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[Londoner]

And besides, you didn't addressed the argument I put forward for this claim. Do you deny the fact that if I draw an accurate circle then I can know a priori that the ratio between it's radius and circumference will be very close to pi?

Yes. You as me to beg your own question by saying it is an 'accurate circle', by which you mean a circle in geometry i.e an unreal circle. The more your claim is true, the less 'real' your circle would be. If your claim was entirely true, the circle would be completely unreal.

I might as well say I could paint something 'white', in which case it will have (to some degree) a quality of 'whiteness', thus the names of colours like 'white' also provide 'a priori' knowledge of the world. 'Mammal' describes all creatures that have mammalian features; I can declare I know for a fact that all mammalian creatures will have mammalian features; does this make the word 'mammal' - and every categorical description - an example of 'synthetic a priori' knowledge?

Perhaps, for you, it does. In which case I can only say that it isn't what is usually understood by the term.

And nor does it fit with your own earlier definition. To know that something is circular or white or mammalian you have to use your senses; to use those terms about an object is to communicate the sensory information another person might expect. But in your definition of 'synthetic a priori' knowledge you declared that such knowledge should be independent of experience.

The question is ambiguous. In one sense, there are triangles in the world, every kid can draw one on a piece paper. And then there are the geometrical abstract notion of a triangle which is an idealized way of describing the necessary properties of spatial objects, like a triangle on a page. And who knows, maybe it's possible for a perfect triangle to exist in the actual physical space, or at least there could've been a different physics that would allow the existence of such objects.

If we could first find that 'synthetic a priori' then it might be able to go on and argue for such a metaphysics, but we can't rest a 'synthetic a priori' claim itself on a 'maybe' or 'could've'!

[Fafner88]

Yes. You as me to beg your own question by saying it is an 'accurate circle', by which you mean a circle in geometry i.e an unreal circle. The more your claim is true, the less 'real' your circle would be. If your claim was entirely true, the circle would be completely unreal.

It doesn't matter how you call it. The question is, can I know very accurate information about the thing that I've drawn on the page without measuring it, yes or no?

I might as well say I could paint something 'white', in which case it will have (to some degree) a quality of 'whiteness', thus the names of colours like 'white' also provide 'a priori' knowledge of the world.

What does it mean to say "the names of colours like 'white' provide 'a priori' knowledge"? Names can't provide knowledge, one can know only propositions, not names.

'Mammal' describes all creatures that have mammalian features; I can declare I know for a fact that all mammalian creatures will have mammalian features; does this make the word 'mammal' - and every categorical description - an example of 'synthetic a priori' knowledge?

No, it's not synthetic a priori, "all mammals are mammals" is analytic, so again it's an irrelevant example.

And a word can't be knowledge, you can know only propositions because words by themselves don't say anything, so the question about the word 'mammal' being synthetic a priori doesn't make sense. You must make the distinctions between a word, its reference, a concept, and a proposition, and the question of a priori knowledge (or knowledge of any kind) can arise only regarding propositions. This is what I meant by confusions about language.

And nor does it fit with your own earlier definition. To know that something is circular or white or mammalian you have to use your senses; to use those terms about an object is to communicate the sensory information another person might expect. But in your definition of 'synthetic a priori' knowledge you declared that such knowledge should be independent of experience.

No, this is not what I say, I don't say that one can know that something is a circle a priori without looking, what I claim is that given that one already knows that something is a circle, then one can also know a priori different properties of that circle.

[Londoner]

Fafner

It doesn't matter how you call it. The question is, can I know very accurate information about the thing that I've drawn on the page without measuring it, yes or no?

No. At the very least you need to use your senses to determine that there exists a drawn object that resembles a circle. Unlike a geometric circle which is an abstraction which need not exist in fact (and doesn't). And when you say 'very accurate information' you mean 'slightly inaccurate'.

What does it mean to say "the names of colours like 'white' provide 'a priori' knowledge"? Names can't provide knowledge, one can know only propositions, not names.

If naming something a 'circle' is a proposition about its shape, why isn't naming it 'white' a proposition about its colour? Either or neither!

You say a round-object will have similar characteristics to an abstract shape; I say a white-object will have similar characteristics to the abstract quality white. Of course it will also differ from that abstract quality, since white only describes a colour but any white-object must be other than pure colour, but say you do not consider the differences to be significant, as long as the object has being somewhat round/white as one of its qualities. Again, either or neither.

You must make the distinctions between a word, its reference, a concept, and a proposition, and the question of a priori knowledge (or knowledge of any kind) can arise only regarding propositions. This is what I meant by confusions about language.

I think I do. For example I distinguish between propositions about geometry from those about real objects. As to the way in which our words and concepts might reference real world objects, that is the thing we are discussing.

But let me suggest an alternative. You argue that real things can resemble abstractions. And that abstractions can give us 'synthetic a priori' knowledge. But since real things are always imperfect copies of the abstractions, surely the 'synthetic a priori' knowledge is only perfectly realised in the abstraction.

In that case, why shouldn't the term 'synthetic a priori' be one that applies to the abstractions? We can simply accept that it is the nature of real objects to be something like 'imperfect copies' of the ideal objects that we access through reason.

I'm not suggesting anything at all original here. I'm pointing out a well-used slip road that will feed us back into the philosophical highway.

[Luisgmarquez1985]

when it comes to this I am ultimately Kantian. we have a priori knowledge because we have certain categories in which we are born with in order to analysis things and bring out the information. Yet at the same time, we need the external world to experience knowledge posteriori. in my view we need both a priori and posteriori. a priori knowledge is not possible if there is nothing from which we can gain experience from something 'out there'. Even your example Scott of an analytic proposition that states, "all bachelors are unmarried" has to be derived from an external experience where we can find all bachelor's are indeed unmarried. at the sometime, we cannot experience knowledge posteriori without an inner mechanism from which to draw information from external objects.

also with Kant, we can only gain knowledge from things that we can experience. Anything that we cannot experience we cannot draw knowledge from, only have faith or beliefs about it. the best example of this is God.

[Fafner88]

No. At the very least you need to use your senses to determine that there exists a drawn object that resembles a circle. Unlike a geometric circle which is an abstraction which need not exist in fact (and doesn't). And when you say 'very accurate information' you mean 'slightly inaccurate'.

Again, forget about how you call it, can one know in advance that the ratio between the diameter and circumference of this thing http://bestclipartblog.com/clipart-pics ... -art-6.jpg will be about 3.14 ant not 1 or 374, yes or no? If you don't believe me, just measure it yourself, and see if my prediction is correct.

If naming something a 'circle' is a proposition about its shape, why isn't naming it 'white' a proposition about its colour? Either or neither!

Naming something is not a proposition, what does it even mean? Shape recognition is not naming, I don't understand you.

You say a round-object will have similar characteristics to an abstract shape; I say a white-object will have similar characteristics to the abstract quality white. Of course it will also differ from that abstract quality, since white only describes a colour but any white-object must be other than pure colour, but say you do not consider the differences to be significant, as long as the object has being somewhat round/white as one of its qualities. Again, either or neither.

I don't understand what's the objection here. As I explained, I don't claim that someone can know that something is circular a priori just as no one can know that something is white a priori, but once someone knows that an object is circular, then he can know a priori empirical facts about that object, whereas knowing that something's white doesn't give you this kind of knowledge, only some analytic knowledge (that it's a colored object for example.

But let me suggest an alternative. You argue that real things can resemble abstractions. And that abstractions can give us 'synthetic a priori' knowledge. But since real things are always imperfect copies of the abstractions, surely the 'synthetic a priori' knowledge is only perfectly realised in the abstraction.

I don't understand what "perfect/imperfect realization of knowledge" is supposed to be.

In that case, why shouldn't the term 'synthetic a priori' be one that applies to the abstractions? We can simply accept that it is the nature of real objects to be something like 'imperfect copies' of the ideal objects that we access through reason.

I'm not a Platonist therefore I don't believe there are 'perfect objects' which physical things are 'copies of'. But we don't have to decide on this issue right now, I only want to defend the claim that this abstract knowledge of geometry, whatever it is, allows you to know empirical facts about the physical reality, and hence geometry must be synthetic and not analytic.

[Daviddunn]

Naming something is not a proposition, what does it even mean? Shape recognition is not naming, I don't understand you.

Londoner is a real genius. Reading his/her post is pure logical symphony. I call him/her the Roger Federer of philosophy. Carry on. One must pay a lot of attention to understand.

[Londoner]

Fafner

Naming something is not a proposition, what does it even mean? Shape recognition is not naming, I don't understand you.

Why is this activity called 'shape recognition' one thing, but 'colour recognition' something else? I'm afraid the failure to understand is mutual.

As I explained, I don't claim that someone can know that something is circular a priori just as no one can know that something is white a priori, but once someone knows that an object is circular, then he can know a priori empirical facts about that object,...

And how did you come to know that object was circular, if not by looking at it and/or measuring it? In that case your knowledge that it is circular is not a priori but empirical.

You know stuff about circles, a priori. You can discover stuff empirically. But you cannot glue the two together and make one 'synthetic a priori'.

I don't understand what "perfect/imperfect realization of knowledge" is supposed to be.

In this case, it is that any physical object can only be an imperfect realisation of a geometric concept.

I'm not a Platonist therefore I don't believe there are 'perfect objects' which physical things are 'copies of'.

I said 'ideal objects'- such as shapes that are ideal because they only exist in two dimensions. But if you agree that such things cannot be copied in the form of objects, then surely you must take my point that what is true of those ideal forms will not be true of the faulty copies?

Again, we are chasing the same points, so I will summarise by saying that I don't think geometry reveals synthetic a priori knowledge because (a) it is not 'a priori' - the information about the physical object must be found through our senses and (b) it is not 'knowledge' because it isn't ever true.

I can see I will not convince you, so I will take a break, saying again that I suggest you look at other philosophical attempts to discuss this topic. Why have they not seen what you take to be so obvious?

http://plato.stanford.edu/entries/analytic-synthetic/

Daviddun says some kind things. But probably the reason I can rabbit on about all this is because before I went to university I carefully read the once trendy but now largely forgotten 'logical positivist' book 'Language, Truth and Logic' by A.J.Ayer. It was a lucky choice as it grounded me in a lot of the ideas and terminology that were to come up later. Does anyone else know it? There is a good entry for it in the well known online encyclopedia (that this site won't let us link to) or you can find the whole thing in pdf.

[Logic_ill]

In this thread I want us to debate whether a priori knowledge is possible. Some philosophers argue that some knowledge is a priori (fully independent from experience). In contrast, radical empiricists argue that all knowledge is a posteriori (derived from experience). Immanuel Kant made the distinction between analytic a priori knowledge and synthetic a priori knowledge. (An analytic proposition is one whose predicate concept is contained in its subject concept, such as "All bachelors are unmarried." And a synthetic proposition is one whose predicate concept is NOT contained in its subject, such as "All bachelors are happy.")

What do you think? Do you think a priori knowledge is possible or not? Why?

I think the answer depends greatly on how we define knowledge and experience.

If knowledge refers to the act of knowing, which requires a conscious being to perform the act, then I believe all knowledge depends on experience in some ways simply because the conscious being itself cannot exist without experience-gained data. In regards to the claim that a conscious being cannot exist without experience-gained data, I believe a functioning conscious being, namely a human or similar animal, is created through experiences that hard-wire it with certain instincts, beliefs, etc. Even before birth, a human baby's brain is experiencing developments as a result of experiences that happened to its mother and evolutionarily-gained traits through experiences that happen to its ancestors over time. But of course all those statements rely on the definition of experience and what is and is not experience.

Anyway, what do you think?

I would ask the philosophers who believe that some a priori knowledge is possible to give examples, Perhaps I'm missing something, but I think it's all a posteriori...

[Fafner88]

Why is this activity called 'shape recognition' one thing, but 'colour recognition' something else? I'm afraid the failure to understand is mutual.

I didn't say they are different.

And how did you come to know that object was circular, if not by looking at it and/or measuring it? In that case your knowledge that it is circular is not a priori but empirical.

I said it a hundred times already, what's known a priori is not whether some object is circular, but some other empirical properties of the object given that it was correctly recognized as a circle and not a triangle or whatever (that you can't know a priori).

Contrast it with a case of empirical knowledge: suppose that you know that Felix is a cat, can you also know that he has a tail solely on the basis of this information? No, because for all you know he might've lost his tail. Now suppose that you see a very symmetrical circle (like in the picture I linked), can you know that its ratio is going to be very close to pi without calculating? The obvious answer is yes, this is something that every kid learns at school. If knowing accurately without calculation a ratio of a physical object is not synthetic a priori knowledge then I don't know what 'synthetic a priori' is supposed to mean on your view.

You know stuff about circles, a priori. You can discover stuff empirically. But you cannot glue the two together and make one 'synthetic a priori'.

Why not? Since Kripke some philosophers even think that there can be contingent a priori knowledge.

it is not 'knowledge' because it isn't ever true.

Not true what? Do you deny that all the symmetrically round objects in the world have a very close ratio to pi?

Daviddun says some kind things. But probably the reason I can rabbit on about all this is because before I went to university I carefully read the once trendy but now largely forgotten 'logical positivist' book 'Language, Truth and Logic' by A.J.Ayer. It was a lucky choice as it grounded me in a lot of the ideas and terminology that were to come up later. Does anyone else know it? There is a good entry for it in the well known online encyclopedia (that this site won't let us link to) or you can find the whole thing in pdf.

The argument of Quine that I've presented earlier was aimed specifically against the doctrine of A.J Ayer, and it was one of the arguments that persuaded philosophers that logical positivism is false. So it is recommended to read some criticisms of Ayer's views because almost no philosopher accepts them today. One good book will be "Philosophical Analysis in the Twentieth Century" by Scott Soames (the chapters about Ayer and Quine).

[Wayne92587]

Fafner88, I was simply responding to Woody's Dragon example.

[Fafner88]

Fafner88, I was simply responding to Woody's Dragon example.

Oh I'm sorry, I thought the post was addressed to me.

[Bohm2]

I would ask the philosophers who believe that some a priori knowledge is possible to give examples, Perhaps I'm missing something, but I think it's all a posteriori...

I'm not a philosopher as my background is in sciences but how about our knowlege in language? Consider the 'Poverty of stimulus' argument with respect the way children attain lingustic knowledge:

A central goal of modern generative grammar has been to discover invariant properties of human languages that reflect ‘‘the innate schematism of mind that is applied to the data of experience’’ and that ‘‘might reasonably be attributed to the organism itself as its contribution to the task of the acquisition of knowledge’’ (Chomsky, 1971). Candidates for such invariances include the structure dependenceof grammatical rules, and in particular, certain constraints on question formation. Various ‘‘poverty of stimulus’’ (POS) arguments suggest that these invariances reflect an innate human endowment, as opposed to common experience: Various ‘‘poverty of stimulus’’ (POS) arguments suggest that these invariances reflect an innate human endowment, as opposed to common experience...In our view, the way forward begins with the recognition that environmental stimuli radically underdetermine developmental outcomes, and that grammar acquisition is a case in point. Then one can try to describe the gap between experience and linguistic knowledge attained, reduce that gap to basic principles that reflect the least language-specific innate endowment that does justice to the attained knowledge, and thereby help characterize the true role of experience in a manner that illuminates cognition.

Poverty of the Stimulus Revisited
http://isites.harvard.edu/fs/docs/icb.t ... isited.pdf

[Daviddunn]

Again, forget about how you call it, can one know in advance that the ratio between the diameter and circumference ofthis thing http://bestclipartblog.com/clipart-pics ... -art-6.jpg will be about 3.14 ant not 1 or 374, yes or no? If you don't believe me, just measure it yourself, and see if my prediction is correct.

The ratio of the circumference to the diameter being pi, holds under the presupposition of euclidean space. In curved space it does not hold. The value of pi changes in curved space. Experience seems to be necessary to verify the proposition c/d=3.14

[Fafner88]

Again, forget about how you call it, can one know in advance that the ratio between the diameter and circumference ofthis thing http://bestclipartblog.com/clipart-pics ... -art-6.jpg will be about 3.14 ant not 1 or 374, yes or no? If you don't believe me, just measure it yourself, and see if my prediction is correct.

The ratio of the circumference to the diameter being pi, holds under the presupposition of euclidean space. In curved space it does not hold. The value of pi changes in curved space. Experience seems to be necessary to verify the proposition c/d=3.14

Can you detect the curvature of space on your monitor with a ruler? It's irrelevant to my argument because I was talking about approximations anyway.

And then one can construct the same argument about a priori knowledge of the non-euclidean properties of space.

[Daviddunn]

Can you detect the curvature of space on your monitor with a ruler? 

The ratio C/d is constant, regardless of the circle's size. For example, if a circle has twice the diameter of another circle it will also have twice the circumference, preserving the ratio C/d. This definition of π implicitly makes use of flat (Euclidean) geometry; although the notion of a circle can be extended to any curved (non-Euclidean) geometry, these new circles will no longer satisfy the formula π =C/d.[3] There are also other definitions of π that do not immediately involve circles at all. For example, π is twice the smallest positive x for which cos(x) equals 0.[3][4]

Basic science skills: if c/d not equal to pi, something is happening! Curvature of space?? Hmm, could be.