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Analytic-synthetic vs priori/ posteriori

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Analytic-synthetic vs priori/ posteriori

Death Monkey
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Posted 07/13/09 - 02:00 AM:	#51
keda, If specifying what the set is, is not the reason why it is nonsensical to say it is not a definition, then what is? I don't understand your question. What properties does numbers describe? Numbers don't describe anything. We can use numbers in our descriptions of all sorts of things. On the other hand, if you understand the proof, and can therefore actually derive the truth of the statement from the axioms that specify what the statement means, then it is a priori, because no reference to sensory experience is needed to make that judgement. Now this sounds more reasonable. Even if you did learn reasnoing by means of sensory experience as you said, you can still derive a priori truths using it. Why not counting? That depends on what you mean by "counting". If what you mean by counting is specified by some set of abstract axioms (for example, poeno arithmetic or set theory), then you can. But then that is purely analytic, because you are only deriving truths about those axioms, not about reality. As soon as you include in what you mean by "counting" something about reality, you need information about reality to derive those truths from. In the case of analytic a priori statements, the truth-value is derived from the axioms that specify the meaning of the statement. In the case of synthetic a posteriori statements, we derive conclusions about reality from information we infer from our sensory experiences. For a synthetic a priori statement, we are dead in the water. The truth value cannot be derived from axioms, because if it could the statement would be analytic. The truth value also cannot be derived from inferences from sensory experiences, because that would make it a posteriori. But that's all we've got. Saying that we derive it "through reasoning" isn't enough. Your "reasoning" has to have something to operate on. Again, this goes back to what I said earlier in this thread about needing a third source of information. So far, you have not supported the claim that any third source of information even exists, much less that it is realiable and can actually be used to justify some specific synthetic truth-claim. See this is the type of information, I would say can be derived from counting. 5+7=12 can be determined by counting together 5 and 7 which can be counted without refering to anything in sensory experience. But then what, exactly, are you referring to? If you are only referring to the abstract natural numbers, which are completely defined in terms of a set of axioms, and make no reference whatsoever to reality, then the statement is analytic. In this case, not only are you not refering to anything in sensory experience, but you are not referring to anything "real" at all. Thus it is purely analytic. If, however, you are referring to a conception of numbers that does somehow make reference to reality, for example, some platonic notion of numbers being "real", or some implicit assumption that numbers represent something about reality, then the statement becomes synthetic, because that conception includes implicit assumptions that could potentially be false. But then you need some information about reality in order make your derivation. And that information has to come from somewhere. If not from sensory experience, then where? Not necessarily. If reality can only be concieved according to mathematical principles, due to how you percieved it, then they apply to reality without basing it on sensory experience, but rather on the way your perception works. But you would not know that this is the case without having that sensory experience. What you describe is exactly an example of drawing a conclusion from information that you have inferred from your sensory experiences. Without those sensory experiences, you would not know how reality can percieved, so you would not be able to draw any conclusions from how it is percieved. of the parallell postulate following from the axioms of euclidean geometry. Sure it is an analytic statement, but it doesn't mean that the parallell postulate itself is an analaytic truth. It is simply not relevant to what I said. The parallell postulate is not an analytic truth about reality. It is an analytic truth about the axioms of euclidean geometry. It is not a truth about reality at all. It is a synthetic truth about reality that the postulate is false, but that is not an a priori truth. It is an a posterioir truth which we have inferred from our observations. For example, if I said "5kg + 7kg = 12kg", that would clearly be both synthetic and a posteriori. How so? what a posteriori evidence could disprove it? I could measure the mass of a 5kg object, and the mass of a 7kg object, and then measure the combined mass, and observe that it is not 12kg. Of course, we know that this will not happen, but the only reason we know that is from our prior observations of how things work. That is a posteriori knowledge. The important thing is that you recognize the distinction between what I am calling mathematical statements, and the metaphysical statements that you refer to as mathematical statements. They are not metaphysical, but are truths about the necessary conditions of experience. What necessary conditions? Everything you know about your experiences you have inferred from your experiences. It is all a posteriori knowledge. You're talking about intuitive reasoning that can be described mathematically. Not sure what that is suppose to mean. Much of the intuitive reasoning that we do (indeed, most of it), is not logical deduction. Nevertheless, we can use mathematics to describe these reasoning processes (for example, pattern-matching, heuristics, and so on). This is, however, just another example of describing reality using mathematics. Those intuitive reasoning processes themselves are not mathematics. They are physical processes. DM
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keda
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Posted 07/13/09 - 02:43 PM:	#52
Death Monkey wrote: I don't understand your question. You said it is nonsensical and provided a reason I showed was insufficient. Why else or what else makes it nonsensical? Numbers don't describe anything. We can use numbers in our descriptions of all sorts of things. How can numbers be used to describe all sorts of things if they don't describe anything? Aren't they redundant then? Surely of a basket of apples, the number 5 can describe the amount of apples in the basket? But then what, exactly, are you referring to? I've already answered this question, yet you seem to avoid commenting on it. But you would not know that this is the case without having that sensory experience It is the other way around. You would not have sensory experience without knowing that it is the case. It is an analytic truth about the axioms of euclidean geometry. It is not a truth about the axioms. It is an axiom of euclidean geometry. It is not a truth about reality at all. Of course it is. Have you ever seen two things that are parallell intersect? No? Well that's because the parallell postulate is true about them. They simply do not intersect. It is a synthetic truth about reality that the postulate is false Analytic truths cannot be false. I could measure the mass of a 5kg object, and the mass of a 7kg object, and then measure the combined mass, and observe that it is not 12kg. Could you give an explanation for it if you measured say 13kg? What necessary conditions? Everything you know about your experiences you have inferred from your experiences. It is all a posteriori knowledge. My sensory experiences are not possible without a priori knowledge about their necessary conditions. Without knowing them, I cannot distinguish experience from illusion. Much of the intuitive reasoning that we do (indeed, most of it), is not logical deduction. Nevertheless, we can use mathematics to describe these reasoning processes (for example, pattern-matching, heuristics, and so on). This is, however, just another example of describing reality using mathematics. Those intuitive reasoning processes themselves are not mathematics. They are physical processes. I'm not talking about pattern matching or heuristics.
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

cosscos
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Posted 07/13/09 - 07:58 PM:	#53
You guys comments remind me of this, Do you learn what you know or What you don't know? In other words, Do you learn a priori memory which had been known to you? cc

Death Monkey
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1 of 1 people found this post helpful Posted 07/14/09 - 01:00 AM:	#54
keda, You said it is nonsensical and provided a reason I showed was insufficient. Why else or what else makes it nonsensical? I said that it is nonsensical to say that specifying what something is does not constitute a definition. The definition of a term is the specification of what the term means. What you cited as a counter-argument to this was not an actual counter-example. Numbers don't describe anything. We can use numbers in our descriptions of all sorts of things. How can numbers be used to describe all sorts of things if they don't describe anything? How can I use a hammer to build a chair when hammers don't build anything? I think we are arguing over semantics here. The point is that numbers are conceptual tools that we use when describing things. Not necessarily. If reality can only be concieved according to mathematical principles, due to how you percieved it, then they apply to reality without basing it on sensory experience, but rather on the way your perception works. But you would not know that this is the case without having that sensory experience It is the other way around. You would not have sensory experience without knowing that it is the case. Sensory experiences are not dependant on knowing anything. Furthermore, tt is not logically necessary that your perception work the way that is does. The only way you know anything about how it does work is through the inferences that you draw from your sensory experiences. If your perception worked differently than it does, then who knows what the consequences of that might be? It is an analytic truth about the axioms of euclidean geometry. It is not a truth about the axioms. It is an axiom of euclidean geometry. It is both. Any statement that can be logically deduced from the axioms of euclidean geometry is a truth about those axioms, and of course this includes the statement of those axioms themselves. It is not a truth about reality at all. Of course it is. Have you ever seen two things that are parallell intersect? No? Well that's because the parallell postulate is true about them. They simply do not intersect. They do when massive enough objects are nearby. Our observations of general relativity are simply not compatible with the claim that space conforms to the axioms of euclidean geometry. Anyway, you are just making my point for me. The justification you just gave for insisting that it is a truth about reality, is a posteriori. If it were the case that, in reality, parallel lines never intersect, the only way you would have of knowing that is by inference from your observations. In fact, prior to about 100 years ago, this was a perfectly reasonable inference to draw from our observations. But it was still an a posteriori judgement. It is a synthetic truth about reality that the postulate is false Analytic truths cannot be false. It's not analytic. I could measure the mass of a 5kg object, and the mass of a 7kg object, and then measure the combined mass, and observe that it is not 12kg. Could you give an explanation for it if you measured say 13kg? All sorts of explanations are possible. But if, through experimentation, we could conclude that it is not a result of error or flaws in experimental procedure, then given enough such evidence we would have to conclude that the principle of addition just does not apply in such cases. What necessary conditions? Everything you know about your experiences you have inferred from your experiences. It is all a posteriori knowledge. My sensory experiences are not possible without a priori knowledge about their necessary conditions. Without knowing them, I cannot distinguish experience from illusion. No. Being able to draw inferences about reality from your sensory experiences is not possible without knowing something about the relationship between reality and your sensory experiences. But even without such knowledge, you are still having sensory experiences. The knowledge that you use to make the judgement that you can draw conclusions about reality from your sensory experiences, itself, comes from your sensory experiences. For example, if there were no consistency to your sensory experiences, so that you were unable to relaibly infer anything about what was going on around you from them, you would abandon that conclusion. Now, you could take the skeptical approach, and attempt to deny that we actually are justified in believing that we can draw conclusions about reality from our sensory experiences, but you cannot reasonably claim that we have some sort of a priori justification for this belief. Again, this comes down to the point of needing information to make judgements. Let's imagine, for the sake of argument, that there are three different sources of information for making judgements. 1) Logical deduction - You can conclude that the statement is true by virtue of the meaning of the statement. It is not logically possible for the statement to be false. 2) Empirical inference - You conclude that the statement is true by assessing empirical evidence. Clearly this requires sensory experience. 3) Non-emprical inference - You conclude that the statement is true by assessing some sort of information that cannot be derived from the meaning of the statement, nor inferred from sensory experience. Now, before you can use the information from (3) to make judgements, you have to first make the judgement that the information you are using is reliable, and that it can be used to provide justification for further judgements about reality. So you do you make that judgement? How do you judge that the statement "this third source of information is reliable for making judgements about reality", is true? If the truth of that statement can be logically deduced from the meaning of the statement, then you are in good shape. But it can't, because the statement is clearly not analytic. If the truth of that statement is inferred from sensory experience, then it is an a posteriori judgement, which in turn implies that any judgements you make based on that third source of information are also a posteriori. The only remaining possibility is that the truth of the statement is, itself, somehow inferred from that third source of information. In other words, that judgement is of type (3) above. Now, in principle this is OK. After all, I would argue that the way we know that empirical information can be used to make inferences about reality, is through sensory information. If we wanted "absolute proof" that we can do this, we would be out of luck. But we don't need that. We just need demonstrably relaible supporting evidence. We already accept that any a posteriori judgements we make are fallible, and thus subject to future refutation. Likewise, we could imagine some sort of methodology, analogous to the scientific method, for evaluating information of this third type. And ultimately, just as we use the scientific method to justify the claim that empirical information can be relaibly used to make judgements about reality, we could use this new methodology to justify that this third source of information can be relaibly used. But then we need a method. We don't have one. We also need a continuous source of new type-3 information, as we have for empirical information. That way we can use the principle of falsification to test the hypotheses we make based on the information we currently have. But we don't have that either. For example, I could imagine a being that possesses some sort of "innate information" in its memory. Facts about reality that it is created "knowing". I put "knowing" here is quotes, because before that being could conclude that these facts actually are knowledge, it would need to make the judgement that this innate information is a relaible source of information about the world. But how could it possibly make that judgement? It cannot analytically determine that it is true. After all, the information could be unreliable. It could test the reliability of that information using the scientific method, but then any judgements based on that innate information would be a posteriori. The only other way it could make the judgement would be by testing the reliability of that innate information in some other way. But testing requires the acquisition of new information. As soon as you have that, though, then you are really just talking about a new sense. DM
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jtoma
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1 of 1 people found this post helpful Posted 07/14/09 - 01:25 PM:	#55
I can't keep up with the reading but here's some comments on the first bit: keda wrote: If a priori synthetic is a contradiction in terms likewise analytic aposteriori, the two distinctions would collapse into one, as they would be synonyms. However they are not. A priori means, independent of experience, a posteriori, dependent on experience. Analytic, true by virtue of meaning, synthetic, not true by virtue of meaning. I would distinguish between thought and sense experience. Sense experience is a posteriori. Thought experience is a priori. Otherwise to whom does the predicate concept appear contained in the subject concept? To whom would the words representing the knowledge be meaningful? The predication is perceived and that perception is an act, implying experience, albeit thought experience. The thought experience is logged in memory, only in a somewhat internal way, just as sense experience is logged. You have memories of it and you can recall them (with language) just as you would with sense experience, just that the objects of your thought experience have exclusively mental representations (no objects acquired against my will—through sense experience. My will is just what I choose to do). SO the objects acquired in sense experience are given to the degree that what I choose affects my sense experience by my will, but the point is that that I have the experience, is against my will. At any point I can switch my thoughts, but I can’t as easily switch the objects of my sense perception. I could listen to 8 genres of music while living in the same house with the same job and same friends. If a priori were independent of experience, then what would it be? I thought I understood some one to be suggesting that thought experience was a priori. An object represented by an element of a set may be experienced or not. Let Z := {5,6,c}. Z is a set, which can represent objects in a group. ‘An object from set Z may be neither 5 nor 6’ is true insofar as it means that there is an object in set Z that is neither 5 nor 6. ‘An object from set Z’ is a predicate whose scope is not exhausted by ‘neither 5 nor 6’. Even in the event of uttering, ‘neither 5 nor 6’, that experience isn’t an act of going through all the members of Z. So whether synthetic is tied to experience or not, ‘an object from set Z may be neither 5 nor 6’ is analytic. If synthetic judgements were tied to experience, then it would be useful to characterize analytic judgments as proceeding by virtue of the meaning of representations, as a matter of linguistic competence and establishment. Analytic judgments don’t use objectively existing representations, but inter-subjectively existing representations. I mean this is a different topic, but analytic judgments always occur because all judgments are according to rule because without rule you can’t judge. So synthetic is new relations of concepts. Analytic is every relation of concepts, in that every relation (judgment) proceeds by rules. Incidentally, this is because the language you use in, for example, thought experience and verbal exchange concerning memories, is of two exhaustive types: 1) an act of reference (object identification) and an attribution of predicate (existing rule) to subject (the identified object—or one of them); 2) attribution of predicate (rule) to concept of already existing subject (object—of knowledge). Not the whole story but off topic. (E.g. the attributive is always a priori, but the referential may be a priori synthetic or analytic and a posteriori synthetic or analytic—it depends on the contents of the proposition or representation that constitutes the judgment). But in order to maintain the difference between the distinctions, synthetic should be tied to new experience (learning). That way, analytic means established; synthetic means new, and a posteriori means sense experience. And a priori means established thought experience—hence the phrase ‘can be known a priori’. This is to take away the glory of a priori knowledge. The knowledge we choose, by choosing the assumptions and rules we acquire, to make accessible a priori, is the knowledge we use to solve problems, as learners (human beings with brains). We put together a priori knowledge, which is familiar specification of context and problem (limited in some cases). Then we attempt synthetic judgments using thought experience (a priori) or sense experience (a posteriori) or both to manipulate rules in useful ways—e.g. predicate; relate subject to object. A judgment concerning sense experience without thought experience is synthetic a posteriori. A new judgment concerning thought experience is synthetic a priori, and old one analytic a priori. Analytic a posteriori would be: perceiving things, perhaps against your will, and not registering modifications (making new judgments) to your old perceptions. Right so ‘57+68=125’ is analytic and I have a priori knowledge of the rules of addition, but I don’t know ‘57+68=125’ in the way I know ‘2+2=4’, so I have to calculate. The objects in my mind used for the performance of the calculation are perceived—e.g. capable of being represented, identifiable, because they are usable (in the calculation!), but I have to use them in a new (synthetic) way to calculate ‘57+68=125’. The representation of the judgment made in the calculation is synthetic and a priori, achieved by analytic a priori knowledge of assumptions and rules. The act can be considered referential in the sense that I have special interest in a pair and an operation that would require calculation to achieve output, and perhaps and easy example. The calculation can also be considered referential in the sense that I had to experience an object of thought; representing that experience, which is an act of reference, and thus (the other half of referential), attributing chosen rules and assumptions. (SHHH!!!@#$$@%so every analytic judgment is as synthetic as the proposition ‘every experience is new’ is true AND your saying every proposition is analytic—and every judgment is represented by a proposition). Qualifying: so displays of contradictions proceed by rule even though the contradictions are not true and don’t seem analytic. But to display a contradiction is to convey a proposition; perhaps it is a proposition, which conveys teaching, failure, or even success (reductio)—all results of rules of action. In the application (occurrence) of a rule of action, the result proceeds by rule. If the representation of the occurrence is true, then that rule predicts truly what would happen in the event of an application of that rule. (The representation of a rule which yields a false result may be a true rule misapplied). keda wrote: see, although I would say rather than "2 + 2 = 4" being a performance I would say it is a proposition of what a performance will accomplish. The + operator denoting the performance of adding and 2 and 4 denoting performances of counting. I suppose you could say a priori synthetic judgments are are similar to this inthat they are about some performance(s), although I wouldn't say they are performances themselves. This is correct. The judgment is not a performance because it is a proposition, which represents a performance. But the way the proposition describing the performance or judgment is expressed needs to be included in the content of the proposition—right so if the performance requires a new act of reference, then the overall predication must be presented as learnt—synthetic. (This is normative—but methodological). But just think of it: we need propositions with readily identifiable objects: e.g. ‘2’ or ‘Two’ represents itself so it is self-aware, otherwise what would ‘two’ be representing? Not implying consciousness, but mere self-identification, which is the basic form of self awareness: you cannot be self aware without self identification, what would you be aware of other than an identity to give you a sense of self? The significance of self-awareness is just that it evidently proceeds by rule—e.g. ‘two’ is just what we define it to be, that is how it represents itself to us (because its math). A priori synthetic judgments are statements intended to represent experience of learning—the act of performing a new rule or a rule in a new way. Synthetic judgments must contain a description of an experience of learning. Analytic judgments, being established relations of concepts, are descriptions capable of teaching. Synthetic judgments are also capable of teaching but that is because everything proceeds by rule. Synthetic judgments, accounts of learning experiences, are capable of teaching because they themselves, the accounts, have to be given. To give an account is to establish. Edited by jtoma on 07/19/09 - 11:05 AM

keda
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Posted 07/15/09 - 04:45 AM:	#56
Death Monkey wrote: It is both. Any statement that can be logically deduced from the axioms of euclidean geometry is a truth about those axioms, and of course this includes the statement of those axioms themselves. No it isn't. From "There is a cat" we can derive "There is an animal" But the latter statement is not about the first, and it certainly isn't an analytic statement. Even if you started with an analytic statement, its derivation would not be a statement about it. But when you say: P = {A1,A2,..,An} \|= S and S actually follows from the axioms, you can say P is analytic and about {A1,A2,..,An} They do when massive enough objects are nearby. Our observations of general relativity are simply not compatible with the claim that space conforms to the axioms of euclidean geometry. As I have stated earlier it is merely a semantic incompatibility. There is a theory called General Lorentz Ether Theory which makes the same predictions as General Relativity (GR), and happens to solve some problems that GR is unable to do e.g. regarding dark matter and the cosmological horizon, but is based on the semantics, and is an extension of Lorentz Ether Theory and thus Euclidean space. Anyway, you are just making my point for me. The justification you just gave for insisting that it is a truth about reality, is a posteriori. Does not follow. There are claims that can be made about reality that are a priori, and a subset of them are about how it must be percieved in order to be so at all. The parallell postulate is an example of the latter, even though Euclid argued of the former but not the latter. It's not analytic. You said it was an analytic truth earlier: The parallell postulate is not an analytic truth about reality. It is an analytic truth about the axioms of euclidean geometry. It is not a truth about reality at all. It is a synthetic truth about reality that the postulate is false, but that is not an a priori truth. The underlined apparently contradict each other. All sorts of explanations are possible. Can you give an example of a possible explanation, given there are no flaws in the experiemental procedure? The only other way it could make the judgement would be by testing the reliability of that innate information in some other way. But testing requires the acquisition of new information. As soon as you have that, though, then you are really just talking about a new sense Why is this the case?
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

keda
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Posted 07/15/09 - 05:23 AM:	#57
jtoma, I haven't read your full post yet, and will respond later, but just making a comment about my earlier claim about numbers refering to performances. While mathematical statements refer to performances, I would like to retract the claim that numbers themselves refer to such. In post #33 I wrote the following: keda wrote: How about the size being an equivalence class of sets where the equivalence relation is specified by there being a bijection between the sets. x is a successor number of y iff there exist an x' and y', such that y' is a member of y, x' is not a member of y', and the union of y' and x' is a member of x. x is a sum of y and z iff there exist an x', y' and z' such that x' is a member of x, y' is a member of y, z' is a member of z, there exist no member w such that w is a member of x' and w is a member of y', and x' is a union of y' and z'. suggesting the notion of countring can be removed from the concept of number, making it more than clear 5+7=12 is a synthetic judgment.
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

Death Monkey
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1 of 1 people found this post helpful Posted 07/15/09 - 09:07 AM:	#58
Keda, It is both. Any statement that can be logically deduced from the axioms of euclidean geometry is a truth about those axioms, and of course this includes the statement of those axioms themselves. No it isn't. From "There is a cat" we can derive "There is an animal" But the latter statement is not about the first, and it certainly isn't an analytic statement. Even if you started with an analytic statement, its derivation would not be a statement about it. But when you say: P = {A1,A2,..,An} \|= S and S actually follows from the axioms, you can say P is analytic and about {A1,A2,..,An} Perhaps I should clarify. When you say that a statement is true, that is a statement about the statement. If I say "axiom X is true", that is a statement about axiom X. Likewise, if statement Y can be logically derived from X, then the statement "Y follows from X" is a statement about X. Likewise, when you say "5 + 7 = 12", unless you specify some units or specific context, I would interpret this to be saying "according to the axioms of arithmetic, 5 + 7 = 12". The "according to the axioms of artithmetic" would be taken by me to be implicit in the context. And this is a true statement about the axioms of arithmetic. Now, maybe you didn't inted the statement that way. But then you have some other context in mind. If so, you need to specify that context. But if that context is such that the statement is one about reality, then it is not what I would consider to be a (purely) mathematical statement anymore. They do when massive enough objects are nearby. Our observations of general relativity are simply not compatible with the claim that space conforms to the axioms of euclidean geometry. As I have stated earlier it is merely a semantic incompatibility. There is a theory called General Lorentz Ether Theory which makes the same predictions as General Relativity (GR), and happens to solve some problems that GR is unable to do e.g. regarding dark matter and the cosmological horizon, but is based on the semantics, and is an extension of Lorentz Ether Theory and thus Euclidean space. According to your own above statement, it does not make the same predictions as GR. It is a different theory. Now, if you wish to argue that it is possible to construct alternative theories to GR for which euclidean geometry still works, I agree, that is possible. That's not the point. The point is that even if you could claim to know that the axioms of euclidean geometry are true statements about reality (and you can't), your justification for this would have to be based on sensory information, because that is the only source of information about the world that you have. The very fact that it is logically possible that they are not true statements about the world, shows that you would need some way to test the hypothesis that they are. It's not analytic. You said it was an analytic truth earlier: The parallell postulate is not an analytic truth about reality. It is an analytic truth about the axioms of euclidean geometry. It is not a truth about reality at all. It is a synthetic truth about reality that the postulate is false, but that is not an a priori truth. The underlined apparently contradict each other. Only because you do not recognize that you are talking about completely different statements. The statement "parallel lines never intersect according to the axioms of euclidean geometry" is an analytic statement. The statement "parallel lines never intersect in reality" is a synthetic statement. There is no contradiction here. All sorts of explanations are possible. Can you give an example of a possible explanation, given there are no flaws in the experiemental procedure? I already did. One possible explanation is that mass is not a conserved quantity under the conditions of the experiment. In other words, that the rules of addition don't apply under those conditions. We know that they do, but again this knowledge is a posteriori. Without sensory experience, we would not even have a conception of mass, much less the expectation that it is a conserved quantity. The only other way it could make the judgement would be by testing the reliability of that innate information in some other way. But testing requires the acquisition of new information. As soon as you have that, though, then you are really just talking about a new sense Why is this the case? Which part are you asking about? That testing is necessary to determine reliability should be clear, as should the fact that testing requires access to new information. As for the source of new information being just another sense, I fail to see what the sources of information about reality that we do call "senses" have in common, other than being sources of information about reality. DM
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Posted 07/15/09 - 09:21 AM:	#59
jtoma, You make some very interesting, and clarifying points. I can certainly see a distinction between what we conventionally think of as our 5 senses, and memories of past thoughts. In this sense, knowledge we have about our past thoughts could be considered to be a priori, because it is not justified by information acquired from the 5 senses. I had not been considering this distinction, because both awareness of memories and perception of sight, sound, etc, are examples of empirical sources of information. I had always considered a posteriori to include judgements that are justified by your own memories. However, even we accept things like me knowing that I was just imagining an apple as "synthetic a priori", I still have to argue that purely mathematical statements are analytic, for the reasons I mentioned in my posts to Keda. Likewise I would argue that metaphysical claims still do not qualify as being a priori. DM
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Posted 07/15/09 - 11:15 AM:	#60
keda wrote: suggesting the notion of countring can be removed from the concept of number, making it more than clear 5+7=12 is a synthetic judgment. Look, I don’t know anything about equivalence class countring. Its just that, loosely speaking, your skeptic boat can go where it is not possible to possess an actual fact (know a proposition) that proves or is even proper evidence for following a rule in the way intended. SKeptic cries, 'I suppose you meant quus (take last digit of sum) rather than plus by 'addition' or '+' in '57+68=125'. (In that case, you meant five and miscalculated 125). But there is no fact about you that distinguishes your meaning 'plus' rather than 'quus' or even from meaning nothing at all!'. I reserve that skeptical talk for 'strictly speaking...' There are lots of ways to experience the proposition ‘5+7=12’, but that proposition proceeds by rules, and so it is analytic. But many ways of expressing the proposition are synthetic—e.g. not having the sum in mind and requiring computation, referring to the action of producing the answer, perhaps for use in answering a different question (5+7=12&scaling by ten preserves ratio→50+70=120—useful in learning computation techniques). Death Monkey wrote: still have to argue that purely mathematical statements are analytic, for the reasons I mentioned in my posts to Keda. Likewise I would argue that metaphysical claims still do not qualify as being a priori. RIght, they are analytic, they proceed by rule from definitions or assumptions. BUT if I prove that every even integer greater than 2 can be axpressed as the sum of two primes, then I would synthetically judge that I had proved it, based on the synthesis of concepts relatable but had not yet been related. This is learning. It is synthetic because I had never proved it before. (ANd i never will). // Likewise metaphysical claims, for example, about whether facts are tensed or not, are chosen assumptions upon which to base reasoning. That act of choice may be an experience, but I think it is a thought experience, so it is a priori. Do you really think metaphysical claims are a posteriori? (I mean, other than in the sense that accumulation of sense data can lend support in some ways (scientifically) and determine synthetic judgments (actually). I mean, all my wealth of physical and conceptual knowledge would be at work (in assumption grabbing field) when I JUDGE something about facts and time. But, still when I have once related the concepts to determine that I think facts are tensed, I am then capable of using ‘tensed facts’ as an assumption in reasoning. It proceeds by rule from all my other assumptions of physical and conceptual knowledge. Anything you derive can be taken to be the case. I hope some comments from the past can be useful because I can’t read the posts quickly. Death Monkey wrote: An analytic statement is one whose truth-value is fixed by the meaning of the statement. That is, the truth-value logically follow from the meaning of the statement. An analytic truth cannot be false because that would lead to a logical contradiction. If an analytic truth is incorrect it is because we no longer assume the relevant meanings or because meanings are no longer taken to represent what they were intended to. Yes, an incorrect analytic statement is a contradiction within the logic generated by the assumed meanings and rules of inference. But it is not a strictly logical contradiction because strict logic doesn’t include assumptions like sense data of your gray car. So an incorrect analytic statement may be false in its application to the facts. For example, teacher asks ‘Whats the next step in the proof’, student answers ‘Pv-P’ when in fact a contradiction has be shown for reductio. ‘Pv-P’ is analytic because it is either an axiom or derivable in common systems of logic. An analytic truth is a proposition that, if true, is true by virtue of meaning. A synthetic truth is (YOU meant to say) a proposition that, if true, is not true by virtue of meaning. Neither analytic nor synthetic propositions need to be true—they each may be disjoint with the logical systems upon which you base truth on. Analytically speaking, I generally think ‘3 + 5 = 8’, but in mod4 I think ‘3 + 5 = 0’. (is that right? I don’t know any math—just looking for clear example). (each proposition is analytic given assumptions of arithmetic and each proposition may be expressed synthetically—additionally, an expression may be mental, a priori, or physical, a posteriori.) Death Monkey wrote: A synthetic statement is a statement which has a truth-value (we will put aside for now statements which have no truth-value), but whose truth-value is not fixed by the meaning of the statement. Truth values are given by fixing meanings. Death Monkey wrote: As mentioned previously in this thread, though, the a priori / a posteriori distinction has to do with judgments. It is a question not of whether the truth-value is fixed by the meaning of the statement, but instead on whether or not we can decide what the truth-value is without making reference to sensory experience. Fixing meaning in a community of people is done through sense experience. Truth value is not contained in meanings or sense experience, it is an assignment of meanings. . keda wrote: It is not abstracted from empirical acts, but refers to acts abstracted from its empirical objects. Yes. Death Monkey wrote: Change those rules, and you change the meaning of the statement. Therefore the truth-value of the statement is fixed by its meaning. Right, but we change the rules a lot. We choose to base truth on one set of rules and then have an analytic statement proceeding from a completely different set of rules, unrelated to the first. Death Monkey wrote: nobody has justified the claim that "sensibility" is a reliable source of information that does not come from sensory experience. We don’t need to.

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