Do Analytic Statements Count as A Priori Knowledge?

Knowledge, whether one can have it, and if so how one goes about getting it are possibly some of the oldest most popular philosophical questions. From the dawn of philosophy with Plato and Socrates, all the way to more contemporary philosophers like Edmund Gettier and Alvin Plantinga the quest for knowledge has continued to draw philosophers’ attention. Over the centuries countless proposals for defining and defending knowledge have been made, some more cogent than others. Indeed the sheer size and history of the conversation makes it a rather daunting one to attempt to join. Nonetheless that is exactly what I will attempt to do here. I will not however try to lend my voice to the entire breadth of the epistemic conversation. Rather I will attempt to constrain my thoughts to a much smaller sub-topic, that of a priori and a posteriori knowledge. Even more specifically my paper will focus on a priori knowledge dealing with necessary or analytic propositions, whether one can have it, and if so how. To begin I will start by defining terms and precisely what I mean to count and consider as candidates for a priori knowledge. Following this I will examine traditional arguments in support of a priori knowledge and critique those arguments, again restricting our conversation to necessary or analytic propositions. It is my intent and purpose to show that our common understanding of this kind of a priori knowledge and the arguments supporting it are insufficient and unconvincing for belief in this kind of a priori knowledge. It should be noted that even if my paper fully achieves proves its thesis, it will not in any way hold that a priori knowledge in general does not exist. In other words, cases of introspection and the like might still be counted as a priori knowledge. It is only propositions that are often called analytic or necessary propositions that will be demonstrated insufficient for being consider as a priori knowledge. Finally one more comment, throughout the course of this paper ‘experience’ will be referred to. This must be understood as describing sense experience unless explicitly stated otherwise. That is, experiences that have come to the subject directly through the five senses.

When it comes to defining exactly what a priori knowledge is, the task is somewhat more difficult than one might think. Most are willing to accept that a priori knowledge is simply knowledge that one has prior to any sense experience. Yet to use this as a definition is perhaps a bit overly simplistic. The truth of the matter is that while this definition might be acceptable for a quick and brief definition, it will not suffice for a paper of this nature. Often times when defining a priori, the proposed definition will include mention of a priori’s counter part, a posteriori knowledge. The first definition I am considering is the definition offered in the Internet Encyclopedia of Philosophy, which contains the following:

The terms “a priori” and “a posteriori” are used primarily to denote the foundations upon which a proposition is known. A given proposition is knowable a priori if it can be known independent of any experience other than the experience of learning language in which the proposition is expressed, whereas a proposition that is knowable a posteriori is known of the basis of experience. For example, the proposition that all bachelors are unmarried is a priori, and the proposition that it is raining outside now is a posteriori.


Given here is both a definition and an example. I will focus on the definition here and the example later. First in order to be considered a priori the proposition must be knowable without any experience, however exclude is the experience of learning the language in which this proposition is expressed. I find this is a curious exclusion. Specifically because learning a language can be one of the most experience laden endeavors in a person’s life. However this exclusion allows for the proposition given as an example of a priori knowledge, all bachelors are married, to actually count as a priori. This is of course because if one could learn the English language, than one would inevitably know that all bachelors were unmarried even if they had never experienced bachelors or unmarried. These kinds of propositions are generally referred to as analytic propositions, because their truth is logically guaranteed. I will put this discussion on hold until later and turn my attention to another proposed definition.

This second definition can be found in the Stanford Encyclopedia of Philosophy. “A priori justification is a type of epistemic justification that is, in some sense, independent of experience.” SEP (Stanford Encyclopedia of Philosophy) also states that there is some debate about whether or not a priori knowledge can be “only of necessary, or analytic, propositions, or at least ones believed to be necessary or analytic. Necessary propositions are ones that cannot be false.” SEP agrees with the first definition I offered, although making no mention of the exclusion of the language learning experience, it seems to imply it. It seems to imply it because the definition grants that a priori knowledge is knowledge that must necessarily be true, or must analytically be true. SEP goes on to say that a priori knowledge is “not based on perception, introspection, memory, or testimony.” But rather it is based on “reason alone, or based solely on understanding of the proposition being considered.” This last clause seems particularly interesting to me, particularly that the proposition being considered must be understood. The definition makes no mention of how the proposition is to be understood. This nuance will have to set aside for future examination. So here again it can be seen that the most often turned to examples of a priori knowledge are those that are considered necessary or analytically true. ‘All bachelors are unmarried’ is perhaps the most popular example of an analytic proposition.

There is one final definition I would like to mention only in passing, and that is the definition offered by Immanuel Kant, as quoted in SEP. According to SEP, Kant claims that a priori knowledge is knowledge “absolutely independent of all experience.” I mention this because as this conversation progresses, we will devote some time to what precisely “independent of all experience” means.  But for now, it seems that the most widely accepted definition of a priori knowledge is knowledge that does not find its basis in any sense experience beyond learning the language in which the proposition in question is stated. However, as is often the case in philosophy, there is one further point that should be made before progressing from this initial defining stage. That is namely this from SEP:

Further, a person can be a priori justified in believing, though, of course,

not know, what is false, and empirical evidence can defeat a priori justification,

and hence, knowledge. As a start, what seems crucial to a priori justification

is that it is based solely on understanding the proposition at issue.


Glossing over the first few statements and focusing in on the final sentence of this quotation which I have already briefly mentioned. Specifically that “a priori justification…based solely on understanding the proposition at issue.” This leads us to the already stated conclusion, that, the best case for a priori knowledge is a proposition that once properly understood, yields a necessary truth that is at least to some degree inescapable. An example of this might be the statement, all A’s are A’s. If you understand the english language than you will understand this is a true statement. You need not have any experiences of A’ness. Here we begin to move from our brief description of a priori knowledge into an examination of the sufficiency of these definitions. Here it seems that when SEP claims a priori knowledge is primarily based on understanding of the proposition at issue, what they have at heart is really similar to IEP’s  (Internet Encyclopedia of Philosophy) “the experience of learning language”. In other words a person must understand the proposition in question. Even if they must learn the language that the proposition is stated in, if it is then possible for the proposition to be known independent of sense experience, than the proposition is considered a priori. Now the question arises, should we grant that learning a language is somehow exempt from counting as a sense experience? I submit here that we should not. To concede this to those who would have us believe in a priori knowledge would be intellectually irresponsible.

So here the conversation must turn briefly to philosophy of language. Specifically why should one think that learning a language does not count as an experience? After all, if the best examples of a priori knowledge is knowledge built on something that should be considered a sense experience, than perhaps we should be suspicious of a priori knowledge. In short, some of the best examples of a priori knowledge comes from necessarily true propositions. This is because many philosophers exclude learning the language the proposition is stated in as an experience that would consequently discount a priori  knowledge. If it can be show that learning a language, specifically the language that the proposition in question is expressed in, counts as a truly a posteriori experience than the very best examples of a priori knowledge rooted in necessary and analytic propositions will be debunked. For this reason we must examine linguistic knowledge and how it is that human beings acquire language, and specifically whether some of that process is innate or not.

There are a significant number of theories regarding how it is that people acquire language. Language is something that many philosophers feel sets the human race apart from any species of animals. In the late 1950’s two different theories of knowledge were offered. The first by psychologist B.F. Skinner, and the second by linguist Noam Chomsky. For Skinner language was learned “when children’s verbal operants are brought under the control of environmental conditions as a result of training by their caregivers.” Skinner believed that because children were either rewarded or punished for successful comprehension in “their various linguistic productions” their “verbal behavior gradually converge[s] on those of the wider language community.” Chomsky on the other hand disagreed quite strongly arguing that “language is stimulus independent and historically unbound.”

Language use is stimulus independent: virtually any words can be spoken in

response to any environmental stimulus, depending on one’s state of mind.

Language is also historically unbound: what we say is not determined by our reinforcement, as is clear from the fact that we can do and say things we have

not been trained to say.


I do not wish to be too sidetracked here, but only to point out very briefly two prominent theories of acquiring language. Neither theory, however, would be considered independent of sense experiences. Both Skinner and Chomsky’s theories require that children (or language learners) experience things with their five senses. Skinner believed this happened through a kind of reward/punishment relationship while Chomsky argued that children learned language from all kinds of things beyond the “meticulous care of their parents or caregivers”, including such activities as watching television or listening to adults converse. The point to gain from this is that both theories describe the language learning process as being significantly sense experience laden.

Now I want to  transition to what is perhaps a more pragmatic consideration, and I will do so by asking a question. Have you ever tried to describe color to a person blind from birth? Such and endeavor is utterly impossible. But why? Why is it impossible for a person blind from birth to fully grasp the concept of color? Well the answer seems somewhat obvious when you think about, because they’ve never seen a color. They have not a single sense experience of it and consequently cannot even begin to imagine what a color is. Words like blue, green, orange, and pink require some sense experience to comprehend. So it is obvious, that if you use the word purple in a sentence addressed to a person blind from birth, she will have no understanding of what you are describing. Purple, would be a word without meaning to her. This, I think, should be easy to understand and agree with. It seems to naturally follow that a person blind from birth would have no concept of color. But do all words function like this? Does every word require some sense experience? What of the statement we have already returned to many times, ‘All bachelors are unmarried’?

One might be tempted to think that the need for sense experience to understand a word only applies to words like blue and green and others like them. But before we make up our minds on this point let us consider the case of the proposition, all bachelors are unmarried. What does it mean to be a bachelor? Well it means to be unmarried. Fair enough, what does it mean to be unmarried? It means that one does not have a spouse, or is not married. We could most likely follow this pattern for quite some time, but eventually we would have to end in a one of two places. The conversation could only terminate in either a sense experience or a memory. Young children learn to understand the concept of married or unmarried on the basis of sense experiences. How do they do this? Well for one, they see that their mother and father sleep in the same bed. They watch as their parents interact and do life together. From these sense experiences they begin to understand what it is to be married. On the contrary side, they see their mother or father alone, and notice that this is different from their friend’s family whose mother and father live together and do all the things previously stated. And so they begin form the concept of being unmarried. Now someone might object that my requirements for knowing that all bachelors are unmarried is far too strong. Isn’t it enough to know that a bachelor is unmarried? Couldn’t someone who was never been exposed to parents or marriage of any kind still agree and know that all unmarrieds are unmarrieds?

I answer this by conceding that someone might indeed come to know all ‘unmarrieds’ (bachelors) are unmarrieds without having a sense experience of married or unmarried. In other words they would not necessarily have to arrive at the knowledge of married and unmarried exactly how I have just described it. But they would have to have another kind of sense experience. Firstly, they would have to have the experience of hearing that, “Bachelor means being unmarried.” Without this experience they could never arrive at the statement, ‘all unmarrieds are unmarrieds’. This relates back to the necessity of the proposition being understood, as mentioned during my section defining a priori knowledge. However, there seems to be no reason to exclude this experience, when it is clearly a sense experience and should thereby disqualify a proposition from being known a priori. If one must use sense experience to understand a proposition, how can knowledge of that proposition be said to be apart from sense experience? Secondly they would have to have some experience of similarity. In other words they would have to experienced objects that were the same or similar, and the only way to do this is to have a sense experience of two objects and judge between their attributes. For example, I know what an apple is. I have picked one up, smelled it, tasted it, seen it, and I have done this with more than one apple. So when I am faced with the proposition ‘all apples are apples’ I am immediately aware of its truth because I know what kind of thing an apple is and I know this because of my sense experience of apples. We must have some sense experience of objects being similar or even identical in order to grasp the concept of all unmarrieds are unmarrieds. As has been demonstrated, the only way to grasp this concept is through sense experience.

There is yet one more kind of proposition to consider and that is mathematical propositions. Mathematical statements are often cited as examples of analytic or necessary propositions. Having already discussed propositions like ‘all bachelors are married’, I will turn my attention to propositions such as 2+2=4. Is this kind of proposition any different? The answer is, of course, no. When a child is taught how to add they are often taught to use their fingers, or other objects as teaching aides. So at a basic level, 2+2=4 might be expressed as 2 [things] + 2 [things] = 4 [things]. We, or the child, might fill in any object in place of “things”. Math is ultimately knowable only because we have sense experiences of reality, and can at least conceptually tie our mathematical formulas to reality. For example, try to imagine you are not actually a living breathing, sensation experiencing being but instead simply a brain in a vat. You have no sense experiences of any kind. You neither hear, see, touch, taste, or smell. Given this state it is utterly inconceivable that you would know 2+2=4. Why? Because, put simply, you have no concept of two. “Two plus two equals what?” Would be something similar to the question, “shnorkelbots plus shnorkelbots equals what?” All this and I have said nothing of your ability to grasp addition apart from sense experiences. But ultimately there seems no need to. It is utterly apparent that apart from any sense experiences one could not know that 2+2=4 any better than one could know that all bachelors are unmarried.


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