Why Atheists Can’t Know That 2 Apples + 2 Apples = 4 Apples...

The title of this article may be a bit misleading. There are obviously very capable and very knowledgeable mathematicians who are atheists. Such people do not only know that two apples plus two apples equals four apples, they can also provide elaborate proofs of the various mathematical theorems that undergird such a truth. This post is not meant as an attack on the intellect of atheists but rather as an attack on atheism as a philosophical system. A more accurate title would be “Why Atheists Can’t Know that 2 Apples + 2 Apples = 4 Apples If They Were Being Consistent With Their Philosophical System”. I know, not very catchy!

But what is it about atheism as a philosophical system that precludes knowledge of a truth so basic and fundamental that even children know it? The short answer is that atheism commits one to an autonomous epistemology—an epistemology that rejects the necessity of divine revelation. Believing that two apples plus two apples equals four apples is easy enough. The problem arises when one is asked to account for that knowledge. How do we know that two apples plus two apples equals four apples?


Well, one obvious answer is that it is an instance of the more general mathematical truth that 2+2=4. We are simply applying this truth to the realm of apples. This raises another question, however: how do we know that 2+2=4? This is where things get a bit tricky.


One might say that we know that 2+2=4 by repeatedly experiencing instances of its truth and then extrapolating to the more general truth. In other words, we repeatedly observe that two things (apples, oranges, books, etc.) plus two things equals four things and from these observations we make the generalization that 2+2=4. There are a host of problems with this however.


Firstly, for this approach to work, we would need to possess the mathematical concepts of twoness, fourness, addition, and equality prior to our experience of the world. If not, then there would be no way to even know that there are two things in front of us. But how do we obtain these concepts? It cannot be through inductive generalizations since we must possess them prior to experience. Perhaps we obtain them a priori (that is, wholly apart from experience). We shall see the problem with this in a bit.


Secondly, such an approach would imply that 2+2=4 is not a universal truth. A universal truth or principle is one that holds true for all members of a class and whose application is not restricted by spatio-temporal constraints. For example, “all bachelors are unmarried” is a universal truth because it applies to all bachelors regardless of time or place. Basically, there are no exceptions to universal truths. However, if 2+2=4 is known through generalizations from experience, then it cannot be said to be universally true because human experience is not universal in scope. No one has observed all instances of such a truth. At best, what can be said is that, as far as we know and have experienced, 2+2=4 holds true. We would have to allow for possible exceptions and admit that there may be some instances where 2+2 is not equal to 4. 


But if it is not a universal truth, then we cannot even say whether or not it applies in our narrow domain of experience. Even in areas where its truth has been previously verified, it could turn out that it no longer holds true. Without universality, 2+2=4 becomes like any other particular fact of history. Saying “2+2=4” would be just like saying “it is raining”—true at some times and in some places, false at others. As such, applying this truth to the realm of apples becomes impossible because we can never know whether or not it is true for those apples or not. We still do not know whether two apples plus two apples equals four apples. 


What other answer could be provided to the question of how we know that 2+2=4? It could be said that we know it’s true apart from experience. This answer may come in different forms—intuition, self-evidence, analyticity, the incoherence of its denial, etc. The main idea is that we can know that 2+2=4 without having to go look into the world. There are problems with this as well.


The biggest problem with this approach is that, although it preserves universality, it severs any connection between the truth that 2+2=4 and the facts of history. 2+2=4 becomes a purely formal, abstract principle with no relation to the realm of apples, shoes, chairs, etc. Why think that its truth is ever instantiated in the world of facts? There’s no reason to think that. If we bring this truth to experience and interpret experience according to it, then we would surely encounter what appear to be instances of its truth. However, we could simply be deluded. The objects of experience (apples, oranges, etc.) may be such that they cannot be numerically categorized. If so, then it’s futile to try and apply such a mathematical truth to them. We still do not know whether two apples plus two apples equals four apples.


Atheism as a philosophical system does not have a solution to this epistemological predicament. This is because, on atheism, there is no God and man is left totally on his own in epistemology. A God who eternally relates all facts into a system and who reveals certain universal truths to man so he can be able to mirror that system would surely be an indispensable ally. Atheism has no such God. And as such, knowledge of such a basic truth is precluded.


Comments

  1. This is laughable. We can account for math without some god just fine. I note that you offered no account for it. To claim that math reflects the nature of God's thinking tells us about God and not math, and to say God is logical and thinking mathematically is utterly question-begging because you are already assuming math in the first place. This view is known as Divine Conceptualism which fails because it leads to an infinite regress of thoughts. Nowhere in the Bible does it state that Yahweh revealed the truth of mathematics. The truths of mathematics are synthetic a priori descriptive abstraction that refer to relationships between quantities.

    Your criticism fails because your revelation is no better than a worldview which denies it. I hold to an external epistemological justification based on evolutionary reliabilism. Since in my worldview there is a reality where there are brute natural regularities and systems where natural selection produces reliable sense experiences and cognitive abilities, I can have knowledge without invoking your god. Evolution is a much better explanation for why our senses co-vary systematically with changes in the world around us than "God makes sure our senses reflect reality around us". Positing such a god doesn't actually explain anything, even IF such a being existed. Further, evolution (a demonstrable set of natural processes) does explain how and why senses would emerge, why memory would be needed and trusted, why certain sorts of inferences would be ways of avoiding error, etc. Positing a mindless reality of stable regularities is actually epistemically more trustworthy than positing a reality that can be changed by the will of a supermind. If that's how reality is, then that's a reason to trust one's senses LESS, not more. The exact opposite conclusion is implied to the one you want to affirm.



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    1. Respectfully an a theistic worldview cannot give an accounting of anything much less math. Nothing created everything by random chance mistakes and mutations in a universe that has no purpose and did not have you in mind, a universe of blind pitiless indifference. You said the Christian worldview is begging the question by assuming math but I will take it a step further and say the Christian worldview begs the question further back than this and in fact assumes the God revealed in the Bible and this leads to our understanding of math. the Christian worldview argues from the impossibility of the contrary. Without the God of the Bible you couldn't know anything. Now, to be fair the atheistic worldview also begs the question when you say "I hold to an external epistemological justification based on evolutionary reliabilism. Since in my worldview there is a reality where there are brute natural regularities and systems where natural selection produces reliable sense experiences and cognitive abilities, I can have knowledge without invoking your god."
      Here your worldview begs the question when you rely on your cognitive/senses and experience making the absolute claim that "I can have knowledge without invoking....
      So what you are saying is you are the ultimate arbiter of what can and can't be known. We all beg the question when it comes down to the ultimate. If you had to prove an ultimate with something other than the ultimate it would no longer be the ultimate.
      Without the Christian God of the Bible you couldn't know anything, but you do know things. You know God but the Bible says you are suppressing the truth in unrighteousness because you hate the idea of being accountable to God. You want to be autonumous, your own god. And the atheistic worldview is consistent in denying God existence so it can do as it pleases. But iñ the end if the atheistic world view were honest with itself (although it has no standard for truth, therefore no reason to be honest) would admit you couldn't know anything coming from a belief that: Nothing created everything by random chance mistakes and mutations in a universe that has no purpose and did not have you in mind, a universe of blind pitiless indifference.

      I pray that you repent and trust in Jesus to save not only your soul from hell but to redeem your mind now.

      Read below to see what God says about your position against Him:

      For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men who suppress the truth in unrighteousness, because that which is known about God is evident within them; for God made it evident to them. For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse. For even though they knew God, they did not honor Him as God or give thanks, but they became futile in their speculations, and their foolish heart was darkened. Professing to be wise, they became fools,
      Romans 1:18‭-‬22

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    2. Floyd,

      “This is laughable. We can account for math without some god just fine.”

      Well, saying so does not make it so. The article explained exactly why knowledge of mathematical truths is not possible on atheism. You’re yet to address the arguments in the post. So your assertion that you can “account for math” without God remains unsubstantiated.

      “I note that you offered no account for it.”

      Yes, because the aim of the article was to show why atheism cannot account for mathematical knowledge.

      “To claim that math reflects the nature of God's thinking tells us about God and not math,...”

      This shows you have not really grasped the nuance or the Christian answer to these questions. If you want to know how the Christian view relates God and mathematical knowledge, just ask.

      Furthermore, to say that such an answer (which is an oversimplification of the actual Christian answer) tells us about God and not math is just false. It tells us about both. It puts math in a relation which God which explicates its place in the metaphysical hierarchy of the Christian system.

      “...and to say God is logical and thinking mathematically is utterly question-begging because you are already assuming math in the first place.”

      I’m not sure you understand what it means to beg the question. Saying God is logical in no way begs the question.

      “This view is known as Divine Conceptualism which fails because it leads to an infinite regress of thoughts.”

      Further evidence that you fail to grasp the nuances in this discussion. There are other views besides divine conceptualism. I go for a more robust Archetype-Ectype Model [Sutanto (2015)].

      “Nowhere in the Bible does it state that Yahweh revealed the truth of mathematics.”

      So what?

      “The truths of mathematics are synthetic a priori descriptive abstraction that refer to relationships between quantities.”

      This view was addressed in the post which you still have not addressed.

      “Your criticism fails because your revelation is no better than a worldview which denies it.”

      Saying “your revelation is no better” is a tacit concession that the critiques presented are successful. That aside, you have given no reason to accept that assertion.

      “I hold to an external epistemological justification based on evolutionary reliabilism. Since in my worldview there is a reality where there are brute natural regularities and systems where natural selection produces reliable sense experiences and cognitive abilities, I can have knowledge without invoking your god.”

      Since the post has nothing to do with the reliability of the senses or cognitive faculties, I fail to see how these (barely intelligible) assertions are even relevant.

      “Evolution is a much better explanation for why our senses co-vary systematically with changes in the world around us than "God makes sure our senses reflect reality around us". Positing such a god doesn't actually explain anything, even IF such a being existed. Further, evolution (a demonstrable set of natural processes) does explain how and why senses would emerge, why memory would be needed and trusted, why certain sorts of inferences would be ways of avoiding error, etc. Positing a mindless reality of stable regularities is actually epistemically more trustworthy than positing a reality that can be changed by the will of a supermind. If that's how reality is, then that's a reason to trust one's senses LESS, not more. The exact opposite conclusion is implied to the one you want to affirm.”

      Again, I’m failing to see the relevance.

      ~Daniel

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  2. 1. Kant's notion of math as synthetic a priori was refuted long ago. Plenty of professional literature on this. Besides, this would committ him to scientific Anti-realism since synthetic a priori's are about how we have to conceive of the world and not how the world is in and of itself. Transcendental Idealism precludes scientific realism, that is, the belief that science gets us epistemic access to the way the world is in and of itself. He can't consistently hold to both.

    2. Evolution doesn't aim to produce organisms with mostly true beliefs. It doesn't select for truth at all. So Evolution undermines Reliabilism. See Plantinga's work on Evolution and Naturalism as defeaters. Plenty of individuals survive with mostly false beliefs and plenty of organisms survive with no beliefs at all and plenty of beliefs have zero survival value.

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    1. //Evolution doesn't aim to produce organisms with mostly true beliefs. It doesn't select for truth at all. So Evolution undermines Reliabilism.//

      Lies in the name of God! What else can we expect from desperately dishonest apologists like you?
      One doesn't need to know all in order to survive, but one needs to have a basic knowledge/understanding of the world in order to survive on a daily basis...if one is a species requiring such a basic understanding of the world. If you over and over misjudge your environment, you won't even survive a single say. And such individuals aren't our ancestors. Only those individuals whose perception work(ed) appropriately contribute(d) to the survival of our species.

      //See Plantinga's work on Evolution and Naturalism as defeaters.//

      Repeating what has been refuted over and over won't help you. It only shows your utter despair. Also, his argument begs the question because according to the argument, the supposed falsehood of 'evolutionary naturalism' must be presupposed in order to 'conlcude' its falsehood...because it argues naturalism gives a 'defeater' for knowledge.
      So either we can know things or we can't. If we can, then we can show your faith to be false. If we can't, then you can't show we supposedly err. Either way, you lose.

      //Plenty of individuals survive with mostly false beliefs and plenty of organisms survive with no beliefs at all and plenty of beliefs have zero survival value.//

      That's because different species have different survival strategies. But intellectual honesty is not your strong suit. Just because there are *other* species surviving with no beliefs doesn't mean the same is true for us.

      ____________

      You people are so bad! If your magical, imaginary genie in a bottle existed, he'd be maximally ashamed of every single one of you people. None of you would make it into imaginary heaven with all your constant lying.

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  3. 2+2=4 *by definition*. Has nothing to do with 'divine revelation'. Math is logic, and logic is independent of whatever god you pretend exists. Even gods depend on logic (that's why logically impossible gods can't exist; the notion of a god having a distinct *nature* distinguishing it from other things presupposes logic).
    The notion of *one* god (and that removing the supposed only one god means "0 god") presupposes math/logic to be already in place. This means that truth - and by extension knowledge - has nothing to do with a god.
    The laws of logic describe the nature of existence. And if your little imaginary poltergeist existed, he'd be a member of the set of things that exist. So once you claim logic/math is derived from your god or his miraculous nature or whatever, then you admit your god to not be part of the set of things that exist for he'd be above/independent of existence.
    So either your god does not exist, or logic/truth/knowledge has nothing to do with you god. IOW: It's not "math presupposes God" but rather "God presupposes math".

    You failed. Epicly. Miserably. Albeit, expectedly.

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    1. "2+2" is another way of saying "4". If we call "II" "two" and write "2", and "IIII" "four" and write "4", and if "addition" means "putting together", then IIII=four=4 is putting together II=two=2 with itself again so to say.

      //A God who eternally relates all facts into a system//

      That's problematic for two reasons:
      1. That system would itself be a fact and thus, leading to an infinite regress. This shows it's not possible to "relate al facts into a system".
      2. "eternally relates" is self-contradictory. If your imaginary friend "eternally relates facts", then he never started relating facts. Your god would be merely eternally aware of those "related facts". That's why "eternal omniscience" precludes authorship and by extension, magical creation because creativity presuppoes ignorance resulting in the emergence of new ideas. Your god could only act upon an eternal stock of ideas he didn't author.

      And this leads to the realization that if your god eternally knows everything, it means how the universe looks like and how we as humans look like and are has nothing to do with your god. Your god could have merely been eternally aware of how the universe looks like and how we as humans look like and are. This means "the image of God" has no origin let alone a divine one. There'd be literally no reason why we are the way we are. So once you claim to be able to offer explanations regarding human nature using a god, you automatically deny it's the god of the Bible.
      Your worldview precludes the concept of "explanation" or how you call it, "accounting for something". IOW: Your worldview is epistemically void. You have no epistemology. You can't know let alone account for anything.

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