Chapter 4: Reason
(pgs. 99 - 102)
(pgs. 99 - 102)
The Classical View of Truths of Reason
I. Analytic Propositions
Let's turn now to an attempt at understanding what truths of reason are, and how they are known to be true.
The classical view (for example following Kant and Leibniz) holds that we know an analytic proposition to be true in virtue of the fact that we can intuitively grasp the "containment relationship" that holds with respect to the elements of the given proposition.
For example, take the concept "bachelor". According to the classical view, this concept can be "unpacked" to reveal the concepts that are contained within it. In this case, the classical view would suggest that the concept of "being unmarried" is a concept that is contained within the concept "bachelor".
So analytic propositions are self-evident truths of reason that are known (according to the classical view) in virtue of some containment relationship that the intellect intuitively grasps. So the proposition
"All bachelors are unmarried" is recognized as self-evident because reason recognizes immediately that "unmarried" is contained within the concept of "bachelor".
II. Necessary Propositions
As I mentioned, according to the classical view truths of reason are always necessarily true. That means that such propositions are true in all possible worlds and so cannot be false.
Why can't they be false? The traditional reason given is that they cannot be false because a denial of them leads to a contradiction. So a truth of reason could only be false if a contradiction could be true, and contradictions are never true. So truths of reason cannot be false.
Ex. "All circles are 360 degrees around". This proposition is analytic . The concept "being 360 degrees around" is contained within the concept of "circle". Thus, to state that "all circles are 360 degrees around" is false is to state that
"There is a circle that is 360 degrees around and not 360 degrees around".
This is a contradiction (a thing cannot both be 360 degrees around and not 360 degrees around).
Notice that an account of the truth of this proposition is different than the account of the truth of the proposition "Dr. Panza's car is silver". This proposition is true, but it is not analytic. If it were analytic, one could know that my car is silver just by understanding the proposition "Dr. Panza's car is silver". But this would entail that the concept "silver" is contained necessarily within the concept "Dr. Panza's car". But there is nothing about the concept "being Dr. Panza's car" that necessitates it being silver. So "silver" is not a part of the concept of "Dr. Panza's car" and so the proposition is not analytic.
To know the truth of this proposition one needs to look to experience. Why? Because the truth is contingent. Dr. Panza's car could have been blue.
Other examples of analytic propositions:
1. All triangles have three interior angles.
2. All bachelors are unmarried.
3. All whales are mammals.
A possible world with a counterexample
of an analytic truth?
III. The Analytic, a priori, and Synthetic
Are analytic truths the only kinds of truths of reason that can be grasped in this intuitive, immediate, and direct manner, and which are always necessarily true?
No. According to the classical account, some truths of reason can be immediately grasped, are necessarily true, but are not analytic. Such propositions are called synthetic propositions.
Example: take proposition R: "Nothing is both red and green all over at the same time".
Is this proposition analytic? If it is, then according to the classical view it must be true in virtue of some kind of conceptual containment relation, and it's denial must lead to a contradiction.
Let's look at the first part -- if it is analytic, it is in virtue of a containment relation. What is that relation? Is it the case that "not-green" is conceptually contained within the concept of "red"?
Although it might look as if this is contained in the concept of red, it actually doesn't appear that the concept 'red' works in that way. To know the concept of red doesn't imply that I know the concept "green". In fact, note that if non-green were contained in the concept of red, so would "not-yellow" and "not orange" etc. So essentially I would have to know all the color concepts if I knew red. But that's absurd. Clearly a person can know one color and not the rest, so it doesn't appear right to say that "red" contains within it "not green" and so on.
If so, then proposition R is not analytic. However, it does appear to be the case that proposition R is necessarily true.
If this is true, then at least some truth of reason are necessary but not analytic. But yet it also appears obvious that we do in fact seem to know that this proposition is true merely by understanding it. And that immediate understanding does seem to involve some kind of manipulation of the concepts involved (though it is not conceptual containment). So the proposition
"Nothing can be both red and green at the same time" is a synthetic proposition.
Propositions that can be known in this way (simply through the use of reason alone, though a sort of conceptual manipulation -- containment or otherwise) are called a priori propositions. The opposite of these are called a posteriori propositions.
What is the difference between "analytic", "synthetic", "a priori" and "a posteriori"? Think of it this way:
- Analytic refers to a way in which a proposition can be true (in virtue of conceptual containment).
- Synthetic refers to a way in which a proposition can be
true (not in virtue of conceptual containment, so all
synthetic propositions are non-analytic).
- a priori refers to a way in which a propositoin can be known (in virtue of reason alone, independent of experience).
- a posteriori refers to a way in which a proposition can
be known (not in virtue of reason, dependent upon experience)
So, to wrap up, according to the classical view
| Proposition |
Truth Known Via |
Knowledge Acquired Via |
| All bachelors are unmarried |
analytic (conceptual containment) |
a priori |
| Nothing can be red and green all over at the same time |
synthetic (conceptual exclusion) |
a priori |
| Dr. Panza's car is silver. |
synthetic (perception) |
a posteriori |
IV. Broad and Narrow a priori
Let's take "known via reason" as the benchmark foundation for the a priori.
Are self-evident propositions the only types that can be known
in this way? No. Let's call such propositions a priori in the broad sense. What this means is that the proposition is not itself self-evident, but it is known a priori because it self-evidently follows from another proposition that is itself self-evident, or follows from a chain of self-evident steps beginning with a self-evident proposition.
Example:
"All bachelors are unmarried or Chris Panza is a billionaire".
This proposition is a priori in the broad sense, because it is not self-evident in itself. The proposition "all bachelors are unmarried" is self-evident, and from this it can be inferred that the proposition "all bachelors are unmarried" can be disjoined (with an "or") to any other proposition and the resultant proposition will be true a priori (because an "or" statement is true if at least one of the disjuncts is true).
So we can say that the self-evident is the foundation for the a priori (according to the classical view) because if a proposition is a priori then either (a) it is self-evident or (b) it follows self-evidently from a proposition that is self-evident.
The remaining type of a priori proposition is obvious.
To be a priori in the narrow sense is to be self-evident.
V. The Empirical
As it turns out, most truths are not known a priori.
Example -- proposition P: "The spruce tree is taller than the maple tree".
Proposition P is a non-a priori truth, one that can only be known empirically, or on the basis of experience. (it is known a posteriori ). How does I come to know that P is true?
Surely not through the use of reason. Let's assume that I am talking about the two spruce and maple trees that are in my backyard. Now let's try to determine whether P is analytic or synthetic.
If P is analytic then P's truth can be determined by conceptual containment. There is nothing (using the classical form of conceptual containment) that tells me that "being taller than the maple tree" is a part of the concept of "the spruce tree". Furthermore, denying the proposition does not lead to a contradiction. So P is not analytic.
If P is synthetic a priori then P's truth can be determined by conceptual exclusion. But there is nothing that tells me that "not being shorter than the maple" is entailed by the concept of "spruce". So it is not synthetic a priori.
Instead, it appears that to determine the truth of P I must look to experience in some manner. For example, may simply utilize my perceptual faculties to determined P's truth. I look in my backyard and see if P is in fact true or not. As such, P is an empirical a posteriori proposition.
There are two facts about emprical propositions that make them different from a priori propositions.
1. Empirical propositions, if true, are contingently true. This means that an empirical proposition can be false, and that even if it happens to be true, it could have been false.
- A priori propositions, on the other hand, are necessarily
true (whether they are analytic or synthetic). So they are never false and
there are no possible worlds in which they are false.
- A priori propositions cannot be falsified because they
are necessarily true. There are no test cases imaginable that could prove
the proposition false. Ex. "There are no circular squares" cannot be falsified
because there are no circumstances imaginable where one could describe a situation
where a circular square exists.
- A priori propositions are only known through reason, either
immediately or mediately.
V. Concept Acquisition
Is experience at all a part of a priori understanding?
At some level, yes. To know that the proposition "if the spruce is taller than the maple, then the maple is shorter than the spruce" is true, I must understand the proposition, which means I must understand it's parts. Some of these parts are "spruce" and "maple". These are concepts that are learned through experience (let's say someone points to a certain type of tree and says "spruce" to me, and this is how I learn the concept "spruce").
However, the classical view states that once I have the concepts, I can simply use reason to analyze those concepts and discover a priori truths. So once I have used experience to acquire the concepts, I no longer need experience to discover a priori truths concerning those concepts.