the Axiom of Infinity, which gets some pretty serious fire, especially from finitists, by considering the apparent paradoxes of physical infinities and the real possibility that there are no physical infinities. Mathematicians avoid this problem with honesty: infinity is (very probably just) an abstraction, not real. Move on.
Now perhaps God is really just meant to be an abstraction--an idea in the human mind--what else are we justified in thinking about it? Again, as the idea of God grows increasingly superfluous as an explanatory mechanism, it gets harder and harder to justify accepting any philosophical position that relies upon it.
And I did all of this without even having to point out that Rodrigues has effectively just argued that his God is unfalsifiable, meaning it's a notion beneath taking seriously.
Now, I think, would be a good time to pick yourself up off the floor, Rodrigues.
Editorial note, a few hours later: I originally published this in a slight rush and thus have edited it slightly for grammar and clarity since.