Jump to content
Objectivism Online Forum

Kant's analytic–synthetic distinction

Rate this topic


Recommended Posts

I'm reading about Kant's analytic-synthetic distinction. Analytic propositions are true simply by virtue of their meaning, while synthetic propositions are not.

I have a question in this reagard: Is "1+1=2" an analytic or a synthetic proposition according to Objectivism?

Edited by Kjetil
Link to post
Share on other sites

Excerpts from “The Analytic-Synthetic Dichotomy" by Leonard Peikoff:

An analytic proposition is defined as one which can be validated merely by an analysis of the meaning of its constituent concepts. The critical question is: What is included in “the meaning of a concept”? Does a concept mean the existents which it subsumes, including all their characteristics? Or does it mean only certain aspects of these existents, designating some of their characteristics but excluding others?

The latter viewpoint is fundamental to every version of the analytic-synthetic dichotomy. The advocates of this dichotomy divide the characteristics of the existents subsumed under a concept into two groups: those which are included in the meaning of the concept, and those—the great majority—which, they claim, are excluded from its meaning. The dichotomy among propositions follows directly. If a proposition links the “included” characteristics with the concept, it can be validated merely by an “analysis” of the concept; if it links the “excluded” characteristics with the concept, it represents an act of “synthesis.”

The Objectivist theory of concepts undercuts the theory of the analytic-synthetic dichotomy at its root. Since a concept is an integration of units, it has no content or meaning apart from its units. The meaning of a concept consists of the units—the existents—which it integrates, including all the characteristics of these units. Observe that concepts mean existents, not arbitrarily selected portions of existents. There is no basis whatever—neither metaphysical nor epistemological, neither in the nature of reality nor of a conceptual consciousness—for a division of the characteristics of a concept’s units into two groups, one of which is excluded from the concept’s meaning.

Link to post
Share on other sites

I'm reading about Kant's analytic-synthetic distinction. Analytic propositions are true simply by virtue of their meaning, while synthetic propositions are not.

I have a question in this reagard: Is "1+1=2" an analytic or a synthetic proposition according to Objectivism?

Objectivism rejects the analytic/synthetic dichotomy.

"1+1=2" is a fact, derived from the science of mathematics.

Link to post
Share on other sites

I'm reading about Kant's analytic-synthetic distinction. Analytic propositions are true simply by virtue of their meaning, while synthetic propositions are not.

I have a question in this reagard: Is "1+1=2" an analytic or a synthetic proposition according to Objectivism?

Hey, kjetil. The posts above are fundamentally correct interpretations of the O'ist position (Obviously, since one of them was just quoting Peikoff.). There is also an article in the Objectivist Wiki about this very issue and it elucidates on some points not completely covered here.

http://wiki.objectivismonline.net/Analytic-synthetic_dichotomy

Link to post
Share on other sites

I'm reading about Kant's analytic-synthetic distinction. Analytic propositions are true simply by virtue of their meaning, while synthetic propositions are not.

I have a question in this reagard: Is "1+1=2" an analytic or a synthetic proposition according to Objectivism?

Like dream_weaver said, Objectivism would simply say "that's a true proposition." But in Aristotelian logic, there is the concept of "apodicticity," so if you want to be technical, all valid mathematical judgments are apodictically true propositions about how quantities behave in reality, its meaning being derived from some original act of observation and subsequent acts of conceptualization and inference about how math works.

Link to post
Share on other sites

Like dream_weaver said, Objectivism would simply say "that's a true proposition." But in Aristotelian logic, there is the concept of "apodicticity," so if you want to be technical, all valid mathematical judgments are apodictically true propositions about how quantities behave in reality, its meaning being derived from some original act of observation and subsequent acts of conceptualization and inference about how math works.

This seems wrong. It seems like a fancy way of saying that some fact of reality is necessary, while others not like it are contingent. Objectivism says that all truths are necessary.

Link to post
Share on other sites

Yes, but don't you think we can differentiate between propositions that we can't conceive of not being true (apodictic), such as "1+1=2," and propositions which we can conceive of possibly being otherwise (assertoric), such as "children ages 9-12 prefer McDonald's to Burger King"? It says is that there is nothing inherently in the nature of those entities that could prevent it from being otherwise, but that we don't know until we observe it and find out which way it is. This seems to be on the same grounds as the metaphysical versus the man-made distinction. Although I kind of see your point, that it could be taken to mean some truths are merely contingent. Certainly, though, we could imagine children preferring Burger King, and yet we can't imagine one plus one not being two, so what shall we call this distinction? Isn't it okay to distinguish between logically true statements and empirically true statements, as long as we keep in mind that what is logically true is true of reality, and what is empirically true is conceptually true, both being necessary?

Edited by 2046
Link to post
Share on other sites

You're pretty much positing the analytic-synthetic distinction, dude.

The truth of a claim is necessary because of its correspondence to reality, not because of the meaning of the terms. Consider that we could simply be mistaken categorically about number terms. For some reason, when we add 1 and 1 we always get 3. We would come to think, that's the order of things.

Patently absurd with such elementary arithmetic, but some higher maths posit things that can be absolutely, deductively valid but we realize "Oh wait, we didn't compute the constituents right.".

That's the real distinction you're looking for, though: 1 + 1 = 2 is deductive. It is, however, not more true or more obviously necessary, even if we perceive it to be that way.

Link to post
Share on other sites

The Analytic-Synthetic dichotomy rests on a theory of concepts where the meaning of a concept is its definition. In other words, only the characteristics of the referents that were chosen for the definition are necessary. Everything else about the referents of that concept are contingent.

An example of the analytic-synthetic dichotomy is the following two statements.

A: Ice is solid.

B: Ice floats in water.

Ice being solid is part of its definition. Floating in water is not part of the definition of ice. According to the dichotomy, this means that A is only true because of the meaning of the concept. And B is only true because we happen to observe it being true at the time.

Under the false theory of concepts, when you say the word "ice", you implicitly add "And by ice, I mean the following description: solid water." But under Rand's theory of concepts, the meaning of a concept is its referents, not its definition. So under Rand's theory of concepts, when you say the word "ice", you implicitly add "And by ice, I mean those things I call ice."

When you're referring to the object in reality, rather than only its description, suddenly there is no more analytic-synthetic dichotomy, because, in the case of ice, being solid and floating in water are both necessary properties of the things we call ice. Being solid is what ice does, and floating on water is also what ice does. Both are connected to reality, and both are necessary.

Link to post
Share on other sites

Actually, after an interesting discussion of this in the chat room with Dante (all credit goes to him for coming up with the answers to my questions about these dilemmas, although it goes without saying that any mistakes are entirely my own), I think we can revive the apodictic/assertoric distinction and show that it is compatible with Rand's theory of concepts (if not in the way generally used by post-Kantian logicians), without having any split between empirical facts and logical facts, or sundering necessary truth into contingency.

It is clear that we are able to make valid judgments that are non-hypothetical and necessary about the truth of a statement based on the meaning of the statements alone (meaning of the concepts being the referents in reality, not the definition) without having to go observe something in reality each time. Such is the case with all valid mathematical judgments, as previously mentioned, e.g. "1+1=2," "a^2+b^2=c^2," "Two straight lines cannot inclose a space."

On the other hand, it is also clear that there are assertoric statements that can possibly go any of a number of ways, and that we don't know which way it is until we observe and find out, e.g. "Children ages 9-12 prefer McDonald's to Burger King," "Chicago is larger than Omaha," "There are more apples in the field than oranges." In contrast to apodictic statements that are necessarily true by virtue of the meanings of the concepts involved, these statements we don't know are true until we go observe them in the world, but there is nothing in their nature that says they can't be otherwise hypothetically.

In the 1+1=2 example, we can't imagine it being any other way, yet in the McDonald's example, we can imagine it being the other way around without any conceptual impossibility. We are immediately clear that 1+1=2 is true and necessary, but we don't know which city is larger until we go observe and find out. What is the reason for this distinction? I think it has to do with the nature of concept formation as involving measurement omission, and the fact that knowledge has structure.

Concepts that are more relatively higher-up in the structure of knowledge have a quality to them that enables us to make immediate and necessary judgments about them because of the way in which we formed them. Take "all bachelors are unmarried" for example. "Bachelor" is a higher-level concept, which we must have already focused on the particular characteristic of a person involved and formed the concept of "marriage" in order to have the concept "bachelor." We had to have already observed the relevant information, and thus we have already retained it in the apodictic judgment, just by the way it was formed.

So once we form the concept based on experience, or based on other concepts based on experience, then we can make apodictic judgments involving those concepts. We can say whether something is analytically true, but it is still a posteriori at root. All concepts involved in a valid apodictic judgment ultimately are rooted in perceptual awareness of particulars, but because of the kind of abstractions we have performed at the lower levels, we can know certain things about the upper levels automatically just because of what we've done.

Assertoric statements, on the other hand, lack that kind of previously integrated substance. We can't make automatic and necessary judgments about them because of the focus of the judgment relative to the aspects used to form the concept. So let's use Dante's example of the atomic structure of gold. "A gold isotope has 79 protons, 79 electrons and 118 neutrons." Since the concept "gold" means its referents, including all its characteristics, then the statement is, in that sense, analytic. But it is also assertoric, in that we originally don't know how many protons, electrons, and neutrons it has, until we go look at it. After all, it could be 78 protons for all we know. Assuming we know nothing about platinum either, no conceptual impossibility arises from considering this. But when we originally formed the concept of "gold," we had no access to this information just through the structure of previously-known knowledge. Just like in the McDonald's example, we have nothing previously integrated to help us. So, in a fundamental sense, apodictic judgments refers to already integrated knowledge, assertoric judgments refers to future integrations yet-to-be performed. We can know certain things just by looking at the concept based on the fundamental nature that we have already observed, or based on other concepts we have already observed in the former, but in the latter we can't know just by looking at the concept.

The reason for this is because during the concept formation process, we omit certain characteristics and/or measurements, whilst retaining only the relevant ones. So with various particular details, such as "this child likes the toy in McDonald's better" we have no way of knowing, and thus no access to that right away because of the nature of concept formation. The information that we do retain, however, we can automatically apply to any specific unit of the concept deductively.

Thus we can clearly differentiate between truth in empirical statements and logical statements without suggesting there is a split between them, only that there is a split between our relation to the different way in which we discover the truth of the two different kinds of statements. When we have previously-known knowledge, we already have "packaged" into the concept some empirical data. If the judgment falls under the concepts in question, we have enough to verity the statement logically just by knowing the concept. If not, then it's an empirical statement, and an assertoric judgment follows.

Interesting note about the contrasting forms of apodicticity: these would be what Kant would consider to be synthetic a priori statements under his epistemology, which he viewed as "pure reason" and yet which Rand would say [synthetic a priori] is impossible. Whilst on the other hand, in Objectivist epistemology, these apodictic statements could be considered analytic a posteriori statements, which Kant believed to be impossible. Rand is the anti-Kant! And in this way, we can draw a direct logical chain between the statements' meanings and abstraction from experience in these types of judgments, and thus in a way, we have arrived at an Objectivist type of "pure reason" in the analytic a posteriori, since their truth is ascertained based on meaning alone, and yet they are at root derived from experience, or from other concepts derived from experience.

Edited by 2046
Link to post
Share on other sites

2046:

"Concepts that are more relatively higher-up in the structure of knowledge have a quality to them that enables us to make immediate and necessary judgments about them because of the way in which we formed them"

Relates to a discussion with Jacob in one of the God threads where I said that certain things can be known to be false based on what we have seen in the past. The possibility of certain claims can be dismissed because it would make what has already been perceived impossible to have been so.

Edited by Plasmatic
Link to post
Share on other sites

2046, I think you've hit on something there. It has always seemed obvious to me that there is something to the notion of analytic/synthetic statements (and, for that matter, "a priori"/"a posteriori"). If I understand your proposal correctly, it goes something like this:

We form concepts through measurement omission. Using the characteristics of the concept which are not omitted in the formation of a concept, we can make certain statements immediately. For example, "bachelor" specifies "unmarried" and "man", but doesn't talk about favorite color or height, etc. And so one can, immediately, say "all bachelors are unmarried", without having to examine anything further about any of the referents of "bachelor". One the other hand, one cannot say "most bachelors favor green to red".

Now, I do want to inquire as to what you would say after I have integrated a new piece of information. For example, if I count and find that there are indeed more apples than oranges in the field, does the statement "there are more apples than oranges in the field" change from assertoric to apodictic? I would not say so, because I would limit "apodictic" to that which comes from the empirical information that is necessarily part of the concept (i.e. that the concept cannot be formed without that information), rather than any and all empirical information that I happen to know applies to the referents of the concept.

By the way, your notion of "analytic a posteriori" applies to all statements in Objectivism, not just apodictic statements (at least if you use them in the same sense that Kant used them).

Link to post
Share on other sites

2046, I think you've hit on something there. It has always seemed obvious to me that there is something to the notion of analytic/synthetic statements (and, for that matter, "a priori"/"a posteriori"). If I understand your proposal correctly, it goes something like this:

We form concepts through measurement omission. Using the characteristics of the concept which are not omitted in the formation of a concept, we can make certain statements immediately. For example, "bachelor" specifies "unmarried" and "man", but doesn't talk about favorite color or height, etc. And so one can, immediately, say "all bachelors are unmarried", without having to examine anything further about any of the referents of "bachelor". One the other hand, one cannot say "most bachelors favor green to red".

Now, I do want to inquire as to what you would say after I have integrated a new piece of information. For example, if I count and find that there are indeed more apples than oranges in the field, does the statement "there are more apples than oranges in the field" change from assertoric to apodictic? I would not say so, because I would limit "apodictic" to that which comes from the empirical information that is necessarily part of the concept (i.e. that the concept cannot be formed without that information), rather than any and all empirical information that I happen to know applies to the referents of the concept.

Yeah, I don't know, I was wondering about that myself. It would seem like "the field" as in, that particular field would have to be considered analytically including the characteristic of having more apples in it. But it is not fundamental to the concept of "field-ness" to have more apples, yet it is fundamental that it has the capacity for having more apples. If we use Dante's gold example that "gold contains 79 protons," we don't immediately know how many protons it has, but once we find out that it does, it would seem to be quite fundamental to the nature of gold. So it would make sense for it to become apodictic at that point, even though most logicians would still consider it assertoric. It seems like if we're going to speak of apodicticity, we can't escape the issue of fundamentality or the context of what characteristic we isolated to form the concept first of all, then adjusting our definitions as we gain more information about it, then maybe the apodicticity of the concept will expand along with it. I don't know, I'm on much more shaky ground here.

By the way, your notion of "analytic a posteriori" applies to all statements in Objectivism, not just apodictic statements (at least if you use them in the same sense that Kant used them).

Yeah, good point. There really is no such thing as "synthetic" or "a priori." There's one paragraph in ITOE that has stood out to me on this point, that probably has a lot to do with this whole discussion:

In one sense, no truths are "analytic." No proposition can be validated merely by "conceptual analysis"; the content of the concept—i.e., the characteristics of the existents it integrates—must be discovered and validated by observation, before any "analysis" is possible. In another sense, all truths are "analytic." When some characteristic of an entity has been discovered, the proposition ascribing it to the entity will be seen to be "logically true" (its opposite would contradict the meaning of the concept designating the entity). (ITOE, 101)

Edited by 2046
Link to post
Share on other sites

I'll object to one premise in that wall of text for right now. May do more later.

Simply because you can or cannot conceive of something does not entail logically the possibility of it. I can conceive of a triangular planet, but the laws of physics tell us that square planets are impossible. I also can't conceive of thought, without language. However, thought without language is indeed possible. I just wanted to object to that for now.

Link to post
Share on other sites

I think you need to flesh out a little more just what part you're criticizing. The argument centers on what is contained within a concept, and how we can sometimes use that to ascertain the truth of propositions concerning that concept; I don't understand how what a person can or cannot conceive of is relevant.

Link to post
Share on other sites

I'll object to one premise in that wall of text for right now. May do more later.

Simply because you can or cannot conceive of something does not entail logically the possibility of it. I can conceive of a triangular planet, but the laws of physics tell us that square planets are impossible. I also can't conceive of thought, without language. However, thought without language is indeed possible. I just wanted to object to that for now.

I perhaps was too liberal in my wording to say "we can't imagine it being otherwise," but what I mean by that is to say that it does not invoke a conceptual impossibility in the statement itself to say "this field has more oranges than apples in it" or to say "this field has more apples than oranges in it." We don't know which it actually is until we go observe the field in question and count the number of apples and oranges growing in it. On the other hand, it would invoke an immediate logical contradiction to say "this field does not extend into space."

The reason being, on this theory, that we have already "packaged" in our concept of "field" that it contains the characteristic of spatiality, based on the way we formed the concept, probably ostensibly by first-observation. So, in that way, the apodictic judgments we are able to make about fields taking up some space is both analytic and (indirectly) a posteriori. We aren't able to make a judgment about this field having more apples or oranges in it, because we had no way to access that information during concept formation of field-ness. We had to omit the measurements of all the particular fields and disregard things like that, thus those judgments are assertoric and rely on empirical investigation to validate.

Link to post
Share on other sites

The reason being, on this theory, that we have already "packaged" in our concept of "field" that it contains the characteristic of spatiality, based on the way we formed the concept, probably ostensibly by first-observation. So, in that way, the apodictic judgments we are able to make about fields taking up some space is both analytic and (indirectly) a posteriori. We aren't able to make a judgment about this field having more apples or oranges in it, because we had no way to access that information during concept formation of field-ness. We had to omit the measurements of all the particular fields and disregard things like that, thus those judgments are assertoric and rely on empirical investigation to validate.

I have hit upon the solution to my earlier question. When I say "this field is extended in space", this is apodictic not because the particular in question (this field) is extended in space, but rather because the concept of which I am declaring it a unit (this field, which is a unit of the concept "field") has as one of its characteristics that it is extended in space. The statement "this field has more apples than oranges" is assertoric not because I do not yet know whether the statement is true or false, but because the concept of which this particular is a unit ("field") says nothing whatsoever about the relative number of apples and oranges (or even if there are apples and oranges in the field at all).

So rather than apodicticity or assertoricity being a quality which is dependent on knowledge of particulars, it is only dependent on the concept of which I, by my statement, am declaring the particular to be a unit. If I said "the red bucket is red", it is apodictic because I classified the object to which I am referring as a "red bucket" to be a red bucket. It doesn't matter if the bucket is actually blue, or if the object is red but is actually a fire truck. My statement is still apodictic, but I am guilty of misclassifying the particular entity. Apodictic statements are statements which, in order for them to be false in reference to a given particular, I would have to be guilty of classifying the particular as a unit of a concept of which it is not, in fact, a unit. Assertoric statements are statements which do not have this property (for example, if I misclassified a dump truck as a "field", the "field" a.k.a. dump truck may still have more apples than oranges in it).

Edited by nanite1018
Link to post
Share on other sites

Actually, I don't know if I like this notion of "apodicticity" as opposed to analytic. I think, actually, apodictic is worse, in its connotations. Apodictic, it seems from my researches, is meant to be a statement about the certainty of the statement, and in particular whether it is "necessary" or "contingent". My revised notion, as described above, of "apodicticity" and "assertoricity" seem more in line with "analytic" and "synthetic". In this sense, an analytic statement would be a statement which deals solely with the specified measurements of a concept, and a synthetic statement would deal with at least one of the omitted measurements of the concepts in the statement. Clearly, this new notion of the analytic/synthetic would not have any connection to the necessary/contingent dichotomy (as all entities are what they are, all things are necessarily the way they are). And of course the fact that we can only form concepts by dealing with the world would make all knowledge a posteriori in usual usage of the term.

Not sure what "apodictic" and "assertoric" would then refer to, specifically, but I suppose they would be about our knowledge of the truth/falsity of the statement. Perhaps they would really just be synonyms to "analytic" and "synthetic", perhaps simply being used in different cases (perhaps referring to our knowledge of the truth/falsity of the statement, rather than referring to the nature of the statement itself?)

In any case, the notion I outlined above seems to be a meaningful distinction to make, even if it has no metaphysical significance like the Kantian/logical-empiricist analytic/synthetic dichotomy did. Whether one wants to use apodictic/assertoric or analytic/synthetic, I don't think it is particularly important.

Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
  • Recently Browsing   0 members

    No registered users viewing this page.

×
×
  • Create New...