The Logic You Need to Understand a Deductive Proof of God’s Existence – Definitions (Proof for the Existence of God Part 4)

بسم الله الرحمن الرحيم

With God’s help, I have been in the process of writing a proof for the existence of God – one that hopes to be very thorough, inshaAllah. It addresses every single objection that I personally have thought of or encountered. However, in the process of this laborious undertaking, I realized that in order for a general audience to follow some parts of the argument, it required an occasional foray into logic. This is not to say the logic is overly complicated, but it does help to work through the reasoning explicitly. Unfortunately, this resulted in a lengthy and somewhat messy article, whereas my original intent was to make the proof as clear and concise as possible without compromising on content. I have therefore decided, with God’s grace, to first go over some basic “not completely obvious” logic that will be used in the proof, and that I can refer readers back to in the course of the argument. I will not be explaining things like the principle of non-contradiction, which everyone is familiar with, but I will instead be explaining what a proof by cases is and other such matters. Here, we begin with the idea of definitions.

Why We Need Definitions and Language

In an ideal world, we would be able to have immediate knowledge of each other’s consciousness. Imagine you could effortlessly glide into my mind and literally see the world as I saw it, and experience everything I experience. And imagine that I could do the same. None of your thoughts or feelings would be private and I could view them as I view my own; imagine everyone was like this. In such a world, you could know what it would be like to be colourblind by stepping into the mind of a colourblind person; or deaf by stepping into the mind of a deaf person; or you could know what weird people who dislike chocolate feel when they taste chocolate. A deep insight or complex process of reasoning could be shared by simply sharing the contents of one’s mind directly. In such a world, spoken language would be entirely unnecessary and misunderstandings would diminish perhaps instantly; for I could immediately see into your mind’s eye directly, and you could see mine. The mystics tell us that the higher rungs of reality allow for such possibilities, but that’s neither here nor there.

But alas, at present most of us remain chained to lower realms. Instead, we must engage in the tedious use of language in order to convey the contents of one mind to another. And this process can be gruelling and arduous, particularly when we attempt to express our most profound insights, or we attempt to work through rigorous reasoning. It can also be extremely rewarding and elating, as the great artists, the wittiest writers, and the most profound thinkers – or their students through the centuries might tell you. This, shall we say, “mechanical” transfer of mental vision from one mind to the next, also requires an honest mutual commitment, otherwise the process will simply break down.

How this transfer occurs is as follows: first, there is the concept, picture, vision, or experience that you have in your mind. Then, you must formulate it clearly into language. Then you must speak it in a language both you and your interlocutor understand. Then, your interlocutor must read/hear correctly what you have said. Then he must understand what you have said. Then he must repeat that process back to you. This is how a conversation occurs.

If anything goes wrong at any stage in this transfer, what was in one person’s mind will not reach the other person’s mind. If you formulate your thoughts imprecisely, it’s game over. If you make a mistake in speaking, it’s potentially game over. If the other person did not read what you wrote or hear what you said correctly, it’s game over. If the person does not understand what you’ve said, it’s game over. This is why conversations about important topics are often extremely difficult.

Here, there is a miscommunication going on. The stages work as follows (regardless of whether the transfer correctly occurs or incorrectly occurs): 1. The conception in the speaker’s mind. 2. Translating that conception into language. 3. The speaker speaks his thoughts. 4. The listener hears what the speaker said. 5. The listener translates what was heard into language. 6. The listener constructs what they believe to be the conception the speaker had. If we could just go from 1 to 6 without any medium, then things would be a lot easier. As you can see in this diagram, something can go wrong at any one of the 6 stages. The speaker has said here that the woman was outside of a burning house and the listener understood the woman to be inside the burning house. We make these mistakes all the time, especially the more complex the conception becomes.d

If an ignoramus wants, he can erroneously assume that he has faithfully received the mental vision that another human being is attempting to confer onto him and then proceed to show its flaws and inconsistencies with stunning arrogance. Unless one is committed to communication, one will likely assume that what they are attacking is in fact what the other person has in mind, rather than a deficiency in their own understanding of the other person’s mental vision. To be sure, it is possible to faithfully receive another person’s mental vision and then proceed to find flaws that the first person did not see, but the point is to make a distinction between what “I” have understood and what the other person has in mind, and not to automatically assume the two are the same, as if one has the capacity to immediately understand the complex thoughts of another always without error. Rather, like Socrates, one should seek clarification, or even help strengthen the other person’s argument and make more coherent their mental vision before attempting to find fault.

An important way to try to make sure you’ve understood the other person is to summarize a person’s argument back to them and ask them if that is accurate. This ensure’s you’re both on the same page. Anytime you’re in an argument with someone that goes awry, this should be your go-to move. The problem might just be that you’ve misunderstood them!

Sharing mental visions between minds potentially enriches both; it is possible to misunderstand and it is also possible to understand and provide critical feedback and counsel. Winning an argument by a concerted effort not to understand is nothing but a fool’s victory. Winning an argument, in general, is seldom a worthy goal (especially in personal interactions.) We usually gain nothing by winning an argument except the momentary satisfaction of feeling like we’re better than another person, but we gain long term wisdom by understanding more deeply the other person’s mind.

Given the necessity of language to communicate, it, therefore, becomes incredibly important to try to be as clear as possible and to establish rules of communication so that all parties know what is going through the mind of the speaker, and the speaker, in turn, can receive genuine feedback. If I claim to have chanced upon a proof for the existence of God that I find convincing, you cannot “step” into my mind to see what I see and thereby verify that claim through immediate knowledge. Rather, you must walk the path with your own mind’s eye. All I can do is attempt to set out the path using language. Once our minds have travelled the same roads, step by step, and you have seen what I have seen, only then, can you potentially accept or reject that mental vision. In principle, this acceptance or rejection should be based on whether the vision I am imparting to you coheres and the steps follow on another – in other words if the reasoning is solid. Perhaps you may have to ask directions while walking upon this road when you reach a certain point that requires clarification, but such is the nature of our deficient mode of communication. So how do we actually make sure we are walking the same path and seeing the same thing with the mind’s eye?

Focus on Concepts, not Words

It is incredibly important to understand the difference between words and concepts. The purpose of a definition in an argument is to make sure we are referring to the same concept every time we use a certain word or set of words. 

Observe that the following words: pen, stylo, and قلم (qalam) all refer to the same thing. They are completely different sounding utterances, yet they refer to the same concept. The actual sounds or written word, in a sense, is almost arbitrary and could be replaced by any other utterance as long as speakers agreed to use the word in that way. But, by social convention certain sounds refer to certain concepts in certain languages.

These totally different sounds/utterances/words refer to the same concept

In ordinary life, often the words we use have multiple meanings. Observe the following argument:

  1. A feather is light.
  2. What is light cannot be dark.
  3. Therefore, a feather cannot be dark.

As you can see, the word “light” has two meanings. Light1 refers to weight, whereas light2 refers to brightness, or electromagnetic waves. The word light here is, therefore, referring to two different concepts.

In general usage, the word “light” can mean two different things. The second picture is supposed to be light weights (as opposed to a loaded barbell). That was the best picture I could find  ¯\_(ツ)_/¯


General Usage Vs Stipulative Usage

Here’s a general problem to consider. For virtually every word you hear or use, you typically understand what concept that word is referring to without an explicit definition being given. We don’t have to sit here and debate “what is the definition of a bird” when I say “there’s a bird flying overtop the house.” I don’t have to define “house” or “fly” or anything else. It’s simply understood from general usage. In the course of one’s life, one will here hear the word “bird” used thousands of times, with a thousand corresponding images or experiences. Accordingly, someone can use a word correctly or incorrectly by comparing it to general usage.

When someone tries to give a definition of something that’s already understood by general usage, they are giving what’s called a descriptive definition. This definition can be right or wrong depending on if it accurately captures what people normally understand by a word. Whenever you hear people arguing about definitions, usually the concept is already understood by general usage, and what they are debating is whether a particular definition captures that idea entirely or not.

Often times, the charlatanism you encounter when hearing people argue about definitions is due to the fact that one person is trying to “define” a word that refers to a concept everyone already understands in a way that excludes certain key features, but suits their argument. The problem is if everyone already understands the concept being referred to by a word, defining it is unnecessary, for the purpose of a definition is precise to help us make sure that the word refers to the concept we want to convey. If I define a terrorist, not as someone who kills innocent people, but rather as someone who kills innocent Americans, for example, what I’ve done is I’ve pigeonholed the word so that I can manipulate it in an argument. This is not how people generally understand the word “terrorist” so to “define” it in a manner that does not accord with general usage is wrong. You can only imagine how much frustration is going to occur in that argument.

But this is not entirely true. We just saw that completely different utterances in different languages can point to the same concept; in a sense the word is arbitrary. Could I use the utterance “bird” to refer to the concept we normally understand when I say “pen”? Well, if I don’t announce that first, communication will become impossible because any word could refer to any concept and we’d all just become confused. But what if I stipulate that every time I use the word “bird” or “blooblah” for that matter, the concept I am referring to is what we normally understand as “pen”?

This is perfectly legitimate. If I say “by definition, a blooblah is not a chair,” this is not simply wordplay. Suppose that I’ve stipulated that “blooblah” will refer exclusively to what we normally think of as “pen” in this discussion, and hence to use the word “blooblah” to refer to the concept “soft drink” is incorrect; for pens and soft drinks are different things. A stipulative definition is when I say “Right, look here. It doesn’t matter how the following term is used outside of this conversation, for the purpose of everything that follows, everytime I use the word ‘x’ its going to refer to the following concept: [a definition that will hopefully succeed in transferring the concept I have in mind into your mind.]” If I stipulate a triangle means “a shape with three sides” and someone asks “well why can’t you have a triangle with four sides?” It’s not incorrect to point out that you cannot have a triangle with four sides because by definition a triangle refers to a shape with three sides. You can have a shape with 4 sides, but you can’t call it a triangle as far as this discussion (or even general usage) is concerned. A four-sided shape can exist, but if we’re to avoid confusion, it must be called something else.

In principle, this is legitimate, although it might lead to much confusion. Stipulated terms refer to whatever concept you stipulate they refer to, within the context of that discussion.

So could I stipulate the word “terrorist” to mean “someone who kills innocent Americans” instead of “someone who kills innocent people” generally? Sure, but then I’d have to distinguish the two concepts, and I’d have to be extremely judicious not to use one to mean the other throughout the discussion. But given the complex nature of language, it’s better to simply use another word otherwise confusion will abound. Furthermore, the implicit implication of using “terrorist” to mean something other than what is generally understood will no doubt seep into the discussion because words usually have multiple connotations some of which elicit strong emotions.

Typically, what we do to avoid these situations is just make up a new word to refer to the concept we have in mind. For instance, we might distinguish a terrorist who kills innocent Americans from a terrorist generally, as an “anti-American terrorist.” Adding “anti-American” makes it a compound word which refers to a more specific concept than the general idea of a terrorist.

How This Applies to the Proof of the Existence of God

In the proof of the existence of God, I will often say “this is impossible by definition.” People unacquainted to thinking in terms of stipulated definitions instead of general usage will think this is some kind of wordplay to negate their point. It is not. It is having razor-sharp precision, precisely to avoid the kind of wordplay charlatans take advantage of. We stipulate the definition of the key terms in the argument (i.e. the concepts those words will refer to) in a very strict way so as to limit misunderstandings.

Here is an example: suppose I define a dependent being as something which requires another being in order to exist, and an independent being as the negation of that (i.e. something which does not require another being to exist).

This is a definition by stipulation. Every time we use the word “dependent being” it refers to this concept. An independent being would just be A alone, with no arrow pointing to B.

Then suppose someone offers the suggestion, that there could be a chain of dependent beings which terminates in the first member that is a dependent being that simply “pops” into being from absolutely nothing.

This is what they’re thinking. “A” here is the first member of the chain that spontaneously pops into existence.

Let’s zoom in on A here and analyze it further.

The concept that the person is probably thinking of is (at least prior to analysis) legitimate. A being that simply pops into existence from nothing. But a dependent being that pops into existence from nothing is not. That cannot be true by definition because we’ve just defined a dependent being as referring to the concept “something that requires another being for its existence.” The concept being proposed here is precisely a being that does not require another being for its existence; after all, it just popped into being! The concept of a being just popping into existence would therefore be a type of “independent being” – a being which does not require another being in order to exist. The concept of a being popping into existence is fine; calling it a dependent being is not, for it would be incoherent. That’s what “can’t be true by definition” means; the concept of a dependent being that pops into existence is like a four-sided triangle. If a dependent being is “popping” into existence from nothing then that is to say that it is not dependent on another being. Again, by the definition of the words “dependent being” and “independent being” stipulated at the beginning of the discussion, a being that does not require another being to exist is an independent being, not a dependent being. To call one the other will confuse the discussion.

This is not wordplay. This is being very precise with our words so that we can refer to coherent concepts and then show how certain things are logically impossible. If we muddy which words are referring to what concept then we can’t have an argument. We’ll be reasoning like the “light feather” example above. Here are some diagrams to clarify the above:

This is what the person is thinking.

But recall, this is the definition of a dependent being.

This is what the person said.

A cannot be both dependent on B and pop into being. This is because “popping into being” just means A is not dependent on B. So the person is unwittingly claiming that A is both dependent and not-dependent on B. This is a clear contradiction.

This is the only way that the original conception the person had could possibly make sense. So we need to use these words and say “a chain of dependent beings that terminates with an independent being that popped into existence” so that we are clear and don’t make mistakes in our reasoning.


Going forward, I hope the following points will stick:

  1. Try to understand what concept a person has in mind when using a particular word. This should ideally appear like a picture in your mind. (Fun fact: the literal word for “concept” in Arabic is tasawwur which means “to picture.”)
  2. In a serious discussion, try to use that word consistently to refer to that concept and only that concept. If you need to make distinctions, use different words or qualify the word with an adjective (e.g. “birds” vs “blue birds.”)
  3. Commit yourself to the mutual transfer of mental vision, and engage in Socratic dialectic, try to understand what the other person is saying and even try to make their argument even stronger before attempting to take it down.
  4. If a person already knows what a concept refers to, there is no need to hairsplit on a definition unless it is somehow relevant to the discussion. Some people ask you for a definition when they already know what you’re talking about as a cheap trick to try to win an argument because definitions are notoriously difficult to give. Don’t fall for this.

If this article has helped you, please share/subscribe. Also consider linking this article the next time you’re having an impasse in a discussion with someone, whether online or off, as I believe it to be of general benefit for learning how to discuss and argue in a more productive manner.