There are some people who like to oversimplify not believing a proposition. They will say things like “You either do believe or you don’t believe, there is no third option!”
On the surface, this statement is correct. The problem is, it doesn’t actually fully capture the type of not believing. This is why conflations of suspending judgment and disbelief seem to appear, and other claims like, “atheism is the default position” or the dreaded “rocks are atheist” debacle.
So, please understand I do accept someone either does or does not believe a proposition, but there is a bit more to it than that.
Law of Excluded Middle / Law of Non-Contradiction
When you are discussing a proposition the law of excluded middle, and the law of non-contradiction, is applied to the proposition itself rather than your attitude.
A proposition is a truth-apt bivalent statement. It is something that can only be TRUE or FALSE, or in binary, we would represent this as 1 or 0. In propositional logic, this would be p v ¬p (p or not p).
- It cannot be both true and false [ ¬(p ^ ¬p) – not true and false].
- It cannot be neither true nor false [ ¬(p v¬p) – not either true or false].
A belief is a positive attitude towards a proposition, or something you think true, most likely, or conclude is the case. If the proposition or p is ‘it will rain tomorrow’ and you think that quite likely, then you believe the proposition or Bp.
As we discussed in my brief and simplified overview of propositional logic, You won’t believe this… (Logic and Belief), to provide a complete, or epistemic, answer we don’t only answer if we do or don’t believe the proposition true but ALSO if we do or don’t believe the proposition false.
This is represented in binary below:
a) Belief the proposition is true & not believing it is false or Bp ^ ¬B¬p
b) Belief the proposition is false & not believing it is true (aka disbelief) or B¬p ^ ¬Bp
c) Not believing the proposition is true or false (aka suspense of judgement) or ¬B¬p ^ ¬Bp
d) Believing it both true and false, which is an absurd contradiction, it essentially says you believe the proposition violates the law of non-contradiction. Some could say the same about c), but this is a misunderstanding, as c) isn’t saying “it is neither”, they understand “it is one or another” but are not yet convinced by the options.
Above we have 2 types of not believing in the proposition is true. We also have 2 types of not believing the proposition is false. And one absurd position.
So we see that the law of excluded middle is what is applied to the PROPOSITION and not ATTITUDE (belief).
Of course, if we phrased each attitude as a proposition, then the law of excluded middle applies again. This is what I think people get confused about. They see each propositional attitude (belief position) as its own proposition.
They will turn the belief position into a proposition like ‘it is True that you believe a)‘ therefore this becomes a proposition with a true and false outcome where you either do or don’t believe.
However, the language they use will be something like; “you either do or don’t hold position a), there is no third option”. This is correct, as I mentioned at the start, you either do or don’t hold position a). What it doesn’t tell us is if you hold b), c), or d). Essentially there are 4 different propositions created if you phrase things this way, rather than the 4 attitudes in relation to a single proposition.
All 4 positions above those speak of a considered & direct response to a proposition though, and not every type of non-belief is a considered or direct response.
Types of non-belief or not believing
Generally speaking, people are not talking about the type of not believing found in a) – not believing the proposition is false whilst believing the proposition is true. They are focused on not holding to a) and they probably wouldn’t even consider d) is an option as it is so absurd. Let’s ignore d) for now for this very reason.
If you don’t hold to a) this could be because you have considered the proposition and either be uncertain if you think it is true or false, c), or believe it to be false, and therefore don’t believe it is true, b).
However, there are other judgements you might back that lead you into a similar position as c) that would not be regarded as suspending judgement.
Suspending judgement is a position where you have considered the proposition, and you don’t believe it true, but also don’t believe it false, or ¬B¬p ^ ¬Bp.
Other attitudes could be described this way though, and be confused with suspending judgement.
For example, if you find the proposition or the language used to describe the proposition to be incoherent you would see the proposition as meaningless to consider. You might even reason that it isn’t a proposition at all and therefore have no truth value to consider. This is much the position of the igtheist. They find the concept of God so incoherent and ill-defined that it is meaningless to consider. Sure, they don’t believe the proposition is true or false, much like the person who is suspending judgment, but for a completely different reason.
If you don’t care whether the proposition is true or false, you probably won’t take the time to consider if it is true or false. Again, you don’t believe it is true or false, but it is different to suspending judgement. It is an attitude of apathy rather than one searching for more information to convince them either way. This is much the attitude of the apatheist. They don’t care if a God exists or not and therefore don’t take the time to consider the proposition and evaluate the truth. Sure, they don’t believe the proposition is true or false, much like the person who is suspending judgment, but again, it is a different mental process.
We then have the attitudes of folks that have never heard of the proposition. The other positions, up till now, are at least someone’s response in regards to the proposition even if not a direct answer. There is some related brain activity involved.
When someone hasn’t heard of a proposition, they are essentially ignorant or naive to the proposition. Another term for this is being innocent of the proposition. Sure, they do not believe the proposition is true or false, but they are totally absent of any mental state relating to it.
Lack of Cognitive Ability
There are also folks that lack the mental abilities to consider propositions or hold attitudes in regards to them. Whether this is due to them having brain damage, or because they are babies is irrelevant. The fact is, they do not believe the proposition true or false, but even if the proposition was presented to them would not be able to understand it. In this regard, they are also innocent of the proposition, especially in the case of the baby whose brain has yet to develop.
We then have inanimate objects that have no mental capacity at all. It is ridiculous to think of them in terms of brain states just as it is absurd to think of them in dietary states or emotional states.
Summary of Non-belief positions
As you can see, there are many types of not believing and whilst some look logically the same as the suspense of judgement position; when you consider the psychology of them, are not the same thing.
Even if you consider the suspense of judgement to be the weak atheist position instead of the agnostic position, we can see that this still does not make atheism (or weak atheism) to be the default state for life or even humans.
The default state is innocence. A complete absence of a position on the topic. No label should be assigned, especially not an -IST for to be an -IST you have to active ascribe to an -ISM. This is one of many Problems with ‘Atheism is the Default Position’ arguments
Confusing the Law of Excluded Middle
Another issue that can occur is people further confuse the law of excluded middle by applying it inappropriately to multiple propositions as one thing and therefore saying the law of excluded middle doesn’t work.
What do I mean by this?
Consider how some turn the belief position into a proposition and say you either believe or you don’t, others will be aware of the other belief positions and therefore say the excluded middle doesn’t work because there are more than 2 options. This, of course, is a misunderstanding of what a proposition is and how the rules of logic work.
We can see this happening on defineatheism.com/logic/ where the example of a traffic light is given saying that the law of excluded middle doesn’t work because the options are not green or red, amber is evidence of a middle that is not excluded.
The problem with this is, each light is its own proposition.
- Green – On or Off (no middle)
- Amber – On or Off (no middle)
- Red – On or Off (no middle)
Therefore it doesn’t actually show that the law of excluded middle doesn’t always work, it shows that the author of the article doesn’t really understand the rules of logic (which you can tell from reading the entire article).
As an aside, there is also another proposition that can be made about the lights too. One light will be on and two will be off (If the lights are working as expected). If this is true, the lights are working as expected, if this is false, they are not. Again there is no middle with this proposition, the lights are either working as expected or not.
Anyway, you can see how people can oversimplify or misunderstand both not believing and the law of excluded middle which can lead to absurd statements and bad logic, all the while projecting their absurdities and ignorance onto you.
It’s like they say, a little knowledge can be a dangerous thing, and in both examples, I believe that this is the case although thankfully it is not likely to cause a massive impact in the world, and to anyone that does understand the rules of logic or some really basic epistemology will see that they are making fools of themselves.
We can see that there are a number of different types of not believing and issues when people talk about logic without fully understanding the topic. In fact, not so much as “fully” understanding it but understanding the basic laws.
Language and logic are both complex and nuanced, so it is not surprising folks get confused, especially when so many words are polysemous, and some folks are in favour of usage that is so broad it makes them either absurd or useless.
I also promote the use of clear and concise language, though I do take in mind that people tend to be broad and/or vague with their language. Even though terms like lack of belief and don’t believe can be used synonymously I see a notable difference between the two, with one describing an active response to a proposition and the other just an absence of a mental state.
For more information on that, please check: What is the Difference Between Does Not Believe and Lack of Belief?
Hopefully, this has at least highlighted how not all types of non-belief are the same, and how people get both the rules of logic and propositions confused.
Below is a list of articles that tie into logic and belief, I am adding to it all the time, so let me know if you have any other suggestions too!
- You won’t believe this… An intro to Propositional Logic.
- What Does it Mean to Be Logical? – An overview of Logic and Rationality
- Propositional Logic and Beliefs – Podcast with PDF on Propositional Logic.
- Propositional Logic and Beliefs – Video Version of the Above.
- Beliefs, Language, and Logic – An overview of Logic, language and beliefs.
- Why should we use the rules of logic? – Demonstration of propositional logic with ‘God exists’.
- GDC: The Basics of the Laws of Logic.
- GDC: Breaking logic: Playing with Modal logic. (False conclusions from valid and sound arguments?).
- So what is this ‘Normative’ thing all about anyway? – Normative language and its ties to logic.
- Normatively Atheist – Why the ‘Belief God Does Not Exist’ definition of atheist is considered ‘Normative’.
- Wiki: List of logic symbols – Really useful guide to logic symbols.
- Wiki: Truth Tables – an overview of truth tables.
- Bad Atheist Arguments – Vol: 02 – Beliefs and Logic
- Beliefs and Rationality – CMT Vol: 10
- Rationality: How Can a Belief Be Rational? – SciPhi Shortz
I’m Joe. I write under the name Davidian, not only because it is a Machine Head song I enjoy but because it was a game character I used to role-play that was always looking to better himself.
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