I’ve been trying to think of another way to explain beliefs as I still hear folks saying they are ‘absent of belief in regards to x’ or ‘have no beliefs’. Whilst I am sure they believe what they are saying, it makes me feel I have failed in my explanations.
Rather than spray out the propositional logic or all the different definitions of a belief, I started thinking about how something like this might be represented in a database, perhaps with binary, and then I adapted my thoughts to make the calculation a little more easy to read. I then also thought about how we could represent a proposition as a football (soccer) pitch, and those involved in the ‘game’ are players somewhere on the pitch.
When we consider a proposition, in its clearest form, it is binary. True or False. This is represented by a 1 (True) [in logical notation this would be p] and a 0 (False) [in logical notation this would be ¬p].
The binary representation on a proposition
If we are to examine most things, they can be split into these binary propositions. They might require further examination after the fact, but the core message is there
‘The lightswitch is on’
This is one of the simplest examples of a logic gate. It only has an on and off position. A 1 and a 0. Even if you were to try and throw a spanner in the works by saying ‘it’s a dimmer switch’ it is still on or off, just with various brightness settings on the ‘on’.
This can be represented like this:
1 – The Light Switch is On
0 – The Light Switch is Off
‘It is raining outside’
When discussing a type of weather, e.g. it is raining, this will still be a yes/no true/false but it will only tell us about that particular weather, not other weather types.
1 – It is Raining Outside
0 – It is Not Raining Outside
‘(at least one entity that could be described as a) God Exists’
In short, when discussing the proposition of ‘God Exists’ we are often more speaking of any entity that could be described with ‘godly’ like abilities. More often and not though, you will be discussing it on the platform of the Omni-God from the Abrahamic religions, but however you are discussing, the result is the same. Either something exists or it does not exist. <– for the sake of the conversation, we include anything that has had an existence as something that exists, e.g. if you think god died creating the universe then we would include that in something like a god exists.
1 – God Exists
0 – God Does Not Exist
Binary Representation on Belief
‘You either believe something or you don’t’ is a common line we hear, and it isn’t wrong but it is misused slightly. That said, we will start here.
1 – I believe
0 – I don’t believe
Pretty simple, but how do we relate that to our proposition?
Binary: Propositions and Beliefs
So now we understand how a proposition is binary, and how a belief can be described as binary in the sense you do or don’t hold that belief, we now have to consider how the two work together.
When discussing a proposition, we are trying to look for a complete answer in relation to it. It is often seen that we only hear half an answer and folks don’t even realise it is half an answer.
Half or Whole?
Now that we understand the proposition is binary, a 1/0 or True/False type deal, we can consider how we answer it a bit better.
The idea is to answer both parts of the proposition not just what you think about half of it. What I mean by that is, you might think (aka believe) it is not true, but does that mean you think it is false?
The lack of clarity can cause confusion about what your position on the proposition actually is and requires further investigation. This is why we answer the whole proposition rather than just giving a read of a psychological state.
Considering the whole
So when it comes to answering a proposition what we are expecting is an answer on your attitude towards both if it is true and if it is false. This isn’t a knowledge claim, or said with absolute certainty, just the direction you are leaning towards.
Below is a small chart in relation to a generic proposition and our attitude possibilities towards it, once having been presented it*.
*Once having been presented it or being aware of it is very relevant to a section later on.
I’ve listed 4 belief positions we can possibly have in relation to any of the propositions mentioned above or any other.
a) You believe the proposition is true and you do not believe the proposition is false.
This is the standard belief in a proposition and can be represented within logical notation such as Bp (the ¬B¬p naturally follows)
For my summary below, as this is a positive belief in a proposition I am going to give this a value of 1.
If we were to think of this in the terms of football (soccer) we could think of their position on the field as forwards.
b) You believe the proposition is not true and you believe the proposition is false.
This is the standard disbelief in a proposition and can be represented with logical notation such as B¬p (the ¬Bp naturally follows)
For the summary below, as this is a disbelief in the proposition, or a belief in the negative, I am going to give this a value of -1
If we were to think of this in the terms of football (soccer) we could think of their position on the field as defence.
c) You don’t believe the proposition is true, and you don’t believe the proposition is false.
This posotion is known as suspending judgement, withholding belief, or the psychological state of being agnostic.
For the summary below, as this is neither belief nor disbelief it makes sense it sits in the middle, so I am going to give this a value of 0.
If we were to think of this in the terms of football (soccer) we could think of their position on the field as the midfield.
d) You believe the proposition is true and false.
This is known as holding 2 contradictory beliefs, is irrational and impossible. Something cannot be both true and false. Unlike the above where you are suspending judgement as you are not convinced, this is one where you have been convinced something illogical is true and therefore are holding an irrational belief state.
This should be excluded from the summary, but will include it as √-1
If we were to think of this in the terms of football (soccer) we could think of their position on the field as the streaker wasted on acid and doing the helicopter with their penis.
There are, of course, other answers to a proposition, although they do not necessarily give a full answer to the proposition.
Most of these would still fit in that 0 position of not having belief either way, but with different reasoning like finding the proposition meaningless or just not caring enough to consider it. They haven’t considered the proposition and ‘suspended judgement’ and therefore lack belief both ways, they have chosen to not fully consider the proposition which has resulted in a lack of belief both ways.
If we were to think of this in the terms of football (soccer) we could think of their position on the field as folks watching from the side line.
Absence of Belief
Absence of belief is an interesting one that I feel is often misused. I explained in detail the difference between not believing something and being absent of belief in Belief: Don’t Believe, Lack of Belief, Absent of Belief – CMT Vol: 11 but in short, if you are truly absent of belief it means you have no mental state in relation to the proposition. However, the second you hear any form of proposition your mind starts to build beliefs around it.
Right now I have some propositions in my head, you’re completely unaware of them, so you are absent of belief in regards to them. The second I mention them you will fill your head with thoughts about them and form beliefs of some description.
- My name is Joe
- My mum caught COVID
- I just did a kickflip
- I once made a rolling paper levitate with the power of my mind
- I have a pet baby elephant
These are, of course, not all true. You will, however, have started to form a belief about each and every one. You might even believe ones that are not true or disbelieve/suspend judgement over those that are true.
The problem is, people are using ‘Absence of belief’ to describe that they don’t believe the proposition is true, which technically they are absent of that belief, but having considered the proposition they are not completely absent of belief in regards to the proposition. Generally, this is done because they think it absolves them of their epistemic responsibility. Either they don’t understand epistemic responsibility, or they are lying.
Anyway, as described, to be truly absent of belief in regards to a proposition you have to either be ignorant of it or unable to understand and process it, like a baby or someone with brain damage.
For the summary below, with this belief position being completely absent of a mental state, we will use the value NULL.
If we were to think of this in the terms of football (soccer) we could think of their position on the field as… someone not even at the game, and completely unaware there even is a game being played.
Summary of the Positions
I have two types of summary I have been building up to, one based on the numerics above, the other based on the game of football (soccer).
This is a simplistic look at the positions and logical notation in relation to a proposition.
|1||Belief||Bp ^ ¬B¬p|
|0||Suspense of Judgement||¬B¬p ^ ¬Bp|
|-1||Disbelief||B¬p ^ ¬Bp|
|NULL||Absent of Belief||N/A|
|√-1||Contradictory Beliefs||Bp ^ B¬p|
If we were to apply this to the proposition ‘God Exists’ we have names for these positions.
|1||Belief||Bp ^ ¬B¬p||Theist|
|0||Suspense of Judgement||¬B¬p ^ ¬Bp||Agnostic|
|-1||Disbelief||B¬p ^ ¬Bp||Atheist|
|NULL||Absent of Belief||N/A||Innocent|
|√-1||Contradictory Beliefs||Bp ^ B¬p||N/A|
I did mention other positions, and I speak about them more in Ontology and the things we lack…
This is more to give someone a bit of a visual aid or a real world comparrison to explain things.
|Midfield||Suspense of Judgement|
|Not in attentdance||Absent of Belief|
|Supporters||Other lack belief positions|
What I am trying to convey with this image and table is, those on the field are the ones whom have actively considered the proposition through and come to a conclusion.
Those on the sidelines are those that have heard the proposition, but not really thought it fully through, perhaps because they find it meaningless or do not care.
Those not on the field are those that have not even heard of the proposition or cannot process it be that either due to age, babies lack the cognitive and language abilities to consider propositions and hold beliefs in relation to them, or due to them having brain damage, or perhaps because it is an inanimate object that is unable to hold brain states at all.
So when someone tells me they are absent of belief or describes atheism as an absence of belief in gods… I have to sit there and think… how? Being charitable, it is likely they don’t actually mean absent of belief, they mean they don’t believe in the proposition/god’s existence. This doesn’t really tell us their position on the field though, does it?
Hopefully this article has helped explain cognitive attitudes a little more. It’s fine to use other definitions of atheism if you prefer them or find they have more utility in your discussion, but what I am focused on here is belief states and helping people be clear in their positions.
- Belief: Don’t Believe, Lack of Belief, Absent of Belief – CMT Vol: 11
- Propositional Logic and Beliefs – Fresh AiR – S03:E02:C01 (VIDEO)
- Propositional Logic and Beliefs – Fresh AiR – S03:E02:C01 (AUDIO)
- Beliefs and Rationality – CMT Vol: 10
- Beliefs, Language, and Logic
- More on Beliefs and Justifications
- Definitional Problems with Lacking Belief
- Bad Atheist Arguments – Vol: 02 – Beliefs and Logic
- What is Agnosticism? How does it relate to knowledge and beliefs?
- The Burden of Proof – Belief vs Claim – Court Room Analogy
- Coherent and Consistent Beliefs
- Unbelief and Disbelief – Conflated and Misunderstood Terms – Volume 6
- Is nonbelief a belief? (hint: you might be surprised) – Conflated and Misunderstood Terms: Vol 8
- Fresh AiR – S01:E05 – Belief, Truth, and Knowledge
- Dirty Words – Conflated and Misunderstood Terms Volume 4: Belief, Faith and Evidence
- SEP: Belief
- You won’t believe this… CMT – Vol: 12
- Is it rational to form beliefs based on testimony?
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