1

[Note: I'm using Kant's terms.]

Analytic proposition, for example "all bodies are extended", or "a=a", seems like an unhelpful type of proposition (contra to the synthetic a priori and a postriori propositions). What do we get from analyzing the concept in the terms we already know of it? It seems that every bit of useful analysis we can get from what can appear to be analytical proposition would in fact be a synthetic proposition ("extendness" is a concept that we synthetically provided to the concept "body", "equalness" is a concept we synthetically provided to the concept "a"; Only after providing those subject concepts with those object concepts, we can provide an analytic proposition that'll simply attach the two together as though they where always one and the same, making the analytical proposition something of a fake synthetic a priori proposition at best).

Yechiam Weiss
  • 3,806
  • 1
  • 15
  • 35

2 Answers2

1

Analyticity, the a priori and necessity

What does Kant say ? That if a judgment is analytic, its denial will involve a contradiction because the predicate is contained in the subject :

That a body is extended is a proposition that holds a priori and is not empirical. For, before appealing to experience, I have already in the concept of body all the conditions required for my judgment. I have only to extract from it, in accordance with the principle of contradiction, the required predicate, and in so doing can at the same time become conscious of the necessity of the judgment - and that is what experience could never have taught me (B 11-2).

The clearest expression is perhaps the following:

For, if the judgment is analytic, whether affirmative or negative, its truth can always be known in accordance with the principle of contradiction (B. 190, italics in original).

The principle of contradiction must therefore be recognised as being the universal and completely sufficient principle of all analytic knowledge; but beyond the sphere of analytic knowledge it has, as a sufficient criterion of truth, no authority and no field of application (B. 191).

These quotations need to be taken in conjunction with Kant's definition of the principle of contradiction: 'The proposition that no predicate contradictory of a thing can belong to it, is entitled the principle of contradiction, and is a universal, though merely negative, criterion of all truth' (B. 190). To take his own earlier example, to say 'This body is not extended' is contradictory because we are both affirming and denying extension of it. But we know we are doing this because the predicate 'extended' is contained in the subject 'body' as part of its definition; it is because 'All bodies are extended' is an analytic truth that the principle of contradiction manages to get a grasp on the situation. In ordinary cases we have to extract a contradiction by putting together an earlier statement of the speaker with a later one: 'Yesterday you said that it was square, but today you refer to its three sides'. In such cases one of the contradictory statements must be given up, though it is open to us which one to surrender. In the case of analytic judgments we have no option; by using that particular word as the subject we are com- mitted to the definition and this is why a 'merely negative' criterion of truth is applicable. (Anthony Manser, 'How Did Kant Define 'Analytic'?', Analysis, Vol. 28, No. 6 (Jun., 1968), pp. 197-199 : 198.)

The (or a) 'use' of analytic propositions appears to be then that in empirical matters they reveal a necessity which 'experience could never have taught me'. Kant does not deny that I need experience (e.g. of bodies and the meanings of words) in order to formulate an analytic judgement or proposition. When Kant says, 'before appealing to experience, I already have in the concept of body all the conditions required for my judgment', he does not mean 'before having had any experience'; he means 'merely using what experience I have' and without having to make further, extra or special investigative appeal to experience.

Geoffrey Thomas
  • 35,303
  • 4
  • 40
  • 143
  • So basically, analytic propositions are used merely to affirm the state (the sum of its general properties) of the subject? – Yechiam Weiss Jul 02 '18 at 10:22
  • In considering an analytic judgement I am 'conscious of the necessity of the judgment - and that is what experience could never have taught me '(B 11-2). The *necessity* of the judgment is *objective*; it is only the *consciousness* of that necessity which is *a state of the subject*. That is my view of what Kant is saying; I have kept the discussion within the bounds of Kant's Critical philosophy because you indicated at the start that you were using a Kantian framework - or so I understood. – Geoffrey Thomas Jul 02 '18 at 12:26
  • yes, I do try to understand it under Kant's philosophy. So analytic judgment gives the objectivity to the properties we subjectively assigned the object? That's actually interesting, but I'm not sure if it's a good proposition, as according to that we can "give" objectivity to any properties we want from the object. So I'm probably mistaken in my understanding. – Yechiam Weiss Jul 02 '18 at 15:19
  • Do you mean that e.g. we subjectively assign extension to body ? Extension is 'contained in' the concept of body : when we say 'body is extended' we learn nothing empirical but we do realise that the analytic statement is necessarily true. The statement acquaints us with necessity which neither the concept of extension nor the concept of body did on its own. Kant can hardly stop us from 'subjectively assigning' properties to objects, nor can anyone else. If analyticity has its proper uses, as in the body/ extension case, it is hardly discredited if 'subjective properties' can be fed into it. – Geoffrey Thomas Jul 02 '18 at 17:26
  • I am constantly impressed by your ability to ask intriguing questions, and equally constantly aware that I cannot answer them to your satisfaction. Perhaps one day one of my answers will suitably interlock with one of your questions. – Geoffrey Thomas Jul 02 '18 at 17:38
  • first of all, thank you, you really don't know how much it means to me. Now, what I say here is that analytic statement stitches the two concepts together in necessity only when we already synthetically want to stitch them together. If I'd wanted to say that "body is liquid", it'll be perfectly fine analytically if I synthetically a priori said that concept "body" and concept "liquidness" should represent the same object. Only then am I able to present the analytic judgment that "body is liquid". – Yechiam Weiss Jul 02 '18 at 18:21
  • And yes, it seem very odd to state such statement, but only because we already chose to attach the concept "extendness" to the concept "body", from the definition of "body"; hence if we chose to define "body" as "liquid", it might not have represented the same object as we could've represented should we choose a different concept to attach it it, but it would surely be a correct analytic judgment to say that "body is liquid". – Yechiam Weiss Jul 02 '18 at 18:21
  • By some random chance [this question](https://philosophy.stackexchange.com/q/474/30235) popped up in the feed, where the answers seem to sound somewhat close (or at least puts us in that mindset) to what we're talking about here. – Yechiam Weiss Jul 03 '18 at 17:16
  • 1
    @Yechiam Weiss. Thanks - a rich crop of answers ! – Geoffrey Thomas Jul 03 '18 at 17:31
0

Mathematics consists of axiom systems and analytical propositions, nothing more. Every mathematical statement is fundamentally a tautology, saying that those axioms imply this theorem. Mathematics is useful. It enables us to transform systems of synthetic propositions into other non-obvious synthetic propositions.

In general, simple analytical propositions aren't going to be useful, but more complicated ones can be.

In the case of Kant's example of a body, a body is defined in a certain way, and from that we know that it is extended. That's not very useful.

If we had minds that could instantly grasp all the consequences of something, math wouldn't be useful. That isn't the case.

Suppose we are going from point A to point B in a vehicle that can maintain a certain speed. Now, the distance is a synthetic proposition, as is the speed. We use the analytic proposition that time taken to traverse a distance at a given speed is the distance divided by the speed to determine how long the trip will take. That's useful. (It's a very simple example, of course.)

David Thornley
  • 1,134
  • 5
  • 7
  • There's no way we defined something in a way that was unknown to us, and according to that definition we learned that the definition is true. It's circular argumenting. – Yechiam Weiss Aug 01 '18 at 04:48
  • Excuse me, I'm not following. Definitions, in the mathematical sense, are neither true nor false. In the case of the body, if the term "body" is defined as something that implies extension, then bodies are extended. The appropriate question is whether something is a body by the definition we're using. The original question was not whether analytical propositions were circular arguments, but whether they were useful. – David Thornley Aug 02 '18 at 20:10
  • the problem is specifically shown in the last sentence in your answer - "body defined in a certain way, from that we know that it is extended": if we define something in a certain way that doesn't make it useful to us that we "know" it's defined that way, because we defined it. We have essentially added no new knowledge on the matter. It's like I can say that a is b, when I don't know what a nor b represents. So now I have a well-defined object, a, that is equal to b. I have gathered no useful knowledge from that statement, unless I know what a and b represent - – Yechiam Weiss Aug 02 '18 at 20:51
  • - and if I do know, that it's not an analytical sentence anymore. – Yechiam Weiss Aug 02 '18 at 20:52
  • Sure. Repeating definitions is not normally useful. Not all analytical sentences are useful. However, I claim that mathematics is useful, and it's nothing but analytical sentences. – David Thornley Aug 03 '18 at 20:01
  • I don't understand how you seperate between "normally useful" and "useful" when considering analytical sentences to only occur with repetitive definitions. – Yechiam Weiss Aug 05 '18 at 17:24
  • Whether something is useful is empirical. Mathematics is a large collection of complicated, non-obvious, and sometimes surprising analytical propositions, and we find it very useful. You could attribute much of its usefulness to being a superb way to manipulate certain synthetic propositions, but lots of people are fascinated by pure math, so it has at least some entertainment value. – David Thornley Aug 06 '18 at 22:42
  • and again I wonder, how can an analytical proposition be useful. You jump straight to "analytical proposition can be useful" but skip what I'm asking - how do you postulate an analytical proposition such that it is useful, because the way I presented, and you've accepted, can't promote any usefulness. – Yechiam Weiss Aug 07 '18 at 05:08
  • Okay, what do you mean by "useful"? I've added an example where the use of analytical propositions does something we normally find useful. – David Thornley Aug 30 '18 at 22:16
  • so the analytic proposition itself isn't useful, but when synthesizing it with another proposition it becomes useful retrospectively? – Yechiam Weiss Aug 30 '18 at 23:08
  • Very few propositions of any sort are useful by themselves. Also, do you consider usefulness to include entertainment value? I've got plenty of recreational math books around. – David Thornley Aug 31 '18 at 20:16
  • yet synthetic propositions, by definition, are always useful - they always add new information on the subject. And as much as I'd personally enjoy it, I wouldn't really consider entertainment to be "useful". At least not on this subject. – Yechiam Weiss Sep 01 '18 at 17:37