Distinction Series: a priori Judgments and a posteriori Judgments

The distinction between a priori and a posteriori plays an important role in modern period philosophy. I will be focusing on Kant's understanding here and so it will be important to keep in mind that the distinction is about a priori judgments and a posteriori judgments.

In my experience, the distinction between 'a priori' and 'a posteriori' is seen as passé. The very word 'a priori' seems to trigger a sense that something is out dated. I think this may result from general problems seen with the methods of philosophers that use the term, and not anything particular about the a priori itself. The more problematic element of this view is that, so far as I see, the people who dismiss the a priori employ a priori judgments just as regularly, and are perhaps worse off for not being familiar with this potential quality of their own judgments. For readers who are skeptical of this, hopefully the rest of this post can clear things up. If not, I am happy to talk through problems in the comments. 

The Distinction

The common ancestor in this distinction is the concept of a judgment generally. The distinction runs as follows: a posteriori judgments use information from experience, while a priori judgments do not use information from experience. 

Here are some examples of a posteriori judgments (from my perspective while writing): I am currently writing; there is a red cup on the table in front of me; I see an object return to me when thrown in the air. 

Here are some examples of a priori judgments: 1 + 1 = 2; 'A & ~A' is false; if I throw something in the air it will return. 

It is very important to remark that a judgment's status as a priori or a posteriori is not a matter of its truth value, nor is it directly tied to a judgment being analytic.

(Kant mostly focuses on what he calls the purely a priori. Pure contrasts with empirical. Purely a priori judgments are judgments that abstract away all empirical content, such as color, and leave only characteristics that can be known about objects a priori. The characteristics of an object knowable purely a priori are analytic with the concept of an object generally, and so there is overlap between the analytic judgments and pure a priori judgments.)

Phenomenological Demonstration

Find an object to examine. Name some visual characteristics of it. You are judging based on your examination, and so a posteriori. If you had someone else find an object and hide it, you could still assert things about it by guessing. Perhaps it is red, or blue. In this case you would be doing this a priori, since you would not be using empirical information. Or, if you consider an object that you know about, but is not in front of you currently, you can judge about certain qualities of it without direct observation; this would also be an a priori judgment. 

Since Kant discusses the purely a priori it will be important to give an example of this as well. If I assume there is an object which I could experience, then this object must be able to be represented in time and space. Any object I represent to myself through the imagination will be represented in time and space, and I know this purely a priori.

Importance in Kant's Work

Frequently Kant makes distinctions in order to narrow down his focus to one side, and this is the case with the distinction between judgments as a priori or a posteriori. Kant's method starts in experience, and then abstracts our empirical characteristics until it is left with the purely a priori. If we add the distinction between empirical and pure, and analytic and synthetic, then we can construct the kind of judgments that are centrally of concern to Kant: (pure) a priori synthetic judgments.
Many authors use a priori to signify something known by reason alone. This must be kept distinct from the topic under discussion here which concerns judgments. Of course judgment can concern knowledge, but this is not essential to the distinction.
Judgments that are a priori are considered to be necessary. For many authors before Kant, this necessity seemed to suffice for their being known with certainty. This seems to be why a priori judgments are so easily combined with the idea of certain knowledge. Leibniz did not take the necessity of a priori judgments to be sufficient for knowledge. In addition to the necessity of judgments Leibniz required the possibility of the object be established. Leibniz established the possibility of these objects through the principle of non-contradition, while Kant developed a criteria of real possibility (which is opposed to logical possibility).

Ambiguities and Questions

Kant almost always uses a priori to mean purely a priori. I am going to develop a distinction for pure and empirical which will need to be kept in mind while using this distinction in Kant.

Understanding Judgments as Thought-Propositions

This will be the first installment in a series of articles regarding judgments in Kant's system.  The aim of the series is to use the judgment as a centering point in the interpretation of Kant's critical project, as well as a tool for deconstructing and interpreting other philosophy from ancient to contemporary.

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"Now the proper problem of pure reason is contained in the question: How are a priori synthetic judgments possible?" CPR B19

In studying Kant there is a tendency to wonder right off what ‘a priori synthetic’ means without attending to what it means to judge at all.  It is clear that a priori synthetic judgments are the core problem of the critical works, and the 'synthetic a priori' presents itself as questionable while 'judgment' in general is so common as to be passed over.  Kant himself seems to take for granted his particular orientation to judgments throughout his work, only spelling out tacitly how we must understand judgments in general as part of his system.

Orientation

It is clear that Kant employs a formal system of terms in his work, and also clear that he only gives a cursory description to many of these terms.  When a formal term is itself discussed it is not in some capacity as an object (of experience), but as it provides a way of talking about the thought of objects.  Kant's need for his vast array of formal terms is a demand of transcendental philosophy itself.  We should understand that the formal terms describe ways of thinking about things.  The formal terms don't refer to things in the world, but instead refer to transcendentally ideal ways of thinking the world and objects in it.  Discussion of the division and unity of the transcendentally ideal and empirically real will be avoided for now; it is enough to say that things that are ideal (formal) do not have objects which correspond with them immanently.

Among formal terms ‘judgment’ has the most central of roles, synthetic a priori judgments being the questionable kind for the critique.  A great difficulty in reading Kant arises from neglecting the formal application of the term 'judgment'.  Judgments should be understood as represented through 'thought-propositions'.  The terms 'thought' and 'proposition' must now be clarified, and their relation made known, so that they can describe ‘judgments’.

Thought

I distinguish first between what I will call phenomenal thought and formal thought.  Phenomenal thought is experienced; it is the inner monologue of the subject - the “talking in your head” that we are all familiar with.  Formal thought, on the other hand, is not constituted by experiences, but refers to our understanding of experience; that is, when I see a chair and understand that I can sit on it, I may say that my understanding is constituted formally by thoughts about the chair.  The term formal is employed here because what thought refers to is not a thing - it is a way of talking about the understanding of experience.

Propositions

What one typically thinks of when they hear 'proposition' (particularly in our analytic tradition) is a sentence which evaluates to true or false; this usage can be granted, and we can be sure that Kant writes propositions like this in his critical work, but we can also be sure that these written propositions are not of interest so long as they are considered merely as written and not thought.  This allows us to distinguish between two possible referents of ‘proposition’, as sentences (written, or spoken), or as descriptions of the content of (formal) thought.  Let us look at a sample proposition:

'This chair is blue.'

This proposition may be analyzed as a sentence – nothing in the concept blue contradicts the concept of chair, but we don’t know what chair is being referred to by the indexical ‘this’, so we don’t know if it is true of any chair in particular.   Kant's interest in this proposition would be as formally thought.  This proposition as thought about the object (chair) would be accounting for our experience of it as blue.  The proposition is then our way of discussing what is contained in formal thought.

Judgment as Thought-Propositions

Given our account of thought and propositions, judging can be understood as thinking a proposition.  A thought can be represented by a proposition, but when we judge we should understand the proposition describing the judgment as thought.  When we represent a judgment through propositions we can evaluate these propositions to be true or false, but when these propositions are considered as formal descriptions of what is thought in a judgment, then we do not evaluate them as true or false, but recognize that they are our reflective evaluations of an actual experience.  This is the difference between how we can doubt an object is blue (there may be a blue light on it), but we can’t doubt that we experience it as blue – this has incredibly crucial implications for reading Kant, in doing transcendental philosophy, we are not interested in the evaluation of judgments as true or false; what is at stake is how to give an account of the forming of judgments – how they are possible.

Application of Judgment as Thought-Proposition

Let us take an example of a proposition which causes some confusion and show how our way of understanding judgments helps us to clarify it:

‘5 + 7 = 12’

Kant’s claim that this is a synthetic judgment is much disputed; the reason that Kant says that it is synthetic is that the concept given by ‘12’ does not contain the concepts given by ‘5’, ‘7’, ‘+’ or ‘=’, so that the combination of the numbers requires a synthesis.  We can see, however, that even though the character ‘5’ is obviously not the same as the character ‘12’, five is contained in twelve because we know that twelve is larger than five.  So if twelve contains five, and it also contains in it, in this same sense, that if you add five to seven you get twelve, then this is analytic and not synthetic, correct?  This is false.  This is treatment of the proposition ‘5 + 7 = 12’ not as an actual thought, but a thought to be further evaluated.

When we consider the proposition in question as a description of what is thought in a judgment (a thought-proposition), then we can see right away that our thought of ‘12’ does not contain ‘5’ or ‘7’.  When I think of the number ‘twelve’, I do not understanding in my experience five plus seven, or thirteen minus one, or three times four.  I can evaluate the number twelve and determine all sorts of things about it and all manner of ways that it can be divided up or constructed, but I don’t consider these merely through thinking ‘12’.