In a recent thread
The Negation in 'Do Not Believe' Statements iamtaka asks about the negation of belief from a linguistic standpoint. His particular concern is how do we distinguish weak atheism from strong atheism within natural language. My intent is to describe weak and strong atheism with an epistemic logic. The point to this exercise is provide the most coherent answer to how weak atheism differs from strong atheism. The approach is to try and fit the oppositions inherent in the terms atheism, agnosticism and theism to a Boolean logic; when this is done we get a binary code for religious belief. If someone asks how weak atheism stands to strong atheism the answer is found in this code. If they go to the effort to unpack the semantics that gives the code its meaning they will hopefully be able to clearly understand the difference.
AXIOM: There are two possible states of affairs: 1/ God does not exist 2/ God exists.
[mrow]God Doesn't Exist[mcol]God Exists
[row][center] Not precarious | Precarious[/center][col] Precarious| Not precarious
In this semantic system there are also two ways of describing a belief. We would like to say a belief is Certain or Uncertain, but the term "uncertain" suggests equivocation. This we wish to avoid. A precarious belief is also uncertain in the sense it might be toppled, but not uncertain in the sense the believer is unsure what they believe. If a belief about a state of affairs is precarious or not precarious, and a state of affairs exists or does not exist, that gives us four possible belief states to describe. This we can do with a yes-no semantics, which we are able to directly replace with a Boolean logic of 1 and 0. The four possibilities means we have 16 valued logic. However this logic remains Boolean (i.e. it is an extension of standard logic). In this extended logic AND (conjunction) is the product (x) of two or more Boolean strings, whilst OR (disjunction) is the sum (+) of two or more strings. I'll give three examples which I hope will be sufficient for a basic understanding of how to combine the code.
[It is also worth noting how I switched the order of precarious and not precarious when considering the opposite state of affairs. This is not necessary but I think it makes for neater looking set of oppositions. This way a strong theist is furthest away from a strong atheist, and an agnostic holds the middle ground].
[mrow]Yes/No Semantics[mcol][mcol][mcol]Boolean[mcol]Examples
[row][center] Yes = Y[/center][col] Y = 1[col] [col] 1 x 0 = 0[col]0011 x 0010 = 0010
[row][center] No = N[/center][col] N = 0[col] [col] 1 + 1 = 1[col]0010 + 0011 = 0011
[row][col] [col] [col]1 x 0 = 0[col]0010 + 0001 = 0011
There are now 16 possible outcomes of which only 14 values describe a meaningful belief state. Of these I'll name eight. The eight values named in blue describe the oppositional logic of theism, atheism and agnosticism
[mrow]God Doesn't Exist[mcol]God Exists[mcol]Boolean [mcol]Epistemic Interpretation [mcol] Theology
[row][center]N | N[/center][col][center]N | Y[/center][col][center]0001[/center][col]Not doubt it is the case God exists [color=brown]= discount it is not the case God exists[/color][col][center][color=blue][b][i]Strong[/i] Theist[/b][/color][/center]
[row][center]N | N[/center][col][center]Y | N[/center][col][center]0010[/center][col]Uneasy it is the case God exists [color=brown]= not settled it is not the case God exists[/color][col][center][color=blue][b][i]Weak[/i] Theist[/b][/color][/center]
[row][center]N | N[/center][col][center]Y | Y[/center][col][center]0011[/center][col]Believe it is the case God exists[col][center][color=blue][b]Theist[/b][/color][/center]
[row][center]Y | N[/center][col][center]N | N[/center][col][center]1000[/center][col]Not doubt it is not the case God exists [color=brown]= discount it is the case God exists[/color][col][center][color=blue][b][i]Strong[/i] Atheist[/b][/color][/center]
[row][center]N | Y[/center][col][center]N | N[/center][col][center]0100[/center][col]Uneasy it is the not the case God exists = [color=brown]not Settled it is the case God exists [/color][col][center][color=blue][b][i]Weak[/i] Atheist[/b][/color][/center]
[row][center]Y | Y[/center][col][center]N | N[/center][col][center]1100[/center][col]Believe it is not the case God exists[col][center][color=blue][b]Atheist[/b][/color][/center]
[row] [center]N | Y[/center][col][center]Y | N[/center][col][center]0110[/center][col]Doubt it is the case God exists [u]and[/u] doubt it is not the case God exists[col][center] [color=blue][b]Agnostic[/b][/color][/center]
[row][center]Y | N[/center][col][center]N | Y[/center][col][center]1001[/center][col]Not doubt it is the not the case God exists [u]or[/u] not doubt it is the case God exists[col][center][color=blue][b]Not Agnostic[/b][/color][/center]
[row][center]N | Y[/center][col][center]N | Y[/center][col][center]0101[/center][col]Mindful it is the case God exists*[col][center][color=blue][b][/b][/color][/center]
[row][center]Y | N[/center][col][center]Y | N[/center][col][center]1010[/center][col]Not Mindful it is the case God's exists**[col][center][color=blue][b][/b][/color][/center]
[row][center]Y | Y[/center][col][center]Y | N[/center][col][center]1110[/center][col]Doubt it is the case God exists [color=brown]= not discounted it is not the case God exists[/color][col]
[row][center]Y | Y[/center][col][center]Y | N[/center][col][center]0111[/center][col]Doubt it is not the case God exists [color=brown]= not discounted it is the case God exists[/color][col]
[row][center]Y | Y[/center][col][center]N | Y[/center][col][center]1101[/center][col]Believe it is not the case God exists or no doubt it is the case God exists[col]
[row][center]Y | N[/center][col][center]Y | Y[/center][col][center]1011[/center][col]Believe it is the case God exists [u]or[/u] not doubt it is not the case God exists[col]
[row][center]N | N[/center][col][center]N | N[/center][col][center]0000[/center][col]Contradiction / Incoherent belief[col]
[row][center]Y | Y[/center][col][center]Y | Y[/center][col][center]1111[/center][col]Tautology / makes sense but the beleief is not meaningful
i.e. it does not express a meaningful idea[col]
The Boolean strings of 1s and 0s record the oppositions and implication that characterise this logic. For example if someone is a theist
or a weak atheist, this means they doubt it is not the case God exists (0100 + 0011 = 0111). It is a contradiction to say they are a theist
and a weak atheist (0011 x 0100 = 0000).
(*)(**)The interpretation of 0101 as Mindful and 1010 as Not Mindful I am not fully convinced of, and may continue to change the interpretations of these two values. I'd gladly entertain any better ideas if anyone has one. I think the rest of the values stack up pretty well.....well they make sense to me.