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By Paul
05/21/03 (Edited 02/27/12)
When we think of a proposition, we think of something which can be true or false. How we go about determining which of those it is depends on the nature of the proposition being considered. Sometimes the truth or falsehood of a proposition is knowable internally, without experience (a priori knowledge), and other times experiences and observations of the world are needed to try to justify it (a posteriori knowledge). Consider the proposition "gold is a color." Assume that we're speaking English and the words really mean what we think they mean. We can now consider how we verify this proposition.
"Gold is a color" can be considered knowable a priori. Once you grasp the meaning of the proposition, you can observe that it is true. Gold, by the definition of the term, must be a color. To say that something is gold is to say that it's within the group of things we call colors, because that's what our definition of gold says. Thus, anyone who understands the proposition as it's intended knows it to be a truth. It's analytically true because of the language.
A skeptic could argue against the knowledge that "gold is a color" is true. Keith Lehrer's skeptical hypothesis attempts to call a priori truths like this into doubt. Lehrer introduces the idea of super-intelligent aliens beaming misperceptions directly into the brain, saying that they could be capable of making us slightly incorrect at random times even while still being able to function -- they would do just enough to prevent us from ever having certainty. If we can't disprove this hypothesis, Lehrer would say we are forced to doubt that things which seem like logical truths to us are actually true... an alien, he says, could theoretically make something seem blatantly internally obvious and logical to us which is not actually true. Thus, it might seem like gold is a color but that could actually be a misconception introduced into you and you'll realize late that gold is actually a shape. Another skeptical argument which could possibly be used here is the fallibility of memory. To consider the proposition "gold is a color" takes time, even if only a very short time, and requires us to assume that there aren't any problems with our memory that can creep in that quickly. It seems theoretically possible, as a skeptic could point out, that a fluke problem of short term memory could make us misconsider a proposition. We could fail to properly remember what gold is by the time we've started thinking about color, and that would throw off our analysis and make us think it's analytically true when it could be false. Short term memory would only have to cause that sort of fluke mistake once every million years in order to introduce doubt into the knowledge claim... if there's no way to verify that this isn't the one time there's a mistake, then knowledge is lost and it's reduced to probability.
Now let us consider a person who's blind from birth, and therefore does not share our experiences of gold. Call this person who doesn't know what a color is "Caecus". Caecus, like the rest of us, will say that gold is a color when he's asked. The way in which he knows this is different, however, from the way we know it. Caecus, never having experienced the sensation of color, cannot know what "gold" or "color" refer to in a phenomenological sense. Instead, he only knows that people have told him gold is a color, and that the meaning of the word gold (in this sense) involves by definition being a color. Caecus can say he knows the proposition to be true a priori, but this only means he knows that the definitions declare it true... he doesn't know what the proposition is actually about. He has learned this linguistic truth a posteriori, through testimony of people who teach him what the linguistic definitions are; however, when the sentence he utters is translated to the proposition describing the content of what he's really saying, it become nothing more than "the sentence 'gold is a color' expresses a truth to English speakers". For Caecus there's no reference to his knowledge other than linguistic usage. When we as sighted people consider the proposition we know what group of experiences the term "gold" applies to and what group of experiences the term "color" applies to, and so we can see clearly how the experience of gold fits into the category of experiences of color. Caecus, on the other hand, knows only the analytic truth without the application.
Consider another proposition: "Gold* is gold#", meaning that any instance of the element gold has the color gold. This proposition is not knowable a priori. The claim must be supported by looking at instances of the element and observing that the sensation produced is the experience of gold. The element Au does not by its definition have to involve the color experience of gold, so there's no way to make it an a priori truth... instead it must be a posteriori. The blind person, Caecus, cannot know the meaning of the proposition "gold* is gold#", because he cannot see the color. His sense of the experience of gold* does not include the color property gold#, so he cannot confirm that gold* is gold# expect by listening to people tell him they think it is.
Caecus, when you ask him, will tell you he knows that gold* is gold#. The content of his knowledge here, however, is different from ours. As sighted people, when we consider the proposition "gold* is gold#" there's an idea of an experience involved. We can imagine the experience of gold# and exactly how it applies to gold*... we understand the categorization of the two groups of experiences and can compare the experience of one to an aspect of another. Caecus, on the other hand, can only rely on testimony from sighted people. He knows that gold* includes being gold# because parents, teachers, friends, etc. have told him throughout his life that it's true. Since he cannot conceive of what gold# is like, this truth that gold* is gold# simply becomes an accepted dogma to him. Caecus can never confirm the validity of what he's being told. It is not essential to the definition of the element that it take on a specific color -- the atomic structure is what's essential to the definition of the element. Knowing the atomic structure of gold* does not in any way lead Caecus to knowing that the element must always be associated with a particular visual sensation. His awareness of the object represented by the word gold* is missing the property of color... he does not know what experience the property of being gold# causes in sighted people. Thus, his "knowledge" in this case is only knowledge by testimony, relying on the sighted people around him to not all be involved in a mass conspiracy to trick him.
Truths of propositions can be investigated either a priori or a posteriori, but within those methods the meaning of the deduction depends on a personal sense of the proposition. A blind person can grasp the theory and grasp the sense of the logical nature of a proposition which involves color, but cannot grasp the actual content of a proposition that involves color. The analytic truth of a proposition, in order to have much use beyond being a general tautology like 1=1, has to have a concept of an experience attached to it. In this way, a posteriori experience is an important part of a priori truths despite the fact that a priori truths are theoretically knowable without experience.
