Logic is an important part of rationality. After all, acting rationally is acting in accordance with reason and according to the rules of logic, among other things. Which means that understanding the rules of logic are important if one wants to claim rationality for oneself.  There is more to logic than simply the rules though.  As William Hodges says in his book Logic, logic is also about consistency with regards to our beliefs.  Another important part of logic is its link to language, and how we use language.  The sloppier our language, the more likely we are to have errors creep into our thinking, and our beliefs; and the more likely our sets of beliefs are inconsistent.  So, understanding language and its link to logic, and understanding the link they both have to beliefs, will help us to think more clearly, and help us to have more consistent sets of beliefs.  It will, essentially, help us to be more logical.  It will also help with understanding other people’s arguments, as well as assessing and breaking down those arguments in a more logical manner.  We will begin with a discussion about what beliefs are.  So, what do we mean by belief?

Contrary to popular belief, belief is not just uneducated knowledge.

Within the contemporary atheist and sceptic community, at least on places like Facebook, Twitter, and YouTube, there seems to be a lot of misunderstanding about what a belief actually is.  Many seem to define it as something like ‘accepting something is true without any evidence’.  Often attempting to define it in such a way that it relates only to religious people, with some attempting to define it in a wholly derogatory way.  With many even going as far as claiming they ‘hold no beliefs’, or ‘only accept knowledge’; claiming that they avoid beliefs because they only accept things with evidence.  Those that argue things like this show a clear misunderstanding of what a belief actually is.  We all hold beliefs, and even when we have knowledge of something, we still hold a belief about it.  Belief is a necessary component of knowledge.  Belief is not sufficient for knowledge, but it is necessary.  What, then, is a belief?

Beliefs and Propositions

Well, when we are discussing beliefs, what we are talking about is our responses to propositions.  There are those here that will argue that a belief is a psychological state, not a response to a proposition.  They would be correct too, of course, as a belief is a psychological state.  However, we do not have access to the psychological states of others, nor can we give others access to our psychological states.  We can only report on those psychological states.  When we discuss beliefs, we can only discuss expressions of belief.  Meaning that we can only discuss propositions, and our responses to those propositions.  What do we mean by a proposition?

A proposition a declarative statement about the nature of the world.  It is a claim that some state of affairs obtains in reality.  In other words, it is a statement that asserts that such and such is the case.  So, the statement ‘God exists’ is a proposition.  It is a statement that asserts that there is an existent being in reality that we label as God.  The opposite proposition to that would be ‘God does not exist’, which asserts that the aforementioned proposition is not true.  There is no existent being that we call God in reality.  A simple rule of thumb to determine whether or not a statement is a proposition is to replace the P in ‘Is it true that P?’ with the proposition in question.  So, if P=’God exists’, we would be left with the question ‘Is it true that God exists?’.  So, if after replacing the P in ‘Is it true that P?’ with whatever statement we have leaves us with a grammatically correct question, then we can consider that the statement is a proposition. 

Propositions as Declarative Statements

This is because not all statements are propositions, some are commands.  For example, ‘Go to the shop and get milk’ is a command, as is ‘Empty the dishwasher’.  If we replace the P in ‘Is it true that P?’ with one of those statements we are not left with a grammatically correct question.  If we replace P with a question, then it too fails to yield a grammatically correct question.  For example, if we replace P with ‘Does God exist?’, then we are left with ‘Is it true that does God exist?’.  Revealing an ungrammatical question.  So, as stated, as simple test to see whether we are dealing with a proposition is to replace P in ‘Is it true that P?’ with whatever string we are dealing with.  If we are left with a grammatically correct question, then P is a proposition.  Our response to this newly formed question is our attitude towards P, or our belief about P.

Consider a proposition like ‘it will be sunny tomorrow’.  This proposition creates a grammatical question by replacing P in ‘Is it true that P?’ with the proposition, showing us that it is a valid proposition.  We are choosing this proposition because it represents several basic ideas about language and beliefs.  The first basic idea is that the same string can represent several different propositions, meaning that it can represent several different beliefs.  If we consider the idea of this belief being stated every day for a year.  While we have uttered the exact same words each day, each tomorrow is a different day.  Each time the belief is uttered it represents the state of the weather the day after the day it is uttered, and therefore represents 365 different beliefs.

Context is Important

Another basic idea that this proposition represents is the idea that the same string can be uttered and can be true on some occasions and false on some others.  It will not always be sunny tomorrow, but it will be sunny on some days.  Each day the same proposition is used, but each day it represents a different belief, and each different belief can either be true or false.  Which leads us to another basic idea that this proposition represents, the idea that context is important.  The references that a proposition makes are an important part of the proposition, giving the proposition its context.  What we are saying is influenced by when we are saying it, where we are saying it, and why we are saying it.  All of these things give us a good understanding of why clarity is important when discussing propositions and beliefs, and why our language should be as exact and precise as possible.  Ambiguous references in a proposition, and belief, can lead to errors in logic, especially when considering sets of propositions and beliefs.  They can also lead misunderstandings when communicating and discussing beliefs.

Going back to the propositions ‘God exists’ and ‘God does not exist’, we can see just how easily ambiguity can come into propositions; propositions that we may not even think are ambiguous.  Think too of the example of it being sunny tomorrow.  Just as the proposition ‘it will be sunny tomorrow’ said several different days in a row represents many different beliefs, the proposition ‘God exists’ said by many different people can represent many different beliefs.  The proposition put forward by pantheist means something very different to the proposition put forward by a Christian, which again means something very different when put forward by a Muslim.  Each of them represents a different belief when said by each of them.  The proposition might sound the same, but each of them is saying something slightly different.  What is needed to make the proposition less ambiguous is a finger pointing word.  The proposition needs to be something like ‘the Christian God exists’ or ‘the Islamic God exists’.

However, just as in the case of the proposition ‘it will be sunny tomorrow’, we can in fact get this from the proposition alone.  We can get this information from the context of the proposition.  Who said the proposition gives us indication as to which God is being spoken about in the proposition.  If uttered by a Christian then it is, more than likely, the Christian God being spoken about.  If uttered by a pantheist, then it is most likely the pantheist definition of the God being spoken about.  Of course, if we know nothing about the person uttering the phrase, then the phrase is ambiguous.  If we replace it with our own definition, such as a generic ‘creator being’, then we will be speaking of a different belief to the one uttering the phrase originally.  We will, essentially, be talking across each other.  Clarity in the proposition is necessary to make sure there is clarity in the discussion, otherwise we may be speaking of two separate things.

The Importance of the Referent

This is because the referent in the word ‘God’ is a different referent.  It is important to have a clear referent, and when discussing beliefs, it is important to ensure that each party involved in the conversation is using the same referent.  As stated above, if each party is using a different referent then they are each arguing different things.  Each party might be using the same words, and uttering the same sentences, but they are actually making different arguments and expressing different beliefs.  They are, essentially, committing a form of lexical ambiguity, where one word is used to express many different ideas, and taken in completely the wrong way.  As with the ‘it will be sunny tomorrow’ proposition, context can help to clarify what the referent is, however sometimes we forget how important context is to the words being uttered.

Expanding the proposition into a fuller statement can help to understand context, and help to understand the belief that is being expressed of course.  Doing so can also help to understand where misinterpretations and misunderstandings are happening.  Consider the proposition ‘it will be sunny tomorrow’.  That proposition can be expanded into a fuller statement as such: ‘[I believe that it is true that] it will be sunny tomorrow [in my local area]’.  If the speaker had intended it to be less localised then the declarative sentence would have been more specific, such as ‘it will be sunny where you are tomorrow’ or ‘it will be sunny in California tomorrow’.  If the phrase is not more specific then it has expressed their belief incorrectly, the lack of specificity has caused ambiguity.

Deriving From Context

Consider it in the form of an exchange such as this.  Imagine two people having a discussion on the internet, one in the USA and one in the UK.  The one in the USA asks the one in the UK ‘what is the weather like outside?’, and the one in the UK responds with ‘How would I know, I don’t live where you live, just look out the window’.  The one in the UK has responded to the question in a way that does not really answer the question the one in the USA has asked.  They have responded to it without the context that the question implies.  The context implies that they were wondering what the weather was like outside where the person in the UK lives.  The person in the UK has responded as if the person in the USA was asking the question locally.  We would, generally speaking, know from what was asked, where it was asked, why it was being asked, and who was asking, that the context was an inquiry aimed at the person in the UK and not a localised question.  If the person in the USA was asking a localised question, then they would have been more specific.  We generally use various shortcuts in our language, shortcuts that are implied and understood by the one we are involved in a discussion with.

The same can be said of our expressions of beliefs, we expect that the person we are expressing the belief to will understand these shortcuts of language.  However, these shortcuts can cause ambiguity, especially if the person we are in discussion with is not behaving with a principle of charity, does not understand the shortcuts, or has an agenda with the language that they use.  Clarity of language can help overcome all of these problems, and these kinds of ambiguity.  If our goal is clear communication, and if during a discussion or argument our goal is understanding and progress.  Other goals may cause problems of course.

The Problem of Ambiguity

Now, returning back to our proposition of ‘God exists’, we can see further ambiguity coming in during discussions between atheists and theists.  Consider the atheist that declares that they are not claiming that God does not exist when responding to a Christian or Muslim that is putting forward the proposition that ‘God exists’.  In this context, they are essentially saying that they are not saying that the Christian or Muslim god is a false claim.  However, often when the atheist says that they are not saying that God does not exist they are not referring to the god of a specific theology.  Indeed, most times when you push the lacktheist for clarification they will declare that they do not believe in any of the gods put forward by religion, which generally includes the version of God that the Christian or Muslim is speaking about when expressing the belief ‘God exists’.  In essence, the lacktheist is expressing a different belief to the Christian or Muslim.  They are speaking at cross purposes.

The same is true when the Christian or Muslim asks the atheist ‘Why do you believe God does not exist?’.  Just as in the case of the person in the USA asking the person in the UK what the weather is like outside, context matters in this question too.  The Christian or Muslim is not asking the atheist why they believe that the Christian God or the Islamic God does not exist.  When the atheist responds with ‘I am not saying God does not exist’ and they are speaking of a more generic version of God, or even the pantheist version of God, they are not responding to the question the Christian or Muslim is asking, or the belief that the Christian or Muslim is expressing.  The atheist is responding to a different question, and expressing a different belief.  Showing again the importance of understanding context, and the importance of clarity in language, to stop us talking and arguing at cross purposes.  The referent in the question or expression of belief gives us the context of the question or the expression of belief, and if we ignore the referent then we ignore the question or expression of belief.  We are, in essence, discussing different sets of beliefs, making our conversation irrational and illogical.

Clarity is Important

All of this shows us why clarity in language is important, and why well-defined referents, as well as making sure that we understand the context of the referent, and the context of the belief or question, is important.  The same is true of our own internal sets of beliefs.  When we use sloppy language, we allow the chance for equivocation to come into our own internal sets of beliefs, and we express those beliefs sloppily.  For example, if we are in a conversation with a Christian and we declare that their god is imaginary, but in the same conversation declare that we are not claiming that God does not exist or that there is no God, then we have committed a form of equivocation.  The context of the referent may have changed for us, but the context of the cross-reference within the conversation has not.  We have expressed two very different beliefs using the same word.  We have made a cross-referencing error, and caused ambiguity.  The Christian will believe that we are still discussing their God, while in fact we are discussing a more generic God.  We have expressed our arguments and our beliefs in a sloppy manner, and we have allowed bad logic, and even perhaps bad reasoning, to creep into our arguments.

It is even possible to express a belief that sounds logical, but because of a badly defined referent it turns out to be an illogical statement.  Consider the statement ‘the keys are in the fruit bowl on the kitchen counter’.  If there is no fruit bowl on the kitchen counter, then we have put forward a statement with a referent that does not exist.  We have essentially put forward a meaningless statement, even if in error, because we have referred to something that does not actually exist.  The same could be true of any referent that is ill-defined, or is simply an empty placeholder word waiting to be defined.  If the referent is sloppy, ill-defined, or simply non-existent, then our statement is such too.


In conclusion, language is important to beliefs and to logic.  We must be wary of our use of sloppy language when we are expressing beliefs, and putting forward arguments to counter other beliefs and other arguments.  An understanding of how context words, and how referents and cross-referencing in statements works, is a vital part to improving our own use of logic.  Those that are concerned with how logical their beliefs are, and how logical their arguments, would do well to pay attention to these things.  We should pay attention to how we express our beliefs, and how others express their own beliefs, and understand how important context is to the belief being expressed, and the declarative statements being made.  The referents are important, who says them is important, why they are being said is important, and what is being said is important.  We can easily use the same words to say very different things, and use the same words to argue very different things, but actually simply be arguing in an illogical manner.

For further reading on beliefs and logic, try Davidian’s excellent article here: