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Atheism, Theism and Agnosticism: Square of Opposition and Semantic Collapse (Short version)

Argument: Atheism, Theism and Agnosticism: Square of Opposition and Semantic Collapse

 

Reviewed by mathematician Josh Garver.

 Note: This is a work in progress. Fair and honest critiquing is appreciated!

Dr. Graham Oppy notes this in “A Companion to Atheism and Philosophy | | Introduction”:

“Some wish to distinguish different kinds of atheism: some distinguish between ‘strong’ – ‘hard’, ‘positive’ – atheism and ‘weak’ – ‘soft’, ‘negative’ – atheism. But, given that atheists can differ in all of the ways discussed in the preceding two paragraphs, and in many other ways as well, it is very hard to believe that any useful purpose could be served by stipulation of a context‐independent distinction between strong atheism and weak atheism. In particular, it seems to me to be a mistake to use a distinction between strong atheism and weak atheism to subsume agnosticism under atheism: strong atheists reject the claim that there are gods, while weak atheists refrain from accepting the claim that there are gods. For, if we accept that there is this distinction between strong atheism and weak atheism, we should surely accept that there is a similar distinction between strong theism and weak theism: strong theists reject the claim that there are no gods, while weak theists merely refrain from accepting the claim that there are no gods. And then we shall have it that agnostics are both weak atheists and weak theists.”

Abstract: Defining subalternations with the same term will result in sematic collapse. Allowing for Bsg ->~Bs~g with both Bsg and ~Bs~g labled as “theism”, Bs~g->~Bsg with both Bs~g and ~Bsg as “atheism”, and agnostic donated as ~Bs~g ^ ~Bsg will effectually result in the possibility of semantic condition of someone being concurrently an atheist, theist and agnostic.

Given:
g is the proposition that at least God/god exists or “God/god(s) exists”
B is the epistemic disposition of “Belief” that affirms a proposition is True.
s is Subject (indexical)

Atheism = Bs~g
Theism = Bsg
Agnosticism= ~Bsg ^ ~Bs~g
“Weak atheism” = ~Bsg
“Weak theism” = ~Bs~g
Bs~g -> ~Bsg is a subalternation
Bsg -> ~Bs~g is a subalternation
Bsg v Bs~g is a contrariety
~Bs~g v ~Bsg is a subcontrariety
Bsg ^ ~Bsg is a contradiction
Bs~g ^ ~Bs~g is a contradiction
Subalternation = by entailment or implication, not based upon truth values. Contrariety = one of two propositions that both can be False, but cannot both be True.
Subcontrariety = one of two propositions that can both be True, but cannot both be False.
Contradiction= one of them is True if and only if the other is False. Can not both be True, nor can both be False.

More specifically, Smessaert H., Demey L. (2014) defines these Aristotelian relations as:

φ and ψ are contradictory iff S ⊨ ~(φ ∧ ψ) and S ⊨ ~(~φ ∧ ~ψ),
φ and ψ are contrary iff S ⊨ ~(φ ∧ ψ) and S ⊨ ~(~φ ∧ ~ψ),
φ and ψ are subcontrary iff S ⊭ ~(φ ∧ ψ) and S ⊨ ~(~φ ∧ ~ψ)
φ and ψ are in subalternation iff S ⊨ φ → ψ and S ⊭ ψ → φ.

By using this schema we can show that any semantic labeling of subalternations as the same term will result in semantic collapse:

Argument: Given φ and ψ are in subalternation iff S ⊨ φ → ψ and S ⊭ ψ → φ.
Then any form of  φ → ψ, where S ⊭ ψ → φ, by S holding to ψ ^ ~φ will result in semantic collapse.

Let φ be Bs~g, ψ be ~Bsg
φ->ψ
Bs~g->~Bsg
~φ =~Bs~g If ~Bsg and ~Bs~g, then ~Bsg ^ ~Bs~g. (conjunction introduction)
Semantic instantiation: Weak atheism and weak theism, then agnosticism. If then we allow “weak atheism” to be atheism and “weak theism” to be theism then: atheism, theism and agnosticism.

Example:

Theism = Bsg

Bsg->~Bs~g or if you believe God exists, you do not believe God does not exist. You can not be ~Bsg as that would be a contradiction.
You can not be Bs~g as contrariety only one can be True.
You are either ~Bs~g or ~Bsg as subcontrariety as both can not be False.
Since you can’t be ~Bsg as that is a contradiction, then you must be ~Bs~g which is the subalternation Bsg->~Bs~g.

We can label these as follows on the square of opposition (Agnostic being the conjunction of the subcontrarities ~Bs~g and ~Bsg):

If atheists label “weak atheism” (~Bsg) as atheism, instead of the normative Bs~g, theist can rename the subcontrariety of “weak theism” (~Bs~g) as theism, and by failing to allow them to do so you’re guilty of special pleading. (See WASP argument: https://greatdebatecommunity.com/2020/02/27/if-bp-is-held-as-atheism-then-bp-can-be-held-as-theism-else-you-are-guilty-of-special-pleading/)

Conclusion: By defining atheism in the weak case we are forced to accept that it results in a semantic collapse where if person is ~Bsg, without being B~g, then they are ~Bsg, ~Bs~g, and ~Bsg ^ ~Bs~g; or atheist, theist and agnostic at the same time.

 


References:

Demey, Lorenz (2018). A Hexagon of Opposition for the Theism/Atheism Debate. Philosophia, (), –. doi:10.1007/s11406-018-9978-5

Smessaert H., Demey L. (2014) Logical and Geometrical Complementarities between Aristotelian Diagrams. In: Dwyer T., Purchase H., Delaney A. (eds) Diagrammatic Representation and Inference. Diagrams 2014. Lecture Notes in Computer Science, vol 8578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44043-8_26

Burgess-Jackson, K. (2017). Rethinking the presumption of atheism. International Journal for Philosophy of Religion, 84(1), 93–111.doi:10.1007/s11153-017-9637-y

Smessaert H., Demey L. (2014) Logical and Geometrical Complementarities between Aristotelian Diagrams. In: Dwyer T., Purchase H., Delaney A. (eds) Diagrammatic Representation and Inference. Diagrams 2014. Lecture Notes in Computer Science, vol 8578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44043-8_26

Oppy, Graham (2019). A Companion to Atheism and Philosophy || Introduction. , 10.1002/9781119119302(), 1–11. doi:10.1002/9781119119302.ch0

10 comments
  1. Ralph Ellis

    “…it is very hard to believe that any useful purpose could be served by stipulation of a context‐independent distinction between strong atheism and weak atheism.” – Dr. Oppy

    The purpose is self-evident: It clearly describes a person to another person in a way that makes their position immediately comprehended.

    “In particular, it seems to me to be a mistake to use a distinction between strong atheism and weak atheism to subsume agnosticism under atheism: strong atheists reject the claim that there are gods, while weak atheists refrain from accepting the claim that there are gods.” – Dr. Oppy

    Yes! This has been my point for over 8 years of this topic on several media sites.

    If we follow that “B” is defined by the APA as: “acceptance of the truth, reality, or validity of something (e.g., a phenomenon, a person’s veracity), particularly in the absence of substantiation.”, then B is not a claim, but merely a psychological state of acceptance of a given P.

    “Acceptance” is not a claim about P, it is a psychological state, and this is so important to remember and keep separate from the biconditional nature of P.

    I would like to submit an exercise to you, Dr. Oppy, for your consideration.

    I call this the “Around The Block” exercise.
    Consider you are standing on the sidewalk, about to walk across the street.
    Mentally, you do your best to assess the state of traffic, looking for the P “It is safe to cross the street”.
    Having used your limited frame of reference and finite perception, you come to the “B” (not a claim, but a psychological state of acceptance) that “p” seems true.
    Thus you Bp.
    As you step out, and off the curb, however, you are still assessing the reality of your limited reference frame/perception, and constantly on guard for new data changing your malleable P. (Squealing tires? Revving engines?)
    So you cross the street, but do so with the clear Kp of “I cannot know or be aware of all factors contributing to the state of safely crossing this street, thus I must constantly sweep and be prepared to move to safety if possible.”

    This person is thus “Bp” but “~Kp” across the same proposition, and there is a distinct reason for this.

    Factually, theists and atheists both occupy this kind of thought modeling.
    I am actually very happy you are pointing out the irrefutable fact that, at their base, neither atheism not theism has a BoP, although they may both have a BoJ.
    It is, as you accurately stated, “special pleading” to insist a theist by default has a BoP.
    To my mind, it is also “poisoning the well” when it comes to immediately insisting a theist makes a hard claim that a god exists, when many do not do this at all.

    Neither, at their base, are more than simple internal acceptance of the proposition that god exists.
    It is only when one or the other assumes a BoP by making a claim (“God exists!”, or “I know god exists!) that they incur a BoP.

    I very frequently watch atheists shows (I identify as an agnostic[~Kp] atheist [~Bp] for full disclosure) and get pretty irritated when they insist, often very vitriolically, that they have a Burden of Proof, merely by identifying as a theist.

    It’s caustic and needs to stop, and I think you pointed that out quite clearly here.

    As to the distinction between agnosticism and atheism, I am sorry, but you remain incorrect.

    There is immense didactic and social utility in delineating what you believe from what you claim to know, and telling someone you are an “agnostic theist” or “agnostic atheist” is immediately informing.

    You immediately know that the person, on the basis of claims of knowledge, says the P is unknown or unknowable, while immediately informing you as to what their belief towards said P is, which are wholly distinct.

  2. Ralph Ellis

    Ah, nevermind.
    I thought this was posted by Dr. Oppy.
    Not somebody who has an express interest in confirming their own definitional bias and smeantic ownership while strawmanning other people.

    Go ahead and delete my responses. You will fail to learn from them anyways.

  3. Steve McRae

    Agnosticism

    “Nowadays, the term “agnostic” is often used (when the issue is God’s existence) to refer to those who follow the recommendation expressed in the conclusion of Huxley’s argument: an agnostic is a person who has entertained the proposition that there is a God but believes neither that it is true nor that it is false. Not surprisingly, then, the term “agnosticism” is often defined, both in and outside of philosophy, not as a principle or any other sort of proposition but instead as the psychological state of being an agnostic. Call this the “psychological” sense of the term.”

    https://plato.stanford.edu/entries/atheism-agnosticism/

  4. Ralph Ellis

    Agnosticism:

    “The view that some proposition is not known, and perhaps cannot be known to be true or false.”

    Oxford Dictionary of Philosophy, 2nd Ed.

    My Ivy League sees your Ivy League. What now Steve?
    Going to pretend your definition is the ruler because you say so?

    Time to grow up kiddo.

  5. Steve McRae

    All you have done is demonstrated you conflate agnosticism in the domain of epistemology vs the domain of ontology.

    I have explained this numerous times:

    “The word “agnosticism” is polysemous and has a number of different meanings in philosophy. I will try to briefly explain a few of them from most broadest interpretation to most narrow and most commonly understood usage:

    1) Agnosticism in the most broad sense was Thomas Henry Huxley’s view of a normative epistemic principle or method similar to evidentialism or even logical positivism which was one should not believe anything that can not be validated, observed, learned by experiment, or proportionally determined to be True or False etc., or according to Huxley that one has no justification to claim knowledge (or even claim belief) that Gods do or do not exist. (archaic meaning)

    2) Agnosticism as an epistemological proposition: The proposition of if the existence of Gods is knowable or unknowable. (sometimes referred to as “weak or soft agnosticism” or “strong or hard agnosticism”)

    3) Modern usage of the word “agnosticism” is merely the belief that one is not justified to assign a truth value or T or F to p where p=”at least one God exist” (theism). In this usage the person has attempted to evaluate the proposition, but believes that they do not have sufficient justification to say p is T or p is F and they are therefore suspending judgment on p. In this context it is the psychological state (as opposed to a normative epistemic principle or epistemological proposition) of being agnostic on p, or someone who tries to evaluate p, but does not believe p is true nor believes p is false.

    Source: SEP (Atheism)”

    https://greatdebatecommunity.com/2019/01/21/agnosticism-in-3-ways/

  6. Ralph Ellis

    I have used an Ivy League school with immense philosophical history’s definition in which it directly states that Agnosticism is about K (JTB).

    K is distinct from B.
    There is great didactic and social utility in delineating K from B in response.

    There is nothing irrational or incoherent about using K as adherent to Oxford’s definition, while using B as representative of Oxfords definition of atheism, which directly states it is about B.

    You have finally caught up to me on the Justificatory and proof burdens of a/theism, Steve, after me telling you (and others) this exact thing in roughly 2018.

    I expect it will take you 3-4 more years to finally learn that representing K and B distinctly, because they *are distinct*, has didactic and social utility.

    Until then, good luck with your myopic assertions and special pleading.

    You grow. You just grow slowly.

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