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7 + 5 = 12 as a synthetic statement

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7 + 5 = 12 as a synthetic statement

makerowner
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Posted 06/08/09 - 10:04 AM:

#31

keda wrote:

But in any case the argument I gave above doesn't apply to natural science because natural science doesn't claim intuitive knowledge of its objects.

I'm making an analogy with natural science, not suggesting natural science is an application. Just because scientists disagree doesn't mean that there is no basis for science, in the same manner just because people disagree about the analyticity and syntheticity of judgements, doesn't mean there is no basis for this distinction. A lot of people can be wrong about something. Its nothing unusual.

There's a crucial difference between disagreements in natural science and disagreements about alleged introspections. As I explained, natural scientists study things in the world, and thus a disagreement among scientists could always be resolved by the discovery of a new fact. The disagreement is the result of a lack of facts; the facts currently available permit two different interpretations; when more facts are assembled, one of those interpretations will be shown to be superior. (Of course this is a highly simplified and "cleaned-up" presentation of scientific research. But the point is that it differs from "philosophical research", in that the people involved can usually tell what it is that they're looking for before they find it, and what would make them change their minds, unlike in philosophy.)

The disagreement about the analytic/synthetic distinction is totally different. If, as Kant claimed, we make the distinction by mentally examining our concepts, then the only way there could be a real disagreement is if one person is better at introspecting than another. But of course there's no way of determining who is better at introspecting; "comparing my introspections with yours" doesn't even make sense. When one side claims that it's intuitively obvious that p is synthetic, and the other side claims that it's intuitively obvious that it's analytic, there's no reason for me to believe one or the other.

One of your suggestions ("I suggest mathematical equations are [...] interpreted differently by various groups, and so they form different judgmenents i.e. their usage of the symbols differ") seems to be something like c); the problem with this proposal is that the only reason to believe that our concepts differ is our disagreement. Our concepts of numbers agree when we're just using them (ie. to perform mathematical operations) rather than talking about them, so the only difference between my concepts and yours is that I think mine make analytic judgments and you think yours make synthetic judgements. (Again, I'm just using this as an example; I'm not taking sides.) Describing a judgement as 'analytic' or 'synthetic' would then say nothing about it, since it would have exactly the same use either way.

The difference of analytic and synthetic judgments *is* a difference in use, since analyticity of a judgment is the quality of having its validity depend on its concepts alone, while the syntheticity of a judgement is the quality of having its validity depend on something external to its concepts. In other words, when you make an analytic judgment, you do so by merely analyzing its concepts, while when you make a synthetic judgment, you do so by appealing to something external to its concepts. This is different usage. If our usage does not differ, our judgments are either both synthetic, or both analytic, and one of us must be wrong.

I know what the words 'analytic' and 'synthetic' mean; that wasn't the point. In fact you've missed the entire thread of the argument. Everything in my last post besides the last paragraph was a reductio ad absurdum of the idea that we can distinguish analytic judgements from synthetic by mentally examining our concepts. I'm not trying to argue that there is no meaning to the words 'analytic' and 'synthetic'; I'm arguing that if we distinguished them by introspection, and if the disagreement were the result of the disputants having "different concepts" (item c. in my last post), then the terms could have no possible meaning.

It's true that the "difference of analytic and synthetic judgments *is* a difference in use", but it's a difference in the use of the words 'analytic' and 'synthetic', not in the use of the signs '5', '+', '7, '=', etc. Everyone agrees that 5+7=12, whether they think it's synthetic or analytic, or whatever else they might think. The judgement "5+7=12" has exactly the same use whether we call it synthetic or analytic. " The quality of having its validity depend on its concepts alone" is exactly what is supposed to be explained (see Quine's "Two Dogmas of Empricism"); it's not a test we can use to determine if a judgement analytic, it's just a definition of the term. Again, if all we have to do is look at our concepts with our "mind's eye" to determine whether or not a judgement's "validity [depends] on its concepts alone", then it's inexplicable how anyone could be mistaken about this. As I explained in my last post, if someone disagrees with you about the results of introspection, you can only a) accuse them of lying, b) accuse them of being an idiot, or c) decide that you speak different languages.

Your second suggestion ("I suggest that they [the groups who claim it is analytical] are not even plain wrong, but unqualified to make a judgment") looks like my b) above. The question here is how is it that you have such a superior analyticity-detecting ability?

It is merely the inability here to form a certain judgment in the first place. If you have no concept of what you are talking about, you are basically speaking gibberish in your own eyes and not trying to communicate anything. It is not so farfetched as some do treat math as some kind of mechanical process that "just works". When they solve equations, they have no idea what they mean until the final result is given. It doesn't have to mean they aren't good at seeing how their judgements are analytic, once they have actually made them, but just writing something down or making a sound doesn't count as making a judgment. To do so you must have a concept of what the symbols actually mean.

You've missed my point again. You suggest that people who call mathematical equations analytical are "unqualified to make a judgment"; my point in the last post was that there's no way for me to tell which one of you is "qualified". You say that introspection of our concepts shows them to be synthetic, they say that it shows them to be analytic; why should I believe you over them? How did you come to be better at introspecting than they are?

This or something similar has been suggested before, and I have suggested this is a play on ambiguety, since the former "1+1+1+1" look visually the same as the latter "1+1+1+1" but they may be semantically different if 4 isn't actually defined as (1+1)+(1+1). But if this is the case, you cannot do the same with 1+3=4. Remember, visual aid must not be necessary to validate an analytic judgment.

There's no reason to add parentheses. If 2 is defined as 1+1, then 2+2 is just 1+1+1+1. This is just associativity in practice. You should have brought up multiplication as a counterexample though, since we do need to take account of the order of operations in multiplication. 2x2 has to be (1+1)x(1+1) and not, eg. 1+(1x1)+1. Again, I have little knowledge or interest in philosophy of mathematics, so it's quite possible that someone has come up with a solution to this problem.

Kant defined concepts as cognitions, so I think it is a misrepresentation to say he was wrong, simply because their analyticity cannot be determined by introspection. You object and say that introspection is not sufficient to solve disgreements, however if I need to determine the analyticity of my judgments, I would rather not have to ask someone else about it each time. Different horses for different courses.

It's not just that introspection is insufficient to solve disagreements, it's that there wouldn't be any disagreements if we could make the distinction by introspection. The point isn't that you have to ask someone else, it's that if someone disagrees with you it's not necessarily because he's an idiot; it may be because the norm in question doesn't in fact cover this particular case.

If we need to solve a disagreement, we invent conventions and try to make clear our usage. If someone intends to not to do so, but deliberately uses confusing and ambiguous language in order to manipulate others, it isn't a particularly unique problem for me.

Making our usage clear is precisely what I've been trying to do. If our concepts 'analytic' and 'synthetic' were dependent on introspection, they would be incredibly unclear, or rather, meaningless, as I've explained above. Realizing that they are instead based on social norms, means that we can make proposals for new norms to cover cases like mathematical equations, rather than insisting on our superior powers of introspection.

For philosophy, Socrates, if pursued in moderation and at the proper age, is an elegant accomplishment, but too much philosophy is the ruin of human life. Even if a man has good parts, still, if he carries philosophy into later life, he is necessarily ignorant of all those things which a gentleman and a person of honour ought to know.

keda
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Posted 06/08/09 - 04:13 PM:	#32
makerowner wrote: There's a crucial difference between disagreements in natural science and disagreements about alleged introspections. As I explained, natural scientists study things in the world, and thus a disagreement among scientists could always be resolved by the discovery of a new fact. The disagreement is the result of a lack of facts; the facts currently available permit two different interpretations; when more facts are assembled, one of those interpretations will be shown to be superior. (Of course this is a highly simplified and "cleaned-up" presentation of scientific research. But the point is that it differs from "philosophical research", in that the people involved can usually tell what it is that they're looking for before they find it, and what would make them change their minds, unlike in philosophy.) If I make an analogy and explicitely specificy its similiarities, harping on about its differences accomplishes nothing, as those are irrelevant. If, as Kant claimed, we make the distinction by mentally examining our concepts, then the only way there could be a real disagreement is if one person is better at introspecting than another. Don't see how this follows. But of course there's no way of determining who is better at introspecting; "comparing my introspections with yours" doesn't even make sense. When one side claims that it's intuitively obvious that p is synthetic, and the other side claims that it's intuitively obvious that it's analytic, there's no reason for me to believe one or the other. You could ask each to clarify what concepts they use, and then try and see if their arguments are valid. I'm arguing that if we distinguished them by introspection, and if the disagreement were the result of the disputants having "different concepts" (item c. in my last post), then the terms could have no possible meaning. I don't see how this follows. If you mean no possible meaning that is agreed upon between the two parties, then granted but so what? It's true that the "difference of analytic and synthetic judgments is a difference in use", but it's a difference in the use of the words 'analytic' and 'synthetic', not in the use of the signs '5', '+', '7, '=', etc. Everyone agrees that 5+7=12, whether they think it's synthetic or analytic, or whatever else they might think. The judgement "5+7=12" has exactly the same use whether we call it synthetic or analytic. I suspect you don't use the word "use" the same way I do. It isn't sufficient in my use, that one agrees that a particular sentence is true for its "use" to be the same. Suppose someone was taught that "5+7=12" means the sky is blue. He would go along agreeing that the sentence is true, yet his usage is completely different from the others, since the signs refer to something else. If 4 was defined as 1+1+1+1, obviously the same would be true. If it were the case that some used the symbols for a synthetic judgment, while others for an analytic judgment, these would necessarily be differing in what the symbols refer to and therefore in use of the symbols. Again, if all we have to do is look at our concepts with our "mind's eye" to determine whether or not a judgement's "validity [depends] on its concepts alone", then it's inexplicable how anyone could be mistaken about this. One is often mistaken when one have not thought out them clearly, but confusedly. As I explained in my last post, if someone disagrees with you about the results of introspection, you can only a) accuse them of lying, b) accuse them of being an idiot, or c) decide that you speak different languages. How does this have anything to do with Kant being wrong about distinguish analytic and synthetic judgments by simply considering the concepts involved? You've missed my point again. You suggest that people who call mathematical equations analytical are "unqualified to make a judgment"; my point in the last post was that there's no way for me to tell which one of you is "qualified". Again, ask them to clarify their concepts. In fact, ask the one who is claiming it is analytic, to define his terms and prove some mathematical statements, and see how far he gets before running into insurmountable problems. You say that introspection of our concepts shows them to be synthetic, they say that it shows them to be analytic; why should I believe you over them? Try introspection and see where it leads. There's no reason to add parentheses. If 2 is defined as 1+1, then 2+2 is just 1+1+1+1. This is just associativity in practice And where exactly did you get associativity from? You can't just rely on that particular operation is associative. You have to prove it per definition, for this associativity my otherwise be a synthetic judgment. It's not just that introspection is insufficient to solve disagreements, it's that there wouldn't be any disagreements if we could make the distinction by introspection. The point isn't that you have to ask someone else, it's that if someone disagrees with you it's not necessarily because he's an idiot; it may be because the norm in question doesn't in fact cover this particular case. Huh? I'm not saying you have to be an idiot, and I don't see why there wouldn't be any disagreements. If our concepts 'analytic' and 'synthetic' were dependent on introspection, they would be incredibly unclear, or rather, meaningless, as I've explained above. I don't see any explanation. Realizing that they are instead based on social norms, means that we can make proposals for new norms to cover cases like mathematical equations, rather than insisting on our superior powers of introspection. To me this is asinine as saying boats are better than cars because cars sink. Nobody will give up introspection for the sake it doesn't solve disagrements, than they would give up a car because it doesn't float. What you should realize is that you can have both boats and cars. Introspection and conventions are not mutually exclusive.
All about making money Free Europe Now How to fix your country In thought, men distance themselves from nature in order thus imaginatively to present it to themselves--but only in order to determine how it is to be dominated - Adorno and Horkheimer

makerowner
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Posted 06/09/09 - 08:05 AM:	#33
Since you continue to miss my point, I don't see any reason to continue this discussion. Thanks for helping me clarify my thoughts, in any case.
For philosophy, Socrates, if pursued in moderation and at the proper age, is an elegant accomplishment, but too much philosophy is the ruin of human life. Even if a man has good parts, still, if he carries philosophy into later life, he is necessarily ignorant of all those things which a gentleman and a person of honour ought to know.

xzJoel
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Posted 06/09/09 - 08:19 AM:	#34
makerowner wrote: <p>Since you continue to miss my point, I don't see any reason to continue this discussion. Thanks for helping me clarify my thoughts, in any case.</p> Not that it matters, M, but how do you feel about my earlier statement that even as to the indivudal, a particular concept could be analytic or synthetic depending on how (or why) the person is considering the concept at that moment?
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makerowner
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Posted 06/09/09 - 10:51 AM:

#35

xzJoel wrote:
Not that it matters, M, but how do you feel about my earlier statement that even as to the indivudal, a particular concept could be analytic or synthetic depending on how (or why) the person is considering the concept at that moment?

(Just a note: concepts can't be analytic or synthetic, it's statments, sentences, propositions, judgements, and the like [ie. combinations of concepts] that are.)

If I understand you correctly, I think I agree with your thought, but I have some reservations about your formulation. I'm not sure this helps with mathematical equations, so I'll use another example, one that Quine mentions in "Two Dogmas": is "All green things are extended (occupy an area of space)" analytic? Whether it is or not depends on whether 'green things' includes, eg. "impressions" in Hume's sense, or "sense-data", that is, subjective experiences of green as opposed to objects in the world that are green. This is another example of norms for the use of a phrase (here 'green things') not being fully defined in all areas. It seems to me that in such cases, individual speakers could (and do) use either meaning, and thus the sentence could be either analytic or synthetic depending on the use.

But it's important to remember that this isn't a kind of "private language" in the sense of Wittgenstein's private language "argument" (it's not quite an argument, but that's another topic). I can't say that "My lawn is wet" is analytic simply because I'm giving a special sense to my concepts. (Or rather, I could do that, but I wouldn't be speaking English if I did.) For words to have meaning, there have to be public norms for their (correct) use. Those norms don't cover every case, since languages allow ambiguities, but that of course doesn't mean that there are no norms, that speakers can mean whatever they want by their words.

Another somewhat related point is that when these kinds of ambiguities come up, we ask the speaker what they mean. We don't, eg. do an MRI on their brain to determine what mental act they're performing as they speak. When the speaker's words are ambiguous, we ask for more words, not for the mental act "behind" the first words.

xzJoel
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Posted 06/09/09 - 11:48 AM:	#36
makerowner wrote: <p></p> <p>(Just a note: concepts can't be analytic or synthetic, it's statments, sentences, propositions, judgements, and the like [ie. combinations of concepts] that are.)</p> <p>If I understand you correctly, I think I agree with your thought, but I have some reservations about your formulation. I'm not sure this helps with mathematical equations, so I'll use another example, one that Quine mentions in "Two Dogmas": is "All green things are extended (occupy an area of space)" analytic? Whether it is or not depends on whether 'green things' includes, eg. "impressions" in Hume's sense, or "sense-data", that is, subjective experiences of green as opposed to objects in the world that are green. This is another example of norms for the use of a phrase (here 'green things') not being fully defined in all areas. It seems to me that in such cases, individual speakers could (and do) use either meaning, and thus the sentence could be either analytic or synthetic depending on the use.</p> <p>But it's important to remember that this isn't a kind of "private language" in the sense of Wittgenstein's private language "argument" (it's not quite an argument, but that's another topic). I can't say that "My lawn is wet" is analytic simply because I'm giving a special sense to my concepts. (Or rather, I could do that, but I wouldn't be speaking English if I did.) For words to have meaning, there have to be public norms for their (correct) use. Those norms don't cover <em>every</em> case, since languages allow ambiguities, but that of course doesn't mean that there are <em>no</em> norms, that speakers can mean whatever they want by their words.</p> <p>Another somewhat related point is that when these kinds of ambiguities come up, <em>we</em> <em>ask the speaker what they mean</em>. We don't, eg. do an MRI on their brain to determine what mental act they're performing as they speak. When the speaker's words are ambiguous, we ask for more words, not for the mental act "behind" the first words.</p> Your point about "concept" vs. "sentence" is well taken. I was a bit careless with my language. You seem to be analyzing the properties of a sentence as expressed and understood (inter-subjectively), and that is certainly fair if we are discussing the use of language to convey concepts between individuals, but isn't the analytic/synthetic divide conceptual and not linguistic? Are you suggesting, in the first instance, that concepts are linguistic such that words must precede concepts? I don't disagree with this, but I wonder what you would make of the concepts of someone without language. When they envision the concept "12", do they imagine something different than we do? Is language necessary for introspection? (I am guessing that someone without language could care less about the analytic/synthetic divide, so this speculation may be without any merit.) I am probably way off base, so feel free to set me straight. I am actually asking, not setting you up for my own talking points.
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makerowner
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Posted 06/10/09 - 08:12 AM:

#37

I don't think you're off base, I think those are good questions. Are there such things as non-linguistic concepts? I don't know. That seems more like a question for psychology than philosophy, but there are obvious philosophical implications.

My first reaction would be to say that no, there can't be non-linguistic concepts, but it of course depends on how we define 'non-linguistic'. If we limit it to verbal language, then maybe we could admit, eg. "musical concepts" or "painted concepts" that are non-linguistic. (I don't mean the concepts of musical technique, but the "meaning" of a musical phrase being counted as a concept.) But I think if we're talking about "musical concepts", we're essentially treating music as a language. In any case, it seems more misleading than useful to call these kinds "meanings" 'concepts'. Other than these "artistic concepts", if we accept them, a non-linguistic concept would have to be private, and thus would run into all the problems Wittgenstein mentions about private languages. A concept implies a norm, that is, there are correct and incorrect applications of it; but if a concept is private, how could anyone know whether or not it's being applied correctly?

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