Tarski Spinoff: God, Dawkins and Logic

[_EAllusion]

I had Swinburne's natural theology in mind when I wrote that because of the reference to him in the OP. There are too many flavors of major classes of theistic argument to unpack them all, but I think the broad categories of cosmological arguments, cosmic and biological design arguments, moral arguments, arguments from miracles, etc. are quite bad. I think the same is true of a priori arguments, but I find them at least more interesting (especially Alston-style epistemic arguments) and useful. I don't think the inductive arguments for God collectively add a little evidence here and there until they tip the scales. And, in a twist of your post, I think the mere existence of a diverse array of bad evidential arguments so widely accepted as the best case for justifying theism by top theistic thinkers is an indicator that there's no good arguments available.

[_Tarski]

I want to think on this for a bit. At first blush, I want to say that the conjunction of A0-2 would entail C:

Γ = {There is a universe X that contains only a line of equally spaced glowing cubes stretching out from some point Y in direction Z is a denumerable ordered set. The first cube glows red. Consecutive cubes glow the same color as each other.}

S1 = There is a universe X that contains only a line of equally spaced glowing cubes stretching out from some point Y in direction Z is a denumerable ordered set. The first cube glows red. Consecutive cubes glow the same color as each other.

S2 = Every cube glows red

OK, I am glad that you feel that A0, A1, A2 implies C. From that I want to get to my next move....

but wait!
??
What is all this about Γ, S1, S2? What are you getting at? Is this supposed to be a reformulation?
I better not move on until I figure out what that was all about.
S1 appears to be a conjuction of statements--not sure what the point of combining them is.
But your conjuction S1 does implies S2 does it not? It is essentially that A0, A1, A2 implies C.
What is Γ as compared to S1? Do the braces mean something here?

[_MrStakhanovite]

S1 appears to be a conjuction of statements--not sure what the point of combining them is. But your conjuction S1 does implies S2 does it not? It is essentially that A0, A1, A2 implies C.
What is Γ as compared to S1? Do the braces mean something here?

Sorry, the gamma is baggage from my modal days. The Gamma and Brackets are just part of the process I’m using to trying to envision entailment, which is a very strong logical connection. When someone says if P then Q, they are saying all of Q is contained in P somehow.

The brackets represent a number of statements, S1 is a conjunction of all those statements with in the brackets, and S2 is not in the bracket. To make sure S2 is entailed by S1 (or Gamma for that matter), I check to see if the negation of S2 and S1 are inconsistent.

I’m ready to move on to the next step. Right now, I’ll agree that the argument has the strength of MP.

[_Tarski]

S1 appears to be a conjuction of statements--not sure what the point of combining them is. But your conjuction S1 does implies S2 does it not? It is essentially that A0, A1, A2 implies C.
What is Γ as compared to S1? Do the braces mean something here?

Sorry, the gamma is baggage from my modal days. The Gamma and Brackets are just part of the process I’m using to trying to envision entailment, which is a very strong logical connection. When someone says if P then Q, they are saying all of Q is contained in P somehow.

The brackets represent a number of statements, S1 is a conjunction of all those statements with in the brackets, and S2 is not in the bracket. To make sure S2 is entailed by S1 (or Gamma for that matter), I check to see if the negation of S2 and S1 are inconsistent.

I’m ready to move on to the next step. Right now, I’ll agree that the argument has the strength of MP.

Now I want to get rid of any residual doubt by stating things in terms of some abstract objects instead of objects from science fiction.

I will assume naïve arithmetic, that is the natural numbers 1,2,3,.....
Suppose now that L is a list of numbers L=(a(1),a(2),a(3),.....)

A1: The number a(1) is prime.
A2: For each n, if a(n) is prime, then is so is a(n+1)
____
C: All numbers in the list are prime.

I think you will agree that this just another deduction that has the same basic form as the glowing cube deduction.
But again. What is it? Does it have a name? Does it need to be unpacked and proved in more detail using several moves like modus ponens? Or is this the rock bottom level for this move--is it a basic logical move?

But what kind of deductions is it? Certainly it is not an MP or anything like it. Whatever it is, it can't only be approached by a a first order predicate calculus. But what deductive form or template does this fit that makes it a valid deduction?


After you comment on that, I will consider how it could come to pass that we can ever establish something like A2 where there seems to be an infinite number of things to check.