There was never a statement that did not depend on prior experience or sensation.
So you put six beers in the fridge and see someone take three of them out. You don't know there's three left until you open the fridge door and verify it by looking.
So you put six beers in the fridge and see someone take three of them out. You don't know there's three left until you open the fridge door and verify it by looking.
Reply to Hallucinogen
Analyticity is related to necessity and a priority. If analytic statements are necessarily true, they are automatically true come what may. If analytic statements are true a priori, they are known without experiential knowledge.
Well let's have a little go at this. Language works by means of distinctions: beer is distinguished from not-beer, otherwise we don't know what we are talking about when we say "beer". and that would be a tragedy, because it is a useful and important distinction, even if it becomes blurry at the barleywine edges.
One of the distinctions that philosophers find useful and important is between the word and the thing, sometimes called the signifier and the signified. The convention is that when one wants to talk about the word "beer", one puts it in quotes, and when one wants to talk about the drink beer, one does not. Thus there is a clear difference, beer is a nourishing drink, whereas "beer" is a word.
So now, philosophers of beer can discuss the defining (necessary and sufficient) features of beer, What makes something beer and not a rabbit? Cue much talk of hops, barley malt, fermentation, and the amount of froth on top. Does it have to be liquid, or is a frozen beer still a beer? Are the yeasty dregs at the bottom of the barrel beer? All this talk is talk about what the word "beer" means, about what counts as beer, we are trying to sharpen up those blurry edges of the distinction between beer and not-beer.
So it is the case that(P1.) Fosters is not beer, but the recycled piss of inebriated Australians, and this is a matter of fact, given our shared understanding of what "beer" means. And this is what we call synthetic proposition, because it turns out that Australians also make proper beer that they do not export, but wisely drink themselves.
However, it is based on not only the facts of the case, but also the analytic proposition that (P2.) the recycled piss of inebriated Australians is not beer. This is analytic, because it is not about beer, but about "beer". The facts of the case - that Fosters call their drink "beer", are not decisive, because to most philosophers of beer that is simply an abuse of language.
Perhaps the Hegelian perspective is useful to you. Analytic thought produces a thesis. The existence of the thesis means that there is an antithesis. If the antithesis is also meaningful, then one can use synthesis to combine the thesis and antithesis and generate a more complete system of explanation. I should mention, some feel that Kant does not use the thesis/antithesis/synthesis method in this manner, although he used those words, and they state that was something Frege first did instead. However I believe they are wrong in tat. The difference, if there is one, was that Frege was the first to indicate that a synthesis is itself another thesis, leading to a dialectic; whereas Kant simply was interested in stating triads of ideas with that relationship, rather than pursuing dialectical investigation.
Reply to Hallucinogen you know there's 3 beers left prior to opening the fridge door. That's all 'a priori' refers to and it's what is called an apodictic truth, i.e. cannot plausibly be denied. The rest is blather.
So, basically, I can't see how dividing all statements into either analytic or synthetic is correct.
It is a distinction that seemed to made sense at the time it was hotly discussed, which was the 16th-17th centuries. That was before a modern understanding of logic was developed, which arose in the late 19th to early 20th centuries. That understanding has revealed that the distinction is an illusion - for instance that the statement '7+5=12', which Kant thought was synthetic, is not different in kind from 'all bachelors are unmarried', which Kant thought was analytic. I presume that is one of the reasons why hardly any professional philosophers discuss it any more, other than as a historical phenomenon.
However the distinction is very important historically. It is important because the controversy about it awakened Immanuel Kant from his 'dogmatic slumber' and goaded him to write the Critique of Pure Reason, which is still very relevant, meaningful, and much discussed today. Many see it as one of the most important philosophical works ever written. The bits of CPR about the analytic/synthetic distinction are obsolete and can be skimmed over in favour of those that give real insights, like the Transcendental Aesthetic, the Transcendental Deduction of the Categories and the Synthetic Unity of Apperception. These give difficult, but highly significant, insights into how we think, how we approach the world.
Reply to Hallucinogen but memory doesn't explain mathematics. You're not struggling to understand something, you're struggling to make any kind of argument.
Analytic thought produces a thesis. The existence of the thesis means that there is an antithesis. If the antithesis is also meaningful, then one can use synthesis to combine the thesis and antithesis and generate a more complete system of explanation."
I'm not sure what this means, could you give an example?
Sure, here is a simple example
analytic: what noise do animals make?
analytic thesis: dogs bark
analytic antithesis: but cats meow
synthesis: different species make different noises.
Analytic things are true by definition, or tautological. Reason is a process of truth retention, and is deleterious by nature. You're to find the necessary by deleting the coincidental.
The precise example of an analytic claim that Kant gave, I believe was "all bodies are extended in space" or something like that. Married bachelors were too simple and obvious for him.
you know there's 3 beers left prior to opening the fridge door. That's all 'a priori' refers to and it's what is called an apodictic truth, i.e. cannot plausibly be denied. The rest is blather.
You're just wrong about this. How many beers are in the fridge is settled by opening the fridge and counting the beers, and the result of this experiment trumps any amount of mathematical and logical reasoning. If there turn out to be 4 beers, then one thought one knew but was mistaken. Perhaps Jesus passed by and turned the milk into beer, perhaps beers can breed, perhaps there was already a beer in the fridge, perhaps a wormhole opened and a beer fell through, or perhaps you miscounted the beers you put in, or the ones taken out, but anyway it is not analytic that there are 3 beers, nor a priori. It is a matter of fact, that might be otherwise.
Perhaps Jesus and passed by and turned the milk into beer, perhaps beers can breed, perhaps there was already a beer in the fridge, perhaps a wormhole opened and a beer fell through, or perhaps you miscounted the beers you put in, or the ones taken out, but anyway it is not analytic that there are 3 beers, nor a priori.
If you think that amounts to an argument then please, go and have another beer.
If you think that amounts to 'an argument', then please, go and have another beer.
These are not arguments, they are examples of explanations one might make if there turn out not to be 3 beers in the fridge. The point is that how many beers are in the fridge is not a priori, it is a contingent fact. What one would not do, however, unless one had had several too many beers, is claim that 6 - 3 = 4, because that is analytic.
But if you forget how many beers were placed in the fridge,
Yes, you could be shot dead en route, or have your brain consumed by a parasitic worm, or some of the beers could be turned into beetroot juice by some as yet unknown process. All this is true, and all beside the point.
If you were not capable of knowing basic maths, then you probably couldn't type anything at all, the fact that you can think of anything to say, even if what you're saying is completely meaningless, relies on the fact that you're able to grasp basic truths of grammar, mathematics and the like.
ultimately it is those experiences of objects in the world that gets plugged into our mathematical thinking when we're learning to count as children
Kant argued that the structures of logic which organize, interpret and abstract observations were built into the human mind and were true and valid a priori. Mill, on the contrary, said that we believe them to be true because we have enough individual instances of their truth to generalize: in his words, "From instances we have observed, we feel warranted in concluding that what we found true in those instances holds in all similar ones, past, present and future, however numerous they may be". Although the psychological or epistemological specifics given by Mill through which we build our logical apparatus may not be completely warranted, his explanation still nonetheless manages to demonstrate that there is no way around Kant's a priori logic. Mill argues: "Indeed, the very principles of logical deduction are true because we observe that using them leads to true conclusions" - which is itself an a priori presupposition.
Wikipedia.
In other words, to make a judgement about whether mathematics corresponds with experience, we must first make a mathematical judgement. Otherwise, how would we know that it corresponds? The knowledge of mathematical truths can't rely on, or be explained in terms of, anything else; it is the source of explanations, not the target of explanations.
The point is that how many beers are in the fridge is not a priori, it is a contingent fact.
The idea that they're 'beers in fridge' is only a rhetorical device to illustrate the fact that 6-3=3 in a rather less boring manner. And that is something that is obviously know a priori - it's simply an example of a tautological truth.
The idea that they're 'beers in fridge' is only a rhetorical device to illustrate the fact that 6-3=3 in a rather less boring manner. And that is something that is obviously know a priori - it's simply an example of a tautological truth.
Then we agree. But your rhetoric serves to blur the distinction rather than clarify it. Change the example:
I put 2 rabbits in an empty hutch with some lettuce, and then see my friend take out 5 rabbits. I do not know that there are - 3 rabbits in the hutch, nor have I proved arithmetic wrong, I know they've been breeding. Experience tells me that rabbits multiply and beers only add and subtract.
I put 2 rabbits in an empty hutch with some lettuce, and then see my friend take out 5 rabbits. I do not know that there are - 3 rabbits in the hutch, nor have I proved arithmetic wrong, I know they've been breeding
You only know that because you can count! So you say - ah, five rabbits, they must have multiplied. And you know that, even if you didn't actually see them at it. ;-)
Reply to Hallucinogen] The first sentence is the SUBJECT of the analysis which directs the investigation to the thesis.
The Kantian method and Hegelian dialectic are considered methods of investigation, so they doesn't really need a justification. Here is the wikipedia reference
Reply to Hallucinogen Two things you need to remember to properly understand the analytic/synthetic distinction (along with the a priori/a posteriori distinction). First, is that Kant mobilises these terms in the context of the problem of causality, and they cannot be understood apart from that context. Specifically, remember that Kant is responding to Humeian skepticism about causality: qua Hume, the constant conjunction of events does not guarantee the universality of causal connection. In other words, causality does not admit of the order of logical necessity. And connection via the force of logical necessity is just what Kant refers to as an analytic connection. By contrast, synthetic connections - in this case causality - are those that admit of extralogical reasons to explain their connection.
In Christian Kerslake’s terms: “Whereas an analytic connection contains its reason solely in the logical explication of the presupposed meaning of a concept, a synthetic connection must involve an extralogical reason. [For Kant,] the concept of a causal relation must be synthetic… [Hence,] Kant’s notion of the synthetic a priori simply names a problem faced by eighteenth-century philosophy – that of how to account for any possible nonlogical a priori connections”.
The second thing to understand then is that the above means that Kant here is dealing with the problem of how to move from the sphere of logic to the sphere of existence. Insofar as analytic statements are those driven by logical necessity, synthetic statements by contrast involve a measure of reality. It is this move from logic to existence that in turn - for example - grounds Kant’s famous response to the cosmological argument: it is not enough to argue - as the cosmological argument more or less does - that God is perfect and that because existence is a perfection He must exist: for this simply begs the question of God’s existence to begin with. Essence - or analyticity - cannot ground existence - which belongs to the order of the synthetic.
So just remember: at stake in the analytic/synthetic distinction is the question of both causality on the one hand, and the move from logic to reality on the other: both of which turn upon the question of logical and extra logical necessity respectively.
Reply to Hallucinogen No. Even if there are no blue dogs, no blue things and no dogs, still all the blue dogs are blue dogs, just as all unicorns are unicorns.
Reply to Hallucinogen Exactly. It's called pure reason, and it has limitations. That's what it means for a proposition to be analytic, that it says nothing about the world. And that is why the number of beers in the fridge, or rabbits in the hutch is synthetic, whereas that 6 - 3 = 3 is analytic. The price of necessity is vacuity.
Where philosophers start to use both together is where they can say interesting and meaningful things.
Reply to Hallucinogen
Logical truths are known by studying logic. Logical truths' truths depend on purely logic. You should distinguish what makes statements true from how we know statements.
There are two somewhat distinct questions that can be discussed in connection with the OP. A historical, philological question concerns Kant's own notoriously ambiguous treatment of the concepts that he coined. What Kant thought depends on who you ask, and different commentators will typically massage and harmonize the text to favor their own views on the matter. It seems to me that StreetlightX's referenced summary is rather too neat. It, for instance, glosses the issue of "containment," also raised by the OP, that Kant seemed to take seriously enough that he would not recognize even simple mathematical statements such as 2+2=4 as analytic (because, the argument goes, "4" is not contained in either "2" or "+").
Apart from specifically Kantian scholarship, modern discussion of the analytical/synthetic owes more to the way these concepts were framed later, when Western analytical philosophy took a logical and linguistic turn. And here the debate is not dead, despite Quine's valiant efforts. The reason, I think, the idea of analytic/synthetic distinction will not go away is that we intuitively feel a categorical difference between groups of statements such as the following:
I.
(1) Some doctors that specialize on eyes are rich.
(2) Some ophthalmologists are rich.
(3) Many bachelors are ophthalmologists.
(4) People who run damage their bodies.
(5) If Holmes killed Sikes, then Watson must be dead.
II.
(6) All doctors that specialize on eyes are doctors.
(7) All ophthalmologists are doctors.
(8) All bachelors are unmarried.
(9) People who run move their bodies.
(10) If Holmes killed Sikes, then Sikes is dead.
(11) If Bob is married to Sue, then Sue is married to Bob.
(12) Anyone who's an ancestor of an ancestor of Bob is an ancestor of Bob.
(13) If x is bigger than y, and y is bigger than z, then x is bigger than z.
(14) If something is red, then it's colored.
Until this distinction is not at least explained away, the work is not done.
The above examples are taken from the SEP article The Analytic/Synthetic Distinction, which offers a comprehensive introduction to the issue.
Terrapin StationJune 11, 2017 at 13:12#767420 likes
I wouldn't completely dismiss the distinction--there's a difference between experience gained via interacting with the world and the way that your brain works because of its structure, function and processing, but it's not at all a black and white distinction, and many people make a mistake of taking the analytic/a priori side to somehow transcend individuals and their brains.
It seems to me that everything turns out to be a combination of a priori and a posteriori, really, with nothing purely one or the other.
Your brain doesn't actually arrive with anything like propositions fully formed. You need to have experiences and to think about them, while your brain physically develops, to arrive at beliefs, propositions, etc.
And you can't just experience the world. Your brain has to process that experience, and it's going to process it a particular way because of its structure and internal interactions.
Reply to Hallucinogen
If we find that everything that has a heart has kidneys, and everything that has kidneys has a heart, then the two sets, things that have a heart and things that have kidneys, are the same. But is saying something has a heart the same as saying it has kidneys? It doesn't seem like it is. It seems like two different concepts, even though they apply to exactly the same things.
On the other hand, would we have to do research to find that everything that has a heart has a body? How would you search for something that has a heart but no body? (Leaving aside Roy Orbison.) It's already built into the concept "has a heart" that it can only apply to things that have bodies. That's the analytic part. So you can know that the one set is a subset of the other without looking. That's the a priori part.
(a) When reading Kant, it is often useful to take a look at his historical predecessors in order to understand how some of his distinctions are actually tactical maneuvers deployed against positions which he rejected (two books that, incidentally, show the power of such an account for Kant is the classic Kant and the Capacity to Judge, by Longuenesse, and, more relevant to this thread, The poverty of conceptual truth, by R. Lanier Anderson, which is entirely devoted to an elucidation of Kant's distinction between analytic/synthetic). Case in point, Kant considered his analytic/synthetic distinction as a weapon against Wolffian metaphysics. Very roughly, this is the idea:
Wolff and his followers apparently thought that every concept could be positioned in a logical hierarchy, in such a way that immediately above it would be its genus and right below it its species. Thus, we could picture this hierarchy as an upside-down tree, with the most general concept at its root (say, the concept of
Reply to Hallucinogen Your version of radical empiricsm simply cannot work (i.e., that all cognition is explainable by experience), and even the logical positivsts understood this, because they saw that one must presuppose the analytic/synthetic distinction for the viability of their empiricst project.
The reason is that syntetic sentences, that is, sentences which derive their meaning from experience, must presuppose some analytic definitions to function as 'synthetic' in the first place. Because think in what sense can a sentence said to be 'derivable' from experience: it must mean that there is some general a-priori rule which justifies you in inferring the sentence from a certain experience. Thus the positivists thought that all empirical terms have a fixed meaning or definition (or at least we can construct such definitions for a 'perfect' scientific language). So for example 'cat' is defined via the experience of such and such shapes and colors occurring in a certain configuration; and therefore in the present of such an experience it follows analytically that you are seeing a cat (because this is what the term means). And this is where their famous verification criteria of meaningfulness comes from: every empirical sentences must be connected to experience (empiricism); to be connected to experience is to be verifiable by experience; and to be verifiable is to have an analytic definition - prior to any experience - that tells you which experience should count as the verification of the sentence. Otherwise, if you don't have such definitions that fix the meaning of your empirical terms, then nothing could follow from your experience, no sentence could be ever verified by experience (and hence you wouldn't have empiricsm).
The conclusion is therefore that there cannot be only synthetic sentences, but also analytic which are true independently of experience. And this is also how they thought that science works: you have a theory from which (by virtue of the meaning of the terms it contains, as they have been defined) a set of certain possible observations follow. Then when you go on testing the theory, if the predicted observations obtain, then the theory is verified; if not then it is disproved. And the idea here is the dame: unless theory and observation are connected by definitions, no observations could follow (deductively or inductively) from any theory, and there will be no way to test it experimentally, in which case science would be impossible.
And as a historical sidenote, it is important to note that though Quine famously attacked the analytic/synthetic distinction, what he was primarily concerned with is the positivists' conception of the 'meaning' of sentences (this is why he talks so much about synonimity in "two dogmas"); however, he himself didn't reject the distinction (which was central to the positivsts as well) between theory and observation, but only claimed that they are mutually interdependent, and that observation cannot verify or disprove individual sentences, but whole theories (and maybe the whole body of science). And so according to Quine, the way experience is connected to our body of beliefs is not via "definitions" but whole theories or world views ("conceptual schemes"), but it still retains the same idea that our experience is mediated by logical connections which themselves are prior to experience.
I don't really understand why Kant made this distinction, was it important for something?
Analytic statements are true by definition, synthetic a priori statements are true not by definition, but because they are self-evident; we do not need to check empirical conditions in order to confirm either, but the latter are not true merely by definition, that is the main point. This distinction is a perfectly valid and useful one, as far as I can tell.
Thank you for taking the time to write that fascinating reply. I see that the a priori / a posteriori distinction is based on the justification of the terms now, - it is an epistemological, not ontological distinction.
I can't see how natural scientific statements or mathematical statements fall exlusively into synthetic or analytic statements. In order to make scientific explanations, causation has to be involved, ways of referring to time and space, or movement. An example would be "the sun is warming this rock". I don't think synthetic statements are able to do this, they're purely associative right? All they can do is refer to how sets of objects overlap.
Well, the whole point of the first Critique is to argue against this idea, that is, to argue that there re synthetic claims which are not grounded merely on empirical association. Kant's argument here (which comprises the entire Transcendental Analytic) is notoriously complex (I myself don't fully understand it---I don't know if anybody does), but the gist of it is that our consciousness of ourselves as abiding (i.e. our consciousness of our own identity throughout time) requires certain conditions which allow us to distinguish between (to use Strawson's turn of phrase) the subjective route of our experiences and the objective world through which it is a route. This distinction in its turn is grounded on certain principles which allows us to distinguish our subjective spatio-temporal order and the objective order of the world (for instance, to use Kant's own example, when I successively experience the different aspects of a house, I hold these to be successive apprehensions of a single object which does not change, whereas if I successively experience the different aspects of a boat going downstream, I hold these to be successive apprehensions of an object in the midst of change, so to speak).
Of course, that does not guarantee that when I judge that something belongs to the objective spatio-temporal order it does in fact belong to that order (unity is never given for Kant, but always produced). Nevertheless, the mere fact that there are such principles which allow me to make this distinction opens up the possibility that some judgments are grounded in these principles themselves, instead of being grounded in my experience of something as this or that. Mathematical judgments, for example, are grounded for Kant in the way we apprehend things as being conceptually identical yet still distinct. And some scientific judgments (Kant thought of his own rather Newtonian Metaphysics of Nature) are grounded in way an objective spatio-temporal order is structured in terms of a community of substances reciprocally acting one upon the other. So for Kant there is a middle term being a judgment being grounded purely in terms of conceptual containment (analytic judgments) and a judgment being grounded merely on empirical association (synthetic a posteriori judgments): some judgments are grounded in principles that make an objective spatio-temporal order possible in the first place (synthetic a priori judgments).
That would be Kant's reply, anyway. For better or worse, it is almost universally rejected today, in part because the supposed principles identified by Kant turned out not to be so necessary---Newtonian physics, for instance, was famously displaced by relativity and quantum mechanics. Some (e.g. Michael Friedman) have attempted to salvage something of the Kantian program by blending it with some variety of positivism: the task of the philosopher would be to identify the conceptual structure that underlies our best scientific theories. Myself, I personally think that the increased power in our logic has given us a much better picture of mathematics, which allows us to defend a variety of (structural) platonism: mathematics describes certain structural features of reality, to which we have epistemic access via proof. On the other hand, I think scientific theories (such as relativity) are not in the business of aiming at truth, but merely of empirical adequacy, of providing nice (generally mathematical) models which save the phenomena, so to speak. These are not merely associations because they turn on certain mathematical or structural features of reality.
Comments (55)
So you put six beers in the fridge and see someone take three of them out. You don't know there's three left until you open the fridge door and verify it by looking.
One of the beers might have been pregnant.
Analyticity is related to necessity and a priority. If analytic statements are necessarily true, they are automatically true come what may. If analytic statements are true a priori, they are known without experiential knowledge.
One of the distinctions that philosophers find useful and important is between the word and the thing, sometimes called the signifier and the signified. The convention is that when one wants to talk about the word "beer", one puts it in quotes, and when one wants to talk about the drink beer, one does not. Thus there is a clear difference, beer is a nourishing drink, whereas "beer" is a word.
So now, philosophers of beer can discuss the defining (necessary and sufficient) features of beer, What makes something beer and not a rabbit? Cue much talk of hops, barley malt, fermentation, and the amount of froth on top. Does it have to be liquid, or is a frozen beer still a beer? Are the yeasty dregs at the bottom of the barrel beer? All this talk is talk about what the word "beer" means, about what counts as beer, we are trying to sharpen up those blurry edges of the distinction between beer and not-beer.
So it is the case that(P1.) Fosters is not beer, but the recycled piss of inebriated Australians, and this is a matter of fact, given our shared understanding of what "beer" means. And this is what we call synthetic proposition, because it turns out that Australians also make proper beer that they do not export, but wisely drink themselves.
However, it is based on not only the facts of the case, but also the analytic proposition that (P2.) the recycled piss of inebriated Australians is not beer. This is analytic, because it is not about beer, but about "beer". The facts of the case - that Fosters call their drink "beer", are not decisive, because to most philosophers of beer that is simply an abuse of language.
It is a distinction that seemed to made sense at the time it was hotly discussed, which was the 16th-17th centuries. That was before a modern understanding of logic was developed, which arose in the late 19th to early 20th centuries. That understanding has revealed that the distinction is an illusion - for instance that the statement '7+5=12', which Kant thought was synthetic, is not different in kind from 'all bachelors are unmarried', which Kant thought was analytic. I presume that is one of the reasons why hardly any professional philosophers discuss it any more, other than as a historical phenomenon.
However the distinction is very important historically. It is important because the controversy about it awakened Immanuel Kant from his 'dogmatic slumber' and goaded him to write the Critique of Pure Reason, which is still very relevant, meaningful, and much discussed today. Many see it as one of the most important philosophical works ever written. The bits of CPR about the analytic/synthetic distinction are obsolete and can be skimmed over in favour of those that give real insights, like the Transcendental Aesthetic, the Transcendental Deduction of the Categories and the Synthetic Unity of Apperception. These give difficult, but highly significant, insights into how we think, how we approach the world.
Sure, here is a simple example
analytic: what noise do animals make?
analytic thesis: dogs bark
analytic antithesis: but cats meow
synthesis: different species make different noises.
The precise example of an analytic claim that Kant gave, I believe was "all bodies are extended in space" or something like that. Married bachelors were too simple and obvious for him.
"All blue dogs are dogs." This statement is true in virtue of logical forms. I think this is true a priori.
You're just wrong about this. How many beers are in the fridge is settled by opening the fridge and counting the beers, and the result of this experiment trumps any amount of mathematical and logical reasoning. If there turn out to be 4 beers, then one thought one knew but was mistaken. Perhaps Jesus passed by and turned the milk into beer, perhaps beers can breed, perhaps there was already a beer in the fridge, perhaps a wormhole opened and a beer fell through, or perhaps you miscounted the beers you put in, or the ones taken out, but anyway it is not analytic that there are 3 beers, nor a priori. It is a matter of fact, that might be otherwise.
If you think that amounts to an argument then please, go and have another beer.
These are not arguments, they are examples of explanations one might make if there turn out not to be 3 beers in the fridge. The point is that how many beers are in the fridge is not a priori, it is a contingent fact. What one would not do, however, unless one had had several too many beers, is claim that 6 - 3 = 4, because that is analytic.
Yes, you could be shot dead en route, or have your brain consumed by a parasitic worm, or some of the beers could be turned into beetroot juice by some as yet unknown process. All this is true, and all beside the point.
If you were not capable of knowing basic maths, then you probably couldn't type anything at all, the fact that you can think of anything to say, even if what you're saying is completely meaningless, relies on the fact that you're able to grasp basic truths of grammar, mathematics and the like.
Quoting Hallucinogen
Wikipedia.
In other words, to make a judgement about whether mathematics corresponds with experience, we must first make a mathematical judgement. Otherwise, how would we know that it corresponds? The knowledge of mathematical truths can't rely on, or be explained in terms of, anything else; it is the source of explanations, not the target of explanations.
Quoting unenlightened
The idea that they're 'beers in fridge' is only a rhetorical device to illustrate the fact that 6-3=3 in a rather less boring manner. And that is something that is obviously know a priori - it's simply an example of a tautological truth.
Then we agree. But your rhetoric serves to blur the distinction rather than clarify it. Change the example:
I put 2 rabbits in an empty hutch with some lettuce, and then see my friend take out 5 rabbits. I do not know that there are - 3 rabbits in the hutch, nor have I proved arithmetic wrong, I know they've been breeding. Experience tells me that rabbits multiply and beers only add and subtract.
You only know that because you can count! So you say - ah, five rabbits, they must have multiplied. And you know that, even if you didn't actually see them at it. ;-)
The Kantian method and Hegelian dialectic are considered methods of investigation, so they doesn't really need a justification. Here is the wikipedia reference
https://en.wikipedia.org/wiki/Dialectic#Hegelian_dialectic
The difference was, Kant kept exploring the same subject until he was sure he had the right assertions, whereas Hegel's method was iterative.
In Christian Kerslake’s terms: “Whereas an analytic connection contains its reason solely in the logical explication of the presupposed meaning of a concept, a synthetic connection must involve an extralogical reason. [For Kant,] the concept of a causal relation must be synthetic… [Hence,] Kant’s notion of the synthetic a priori simply names a problem faced by eighteenth-century philosophy – that of how to account for any possible nonlogical a priori connections”.
The second thing to understand then is that the above means that Kant here is dealing with the problem of how to move from the sphere of logic to the sphere of existence. Insofar as analytic statements are those driven by logical necessity, synthetic statements by contrast involve a measure of reality. It is this move from logic to existence that in turn - for example - grounds Kant’s famous response to the cosmological argument: it is not enough to argue - as the cosmological argument more or less does - that God is perfect and that because existence is a perfection He must exist: for this simply begs the question of God’s existence to begin with. Essence - or analyticity - cannot ground existence - which belongs to the order of the synthetic.
So just remember: at stake in the analytic/synthetic distinction is the question of both causality on the one hand, and the move from logic to reality on the other: both of which turn upon the question of logical and extra logical necessity respectively.
What about "all former students are students"?
Shouldn't it read: " all former students were students" the other way round mixes up tenses.
That's the problem with quine's claim that "All blue dogs are dogs" is true by virtue of its logical form, i.e. all X-type Ys are Ys.
Meaning matters.
Where philosophers start to use both together is where they can say interesting and meaningful things.
Of course not. Logical truths depend on logic.
Logical truths are known by studying logic. Logical truths' truths depend on purely logic. You should distinguish what makes statements true from how we know statements.
Apart from specifically Kantian scholarship, modern discussion of the analytical/synthetic owes more to the way these concepts were framed later, when Western analytical philosophy took a logical and linguistic turn. And here the debate is not dead, despite Quine's valiant efforts. The reason, I think, the idea of analytic/synthetic distinction will not go away is that we intuitively feel a categorical difference between groups of statements such as the following:
I.
(1) Some doctors that specialize on eyes are rich.
(2) Some ophthalmologists are rich.
(3) Many bachelors are ophthalmologists.
(4) People who run damage their bodies.
(5) If Holmes killed Sikes, then Watson must be dead.
II.
(6) All doctors that specialize on eyes are doctors.
(7) All ophthalmologists are doctors.
(8) All bachelors are unmarried.
(9) People who run move their bodies.
(10) If Holmes killed Sikes, then Sikes is dead.
(11) If Bob is married to Sue, then Sue is married to Bob.
(12) Anyone who's an ancestor of an ancestor of Bob is an ancestor of Bob.
(13) If x is bigger than y, and y is bigger than z, then x is bigger than z.
(14) If something is red, then it's colored.
Until this distinction is not at least explained away, the work is not done.
The above examples are taken from the SEP article The Analytic/Synthetic Distinction, which offers a comprehensive introduction to the issue.
It seems to me that everything turns out to be a combination of a priori and a posteriori, really, with nothing purely one or the other.
Your brain doesn't actually arrive with anything like propositions fully formed. You need to have experiences and to think about them, while your brain physically develops, to arrive at beliefs, propositions, etc.
And you can't just experience the world. Your brain has to process that experience, and it's going to process it a particular way because of its structure and internal interactions.
If we find that everything that has a heart has kidneys, and everything that has kidneys has a heart, then the two sets, things that have a heart and things that have kidneys, are the same. But is saying something has a heart the same as saying it has kidneys? It doesn't seem like it is. It seems like two different concepts, even though they apply to exactly the same things.
On the other hand, would we have to do research to find that everything that has a heart has a body? How would you search for something that has a heart but no body? (Leaving aside Roy Orbison.) It's already built into the concept "has a heart" that it can only apply to things that have bodies. That's the analytic part. So you can know that the one set is a subset of the other without looking. That's the a priori part.
(a) When reading Kant, it is often useful to take a look at his historical predecessors in order to understand how some of his distinctions are actually tactical maneuvers deployed against positions which he rejected (two books that, incidentally, show the power of such an account for Kant is the classic Kant and the Capacity to Judge, by Longuenesse, and, more relevant to this thread, The poverty of conceptual truth, by R. Lanier Anderson, which is entirely devoted to an elucidation of Kant's distinction between analytic/synthetic). Case in point, Kant considered his analytic/synthetic distinction as a weapon against Wolffian metaphysics. Very roughly, this is the idea:
Wolff and his followers apparently thought that every concept could be positioned in a logical hierarchy, in such a way that immediately above it would be its genus and right below it its species. Thus, we could picture this hierarchy as an upside-down tree, with the most general concept at its root (say, the concept of
The reason is that syntetic sentences, that is, sentences which derive their meaning from experience, must presuppose some analytic definitions to function as 'synthetic' in the first place. Because think in what sense can a sentence said to be 'derivable' from experience: it must mean that there is some general a-priori rule which justifies you in inferring the sentence from a certain experience. Thus the positivists thought that all empirical terms have a fixed meaning or definition (or at least we can construct such definitions for a 'perfect' scientific language). So for example 'cat' is defined via the experience of such and such shapes and colors occurring in a certain configuration; and therefore in the present of such an experience it follows analytically that you are seeing a cat (because this is what the term means). And this is where their famous verification criteria of meaningfulness comes from: every empirical sentences must be connected to experience (empiricism); to be connected to experience is to be verifiable by experience; and to be verifiable is to have an analytic definition - prior to any experience - that tells you which experience should count as the verification of the sentence. Otherwise, if you don't have such definitions that fix the meaning of your empirical terms, then nothing could follow from your experience, no sentence could be ever verified by experience (and hence you wouldn't have empiricsm).
The conclusion is therefore that there cannot be only synthetic sentences, but also analytic which are true independently of experience. And this is also how they thought that science works: you have a theory from which (by virtue of the meaning of the terms it contains, as they have been defined) a set of certain possible observations follow. Then when you go on testing the theory, if the predicted observations obtain, then the theory is verified; if not then it is disproved. And the idea here is the dame: unless theory and observation are connected by definitions, no observations could follow (deductively or inductively) from any theory, and there will be no way to test it experimentally, in which case science would be impossible.
And as a historical sidenote, it is important to note that though Quine famously attacked the analytic/synthetic distinction, what he was primarily concerned with is the positivists' conception of the 'meaning' of sentences (this is why he talks so much about synonimity in "two dogmas"); however, he himself didn't reject the distinction (which was central to the positivsts as well) between theory and observation, but only claimed that they are mutually interdependent, and that observation cannot verify or disprove individual sentences, but whole theories (and maybe the whole body of science). And so according to Quine, the way experience is connected to our body of beliefs is not via "definitions" but whole theories or world views ("conceptual schemes"), but it still retains the same idea that our experience is mediated by logical connections which themselves are prior to experience.
Analytic statements are true by definition, synthetic a priori statements are true not by definition, but because they are self-evident; we do not need to check empirical conditions in order to confirm either, but the latter are not true merely by definition, that is the main point. This distinction is a perfectly valid and useful one, as far as I can tell.
I'm glad you found my reply useful.
Quoting Hallucinogen
Well, the whole point of the first Critique is to argue against this idea, that is, to argue that there re synthetic claims which are not grounded merely on empirical association. Kant's argument here (which comprises the entire Transcendental Analytic) is notoriously complex (I myself don't fully understand it---I don't know if anybody does), but the gist of it is that our consciousness of ourselves as abiding (i.e. our consciousness of our own identity throughout time) requires certain conditions which allow us to distinguish between (to use Strawson's turn of phrase) the subjective route of our experiences and the objective world through which it is a route. This distinction in its turn is grounded on certain principles which allows us to distinguish our subjective spatio-temporal order and the objective order of the world (for instance, to use Kant's own example, when I successively experience the different aspects of a house, I hold these to be successive apprehensions of a single object which does not change, whereas if I successively experience the different aspects of a boat going downstream, I hold these to be successive apprehensions of an object in the midst of change, so to speak).
Of course, that does not guarantee that when I judge that something belongs to the objective spatio-temporal order it does in fact belong to that order (unity is never given for Kant, but always produced). Nevertheless, the mere fact that there are such principles which allow me to make this distinction opens up the possibility that some judgments are grounded in these principles themselves, instead of being grounded in my experience of something as this or that. Mathematical judgments, for example, are grounded for Kant in the way we apprehend things as being conceptually identical yet still distinct. And some scientific judgments (Kant thought of his own rather Newtonian Metaphysics of Nature) are grounded in way an objective spatio-temporal order is structured in terms of a community of substances reciprocally acting one upon the other. So for Kant there is a middle term being a judgment being grounded purely in terms of conceptual containment (analytic judgments) and a judgment being grounded merely on empirical association (synthetic a posteriori judgments): some judgments are grounded in principles that make an objective spatio-temporal order possible in the first place (synthetic a priori judgments).
That would be Kant's reply, anyway. For better or worse, it is almost universally rejected today, in part because the supposed principles identified by Kant turned out not to be so necessary---Newtonian physics, for instance, was famously displaced by relativity and quantum mechanics. Some (e.g. Michael Friedman) have attempted to salvage something of the Kantian program by blending it with some variety of positivism: the task of the philosopher would be to identify the conceptual structure that underlies our best scientific theories. Myself, I personally think that the increased power in our logic has given us a much better picture of mathematics, which allows us to defend a variety of (structural) platonism: mathematics describes certain structural features of reality, to which we have epistemic access via proof. On the other hand, I think scientific theories (such as relativity) are not in the business of aiming at truth, but merely of empirical adequacy, of providing nice (generally mathematical) models which save the phenomena, so to speak. These are not merely associations because they turn on certain mathematical or structural features of reality.