Matt Dillahunty has said on the Atheist Experience that it is impossible for someone to neither be atheist nor theist…and yet here I am…neither atheist nor theist. Matt has what is called a modal scope fallacy by making such a claim as he is by his usages holding ~A → □T or ~T → □A meaning if not atheist by necessity you must be a theist or not theist by necessity you must be an atheist. This is merely a relative necessity. There is no metaphysical necessity for anyone based upon the logical verities for someone by logical necessity to be theist or atheist. The correct modal form would be □(T V A) meaning locally by the scope of Matt’s definitions you must be theist or atheist…if you don’t accept his definitions, which I do not, then there is clearly no metaphysical or logical necessity that entails one must be theist or atheist.
The same modal fallacy can be better demonstrated in ponens form:
p →q If Steve is not a theist, then he must be an atheist
p Steve is not a theist
:.q Steve must be an atheist.
Modally this would seem to mean:
S → □A
(S=Steve is not a theist, □A= Steve must be an atheist)
Clearly there is no logical reason that I *must* be an atheist though. It is only because of the way Matt Dillahunty prescribes “atheist” as anyone who doesn’t have a God belief. This is a local argument and merely a relative necessity. Just like if the argument was if Steve has 2 dogs and a cat, then Steve has to have at least 1 cat only means that given the scope of the argument I have to have at least one cat…but again clearly there is no metaphysical necessity that I “have to have” at least one cat. I can of course have no cats. Another example would be if I said do you want chicken or fish for dinner. If you do not want chicken then you must have fish. But there are clearly many more foods that exist than just chicken or fish so it isn’t I “must ” have fish…it is I am limited in my choices by an artificial limitation in scope which are merely that there are only two arbritary options being provided to me.
Matt is creating a synthetic and arbitrary set of classifications based upon merely semantics. My Matt claiming by fiat that not theist = atheist it would be like me saying:
Let’s define “not theist” as “dog”.
Theist or dog
Not theist then dog.
:. It is impossible to be anything but a theist or a dog.
It becomes merely a semantics game of what word is being used to represent “not theist”. But semantic changes are not logical entailments one must use that specific signifier. I reject that not theist = Dog the same way I reject not theist as being synonymous atheist.
The correct way to interpret Matt’s argument locally and with in a limited scope is:
□(S → A)
It is relatively necessary given the scope of Matt’s choice of usage of the term “atheist” that if Steve is not a theist then he is an atheist. Which is perfectly logically true…But if Steve rejects the limited definition of the term then there is nothing that requires by any logical deduction that Steve *must* be a theist or an atheist. It would be no different from the example of not theist=dog. You must be then either a theist or a dog. Perfectly logical, but would most atheists accept that? Probably not. Just like I don’t accept Matt’s semantic assertion that nontheist=atheist.
Matt’s claim also requires a logical proof that it is “not possible” (which means impossible which means can not exist in any possible world) for a person to be neither atheist nor atheist. To show something is “impossible need prove it using logic by like a proof by contradiction or by modal logic (~◊ = not possible). The most we can show using logic deductively and not trivial usage of semantics is:
LNC :=~(p V ~p)
p V ~p ≡ T (Negation law)
Theist or Not Theist
So can Matt show given ∀x(P(x)) given P(x)=”can be neither theist nor atheist” without loss of generality (∀x(P(x)) is true for all x ∈ S) that ~◊x to be neither theist nor atheist by proof by contradiction (⊥) and that P(x) is false s.t. x can not be neither theist nor atheist?
Since theist and not theist are mutually exclusive and jointly exhaustive (if x ∈ theist then x ∉ not theist. ) then x must either be theist or not theist and can not be neither by necessity and it is impossible for x to not be in at least one of those two sets.
I would like to see a proof that one *must* by necessity and starting with axioms that it is “not possible” to be neither theist nor atheist as a matter of logical necessity rather than resort to silly semantic arguments which are not by necessity and a modal scope fallacy.
There are also other logical reasons to reject such a semantic substitution.
Changing not theist to atheist presents an intensionality problem where changing the words not theist results in a change of truth value to a proposition. Leibnez has said that “Two terms are the same (eadem) if one can be substituted for the other without altering the truth of any statement (salva veritate).” So let’s test that shall we?
Let me try to explain this concept of intensionality first.
p=”Steve believes that someone is not an atheist”
Read de re (‘of, or concerning, a thing’) this statement is Steve believes that “Someone” specifically is not an atheist. (for example Steve believes he himself is not an atheist). This would make the statement “transparant”(Truth value does not change) to such a substitutional change of “Someone” with “he himself” so you have p=”Steve believes that he himself is not an atheist”. The truth value remains unchanged if Steve believes he himself is not an atheist.
Read de dicto ( ‘of, or concerning, a dictum’) this statement is ambiguous because Steve could just be saying in general that he believes that there are atheists. Read de dicto if the truth value can change which would make the statement “opaque” (truth value may change) if for example we substitute “someone” with Matt Dillahunty. As then the propositional value changes if Steve believes that Matt Dillahunty is actually an atheist.
De re is truth preserving. De dicto is not always truth preserving and may fail to preserve the truth value of the proposition if a co-referential term is used and it is not then a valid form of inference.
If we substitute “atheist” for not theist this presents a similar intensionality problem:
p=”Steve believes that he is a nontheist”
If we substitute “nontheist” for “atheist” then the statement becomes opaque as the truth value can change since p=”Steve believes that he is an atheist” may or not be true. Nontheist and atheist would only be co-referential terms that don’t change the truth value if Steve holds that nontheist is completely interchangeable with atheist. As I am Steve I do not hold that nontheist is completely interchangeable with “atheist” as I hold an atheist to be a person who believes that there are no Gods and reject Matt’s usage as someone who merely does not hold a God belief. This does not mean I reject calling someone who merely does not believe God exists an atheist as “atheist” at that point merely becomes a semantic label that one someone can use for themselves, but would be intellectually dishonest to try to apply to anyone else…Including trying to apply to me.
I am neither theist nor atheist and I challenge anyone to logically show by necessity that it can be no other way (that in all possible worlds I *must* be either theist or atheist).
“I’m confused because normally they list next to each name whether it’s a theist or an atheist so we can give priority to theists and next to yours it says neither and that’s not possible” -Matt Dillahunty 4/16/2017