Locke’s Proof Against Innate Mathematical Knowledge

John Locke proves that mathematical knowledge is not innate in An Essay Concerning Human Understanding by contrasting Plato’s theory to learning through sensation and perception, thus curating the theory of empiricism. Through his arguments, Locke proves mathematical knowledge is not something that you are born with, clarifying that Plato’s universal consent proves nothing. Knowledge is not imprinted; it is learned through observation, sensations and experience. Locke assesses the situation between Socrates and the Greek boy in the Meno, and how the boy actually assented to multiple correct answers, and deduces that all knowledge is adventitious.

While Plato argues all knowledge is innate, Locke disagrees and justifies empiricism. Plato displays his theory of innate knowledge through universal consent, the idea which because humanity can agree, it authorizes his theory of innateness. Locke argues this by stating that universal consent proves nothing, “if there can be any other way shown how men may come to that universal agreement, in the things they do consent in, which I presume may be done.” (Locke 1) Because people agreeing on something, doesn’t mean it was knowledge that came from their souls. Plato needed to rely on this to justify innateness, it was his only explanation to show that the boy was able to assent to correct answers without being taught. However, Locke suggested learning is a recipe, through observation, sensation, and reflection you gain knowledge. This boy in the Meno was Greek, “He is Greek, and speaks Greek, does he not?” (Plato 2). Therefore he knew the language Socrates spoke, and was able to answer questions. However, nobody is born with language. Language is learned; if Socrates were speaking to the boy in German, for example, the boy would not be able to answer the questions, and thus correct language authorizes answers. Mathematical knowledge is simple compared to a subject like language. Which is why Plato chose it rather than another subject which would be harder to prove his theory with, through asking the Greek boy simple questions, the boy was able to do simple mathematical actions such as add, and multiply. Plato took this as explanation, whereas there is better explanation as to why the boy was able to answer correctly; Plato asked leading questions. Plato asked the boy yes or no questions, where the boy hardly had to think about the question, but more about the right answer Socrates was leading him toward. There was a point where the boy answered incorrectly, which is when Socrates stopped as it began disproving his theory. Socrates manipulated the boy into saying yes to his questions, which highlights how Plato’s theory fallacious.

Locke defamiliarizes the theory of innate knowledge and spotlights Plato’s approach to justify his hypothesis was in fact, faulty and incorrect. Locke continues by using “children and idiots” (Locke 1) as examples regarding lack of innate knowledge. Locke clarifies that, if “children and idiots” have souls, innate knowledge should be there just as all of mankind, as Plato had proposed. He clarified that Plato’s claim contradicted itself: “it is evident, that all children and idiots have not the least apprehension or thought of them.” (Locke 1) Locke reminded us, if all knowledge is innate, it’s illogical for people to have variations of intelligence. Why would “children and idiots” know less than say, a mathematician or scientist? Locke would say it’s because children and idiots haven’t learned, or are incapable of learning. This justifies why some are better at certain subjects than others. “Children and idiots” might be able to complete simple mathematical questions, because they have learned how to reason. To justify this, let us look at how the Greek boy is able to answer the questions. Socrates explains a mathematical fact, “And you know that a square figure has these four lines equal?” (Plato 2) Socrates questions the boy, “Certainly” (Plato 2) is all he has to respond with to prove the argument. If Socrates had asked the boy, “What geometric shape has all equal sides?” the boy would have to think for himself, and because he was not taught mathematics, he would not have an answer and therefore Socrates would have no argument.

Locke highlighted that Plato’s argument is illogical: “For to imprint anything on the mind without the mind’s perceiving it, seems to me hardly intelligible.” (Locke 3) Stating that if the mind was imprinted, it should be possible to recollect all the knowledge we have. For a person to know of something without recognizing that they have the knowledge, makes no sense. If the slave boy had mathematics imprinted in his soul, he should have been able to answer more than simple ‘yes’ or ‘no’ questions. If knowledge is innate, then the boy would be able to justify his answers. The boy wasn’t able to answer all of Socrates questions, “Indeed, Socrates, I do not know” (Plato 5) because he had not been taught mathematics. Any child could stand in front of Socrates and agree with him, but that doesn’t prove innateness. The child did not recollect the knowledge, if it were recollection then all humans could learn through being asked provoking and leading questions like Socrates tried to do with the boy. We know that is not how we learn, rather we learn through examples, explanations, and reasoning. Therefore Locke has disproven Plato’s theory of innate knowledge by demonstrating how Plato manipulated the situation, rather than truthfully proving his theory.

Plato may argue against Locke by stating that you cannot recall your past lives, which is why you must experience life to recollect information. Plato believed that all knowledge was innate; you could argue that if that was the truth, shouldn’t all mankind have only that theory of knowledge imprinted on their soul? If the soul carried all truths, there could only be one answer to human knowledge, but since there are many, we can deduce that we experience different sensations that lead us to our individual hypothesis. If all information was innate, why do mathematical and scientific discoveries happen? Discoveries occur when there is a new realization of understanding a certain subject, it is clear that if knowledge were imprinted on the soul, these would not happen. We would have had a heliocentric solar system since the beginning of time, knew the earth spherical, and understood medical procedures; if knowledge was innate. It’s obvious that we’ve had these discoveries because of learning, through sensation and perception we understand the world. Plato also may attempt to contradict Locke’s argument by saying that “children and idiots” have not experienced the right sensations to lead them to discovery of knowledge that others have. Locke might then argue that innate knowledge is not present in anybody whether “child”, “idiot”, or average person. Sensations begin from birth and throughout life we learn. We learn through examples, explanations, and reasoning. Locke could succeed in proving his theory against any counterclaims, making his argument sound against mathematical knowledge being innate.

Locke has a large array of arguments to justify empiricism; on the basis of his ideas, it is evident that we gain knowledge through experience, and that mathematical knowledge is not something innate. His arguments disprove Plato’s theory, showing that through sensation and perception, we learn. Through Locke’s arguments he was able to successfully prove that mathematical knowledge is not innate. Locke thus disproves universal consent. He also argues that innate knowledge is not evident in “children and idiots”, and he further clarifies his theory by explicitly explaining how we learn through observation, sensation and reflection. Locke successfully corroborates his theory of empiricism, as well as disproving Plato’s theory of innate knowledge in the immortal soul.