About a month ago, a student skeptical of the existence of God asked, “How do we know if we know anything?” This question is much deeper than you may at first suspect.

A baby is born. Within a month or two the child notices a face looking at it and, for a reason that I suspect will someday shock modern science if it is discovered, the eyes of the infant lock on to the eyes of what we call “a face” (though the infant has no words yet to label things with) and she smiles. What is going on?

You might say that she is “looking at” someone's eyes, but put yourself back to being an infant. You have just made a major assumption—that there is a reality outside your mind and you have the ability to perceive it, experience it, and learn facts about it that you assume to be true and not false.

How do we know that there is a reality “out there” and how can we know what is true about it? You will find this article to be an excellent mental exercise that may enhance your ability to think and make rational decisions if you are willing to slug your way through it.

The Problem: If we take a purely materialistic view, the laws of physics control all physical, chemical, and biological reactions so all there is in the infant’s brain while gazing at the eyes of another person, is a physicochemical state we label as a “sense perception”. Electrons are moving in micro-circuits, chemical reactions are occurring, and micro electric and magnetic fields are fluctuating resulting in a “brain state” that is, in principle, no different than a pot of soup simmering on the stove. The soup-state comprehends nothing about a reality “out there”. It simply just sits in the pot simmering away.

Although the brain has more physical reactions occurring and is more complex, it is still (from a materialist perspective) just a physical mass in a brain state controlled by the same laws of physics that control the soup.

Question: How does the brain “know” from the physicochemical state it is in, that there is an external reality that can be known and from which “facts” can be inferred, and added to a repository we call “knowledge”— and how does it know the difference between true facts and false premises and perceptions?

What the research shows: More than 30 years ago, I became aware of research on infants, revealing that the fundamental axioms (or laws) of logic and mathematics are already pre-programmed into their minds. (see footnote 1) For example, the infant automatically knows that the sense perception it is experiencing is actually caused by something external to itself, demonstrating that the causal principle appears to be programmed and present at birth.

Another law of logic pre-programmed into the minds of infants is the law of non-contradiction which means that something cannot both be perfectly true and perfectly false at the same time. This enables an infant to see something shiny on the floor, accept it as “true”, and crawl toward it. Of course, she does not consciously think, “I conclude that I have experienced a true sense perception” -- we are seldom conscious of the thousands of conclusions and decisions we make each day. However, the laws of logic, coupled with the infant’s perceptions, create the problem of how to experience that shiny object better. The solution for the infant is to decide to move toward it for closer investigation.  As the infant plays with the shiny object, memories are stored that can be labeled as “knowledge”. To clarify, without the law of non-contradiction, the concepts of “true” and “false” would be nonsensical, neither the infant nor anyone else would know what to do with a sense perception that could be both true and false. Furthermore, there would be no facts to know in a world where everything was both true and false, and one could not draw conclusions or accumulate knowledge about anything at all in that world.

The laws of logic: Sometimes there can be a massive “elephant in the room” and few people even realize it is there. In this case, I’m talking about the fundamental laws of logic and mathematics—let’s call them axioms. An axiom is a foundational law or principle one cannot prove or derive without using that law in the proof—a circular problem but, at the same time, it is impossible to draw logical or mathematical conclusions without it. Axioms are the starting points for reason and mathematics, but they are more than that. For example, it is impossible to prove the law of non-contradiction without depending upon the truth of that law in one's attempt to prove it. The same goes for the causal principle – it is impossible to prove there is a causal relationship between the premises and the conclusion without assuming a causal relationship between the premises and the conclusion – a most enlightening fact that my logic professor pointed one lecture during my graduate studies in philosophy. The axioms that seem to control both the material world as well as the immaterial world of logic and mathematics are both real but immaterial—a fatal challenge to the assumption that all reality is material or physical.

The laws of nature: During my first year of undergraduate physics, one of my professors said something that has stuck with me ever since. He said that no one knows what or where the laws of physics are. All we can do is create mathematical descriptions of how these laws of physics control space, time, matter, and energy. The physical world does not control the laws of physics; it is the other way around. But these laws of nature appear, themselves, to be subject to deeper fundamental laws of logic and mathematics, such as the law of non-contradiction and the causal principle. But this opens the door to a disturbing problem—the belief that science explains everything, or that the only thing that exists is the physical domain of space, time, matter, and energy, and here is why.

The stunner: The laws of physics, themselves, are not physical. They are not made out of space, time, matter, or energy; therefore, they are non-physical (i.e., immaterial), but they control the physical world. The laws of physics, however, are themselves subject to yet another higher level of non-physical reality—the axioms of logic and mathematics. For example, the laws of physics could not govern the physical world without the axiom we can call the causal principle, enabling them to have a causal effect on space, time, matter, and energy that is so consistent that we can describe these effects with mathematical equations. We can infer from this that the causal principle itself spans both the immaterial reality of the laws of physics and the material reality of physical interactions. These laws of physics (or the laws of nature) are also subject to the axiom known as the law of non-contradiction to the extent that our scientific method depends upon it when it comes to the falsification of predictions. The law of non-contradiction is also how we know that our current understanding of certain aspects of quantum mechanics, for example, is incomplete or flawed.

Three levels of reality: We are forced to concede that there are at least three levels of reality. We can arbitrarily label the physical world of space, time, matter, and energy as material reality or, in other words, level one. Material reality is itself subject to a higher level of reality (i.e., the laws of physics) that is non-physical or immaterial—level two. But the laws of nature, themselves, are subject to a higher non-material reality of the axioms of logic and mathematics—level three.

We now know that science depends upon the existence of an immaterial, non-physical reality that contains the laws of logic and mathematics that are prerequisites to the physical world. As to what the options are for this reality, that is another discussion; however, the option with the greatest explanatory power is that there is an ultimate non-material conscious mind behind physical reality and the axioms of logic and mathematics are actually attributes of that ultimate mind.

Back to the infant: It is impossible for the infant experiencing a sense perception we would describe as “seeing a face and locking onto the eyes of that face” to infer a reality that exists external to the inside of her head unless there are basic laws of logic already “pre-programmed” into the child’s mind. The same holds for the axiom of non-contradiction. 

To summarize, these pre-programmed axioms of logic and mathematics enable the infant to start building a body of knowledge that would not otherwise be possible.

Next steps in acquiring knowledge: We have already seen above how the basic process of acquiring knowledge takes place. But there are still some remaining questions:

1. How do we define a true belief?

2. How do we know there is an external reality?

3. How can we acquire beliefs and make decisions that are likely to be true?

What is a true belief?: The everyday, common sense way people cross the street can be described as the correspondence definition of a true belief—a belief is true if, and only if, it corresponds to reality. The problem then moves to the question of “what is reality?” This is true whether we are talking about physical reality and scientific hypotheses or moral reality and moral truths. In every case, true beliefs must correspond to reality. Even a contemporary, post-truth person, who believes that truth is defined by their personal beliefs and experience, still does not casually step out to cross the street without checking both ways, suggesting that although they cherish the concept of “my truth”, the correspondence theory of truth is what they practice when crossing the street in the real world.

Is there an objective, external reality?: Let us suppose for a moment that everything you experience is imaginary—occurring only in the head you imagine you have. Why is it that there are lots of multi-millionaires in your imagination, but you are not one of them? Why are you imagining yourself to be inexorably aging, when there are lots of young people in the prime of life that are being constructed by your imagination? And why, in your imagination, are you forced to comply with bad laws made up by imaginary politicians if it is all just in your imagination?

Since most of what we experience is beyond our control and is consistent in how it functions, the best explanation is that there is a reality ‘out there’ external to myself and things work best when I ensure that my set of beliefs correspond to that reality.

A logical argument for an external reality:

Starting with the laws of logic we were pre-programmed with, the case for reality that is external to our minds can be summarized as follows:

1. Part of what I experience is consistent and not controllable by myself.

2. If (1) is true, then the best explanation is that the consistent, non-controllable portion is caused by reality external to my mind.

3. Therefore, there is a reality external to my mind.

So, if there is reality that is external to our minds, how do we acquire knowledge—a collection of beliefs that corresponds to the reality that is out there?

Four ways we know things::

1. Foundational knowledge: We simply accept the axioms of logic and mathematics that come pre-programmed in our minds from infancy, as true. Without those, we cannot even process or understand the sense perceptions we experience. True and false would not exist in any meaningful way, and we cannot even take the first step in reasoning. We can call this foundational knowledge, and it is our starting point.

2. Deduction: If the evidence is true, then the conclusion must be true. This is called a deductive conclusion. (see footnote 2) For example, it would be a violation of the law of non-contradiction for nature to cause itself to come into existence. This leads to the following deductive argument:

1. The cause of nature is either natural or non-natural (immaterial).

2. It is logically impossible for nature to cause itself.

3. Therefore, the cause of nature must be non-natural (immaterial).

3. Induction: If the evidence points to a conclusion that is likely or probably true, then the most rational move is to accept the most probable conclusion. This is called an inductive conclusion. (2) For example:

1. Of the few thousand copies and fragments of early New Testament manuscripts that have been found, for most variations, the vast majority of early manuscripts do not contain those variations.

2. If (1) is true, then we can inductively infer with a high degree of probability that what the consensus of early manuscripts states is what was originally written down. 

3. Therefore, the New Testament we have today has accurately preserved what was in the original manuscript.

Note the inductive move from “high degree of probability” in (2) to “actually” in (3).

4. Abduction: If, when all the evidence is examined, there is one conclusion that accounts for that evidence more completely than some other option, then the most rational conclusion to choose is the one with the most explanatory power. This is called an abductive conclusion. (2) For example:

1. There is substantial historical evidence that on the third day after the crucifixion of Christ, his tomb was empty even though it was guarded by 4 to 16 Roman soldiers, and over the next 40 days Jesus physically appeared to individuals and groups as large as 500 people.

2. The best explanation for (1) is that Jesus physically rose from the dead on the third day. (see footnote 3)

3. Therefore, Jesus rose from the dead on the third day.

Note: Although at least six different theories have been advanced to explain the known historical facts, only one theory—that Christ physically rose from the dead, accounts for all the evidence. We can, therefore, by abductive inference, conclude that Jesus rose from the dead on the third day. (3)

Four fatal mistakes: At present in our society, irrationality has exploded in epidemic proportions to the extent that many people in our culture today hold beliefs that have crossed the line into irrational insanity. Here are four fatal mistakes:

1. “If it cannot be proved with 100% certainty, then I have rational grounds for skepticism.” This is false. The question one must ask oneself is, “In light of the evidence, what argument or evidence do I have to justify my skepticism?” The assumption that one does not have to rationally justify their skepticism is a common mistake

2. “If the evidence supports a particular conclusion and then some other random person suggests a different possibility supported by little, if any, evidence, then both conclusions carry equal weight.” Competing options almost never have equal weight! “Suggestions” often can have little or no supporting evidence that can be tested. Always ask, “What evidence is there for this “suggestion” and how does it compare with the evidence pointing to the other option that we already have?

3. “I define what is true by my own experience, feelings, and personal beliefs.” This “my truth” definition of true beliefs detaches itself from reality. The fatal mistake is that beliefs that are detached from reality will collide with reality at some point, often with very unfortunate circumstances.

4. Closely related to (3) is the belief that logic and reason are “colonial concepts” despite the fact that in even the most ancient writings of human civilization, the basic axioms of logic can be observed. Secondly, such a belief is self-defeating, pulling the rug of rational justification out from under the woke ideologue’s feet: the moment they attempt to justify their belief, they contradict the very belief they are trying to justify. To hold such a non-rational belief denies the very foundational laws of logic and mathematics that are required to even begin to acquire knowledge.

The missing link: As I mentioned earlier, apart from certain logical and mathematical proofs, there is very little we can know with absolute, 100% certainty. So what is the missing link that crosses the gap of uncertainty to confidence, such that we can say we “know” something?

 We constantly do it every day and it is called faith–which ranges anywhere from a total blind leap in the dark (irrational, 100% faith) to absolute certainty (0% faith). For example, if the probability your flight will safely arrive at your destination is 99.99%, then there is not much faith required to board the aircraft—only 0.001%. Given this, boarding the aircraft would be a rational decision even though a small amount of faith is still involved. Submitting yourself for brain surgery might require a higher degree of faith. On the other hand, purchasing a lottery ticket to fund one’s retirement with a probability of 1 chance in 10 million requires what we might call blind, irrational faith.

Blind faith vs. justified faith: Quite simply, a total blind leap in the dark with zero justifying evidence to base it on is irrational foolishness. A sound, rationally justifiable faith should have a solid basis upon which to stand. Your observations might include facts like the reliability record of chairs when sat upon, the safety record of airlines, or the consensus of thousands of early New Testament manuscripts.

Back to the student discussing the existence of God … Richard Dawkins has often described the special case of religious faith as believing something that contradicts the facts, and with absolutely no supporting evidence. This is about an extreme as a misrepresentation possible. The process of how we know things, coupled with a rationally justified faith enables us to acquire an enormous amount of knowledge of reality, including the material world and immaterial reality that controls and governs it.

References:

1. Laws of logic and mathematics pre-programmed into our minds:

• Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1-B11. This paper explores the capacity of infants to discriminate between large sets of objects, supporting the idea of an early "number sense.”

• Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389), 749-750. This study demonstrated that infants as young as five months old showed surprise at unexpected outcomes in simple addition and subtraction scenarios.

• Piaget, J. (1954). The Construction of Reality in the Child. Basic Books. This work is foundational in developmental psychology, detailing Piaget's stages of cognitive development, including the development of object permanence.

• Baillargeon, R., Spelke, E., & Wasserman, S. (1985). Object permanence in five-month-old infants. Cognition, 20(3), 191-208. This study challenges some of Piaget's findings by demonstrating object permanence at earlier ages through "violation of expectation" paradigms.

• Baillargeon, R. (1987). Object permanence in 3½- and 4½-month-old infants. Developmental Psychology, 23(5), 655-664. This paper extends the idea that infants have early expectations about physical events, such as the solidity and permanence of objects.

• Spelke, E. S. (1990). Principles of object perception. Cognitive Science, 14(1), 29-56. Spelke discusses core principles that guide infant perception and expectations regarding objects' physical properties.

• Téglás, E., Girotto, V., Gonzalez, M., & Bonatti, L. L. (2007). Intuitions of probabilities shape expectations about the future at 12 months and beyond. Proceedings of the National Academy of Sciences, 104(48), 19156-19159. This study indicates that infants can make rudimentary probabilistic judgments based on observed events.

2. Types of Inferences, Openstax.

3. Michael R. Licona, The Resurrection of Jesus: A new historiographical approach. IVP Academic, Downers Grove Illinois, USA and Apollos, Nottingham, England, 2010.