Philosophy Discussion Forums

Posted: **May 23rd, 2014, 6:44 am**

Consul

As for the question of convincing examples, there are doubtless numerous convincing examples of analytic knowledge a priori at least...

What about convincing examples of synthetic knowledge a priori? Well, it turned out that such examples are very hard to come by....

I don't know why you are telling me this; that was my point, except that rather than examples of 'synthetic knowledge a priori' being hard to come by, I don't know of any. Unless you mean something different by 'synthetic a priori' ...see below.

I thought we were discussing the argument quoted in post 199.

"Synthetic knowledge" is not synonymous with "empirical/a posteriori" knowledge...

Again, surely that was what I had just pointed out. I am pleased we agree, but I don't see where the argument is directed. As for your distinctions between 'a priori', 'analytic' and the rest, it is no good insisting on such definitions in an argument where some of the participants deny that that a priori/a posteriori or an analytic/synthetic distinction exists at all! Again, I make the point that although you may agree with those definitions - and you may have excellent arguments for doing so - the subject in this case is what 'empiricists' think.

For the empiricists and the rationalists do understand their own and their opponents' position sufficiently well.

It isn't like two football teams. We can try to lump together groups of philosophers, saying 'they seem to have certain ideas in common', but it doesn't follow they must share the same position. For example, they may reach similar conclusions via quite different - and contradictory - arguments. They will agree in one area but differ in another.

So why not be specific? Which philosopher do you think is both an empiricist and would agree that their assertion 'there are no synthetic a prioris' is to give an example of a synthetic a priori'? I think that as soon as we even consider linking that simplistic claim to the depth of arguments deployed by somebody like Russell we will realise we are way out of our depth.

There is a difference between claiming that the truth of a synthetic proposition is not strictly knowable a priori, and claiming that there can be no belief-justifying a priori evidence for the truth of synthetic propositions. That is, there is a difference between saying that synthetic propositions cannot be known to be true in a non-empirical way and saying that they cannot even be justifiably believed to be true in a non-empirical way, in the sense that there cannot be any non-empirical evidence for their truth, be it conclusive or inconclusive.

'Justifiable belief', 'not strictly knowable' etc. won't cut it. We have no end of things that can pass that test. What empiricist, or anyone else, would claim that we can't - or don't - have justified (though inconclusively) beliefs?

The reason we are interested in a 'synthetic a priori' in the sense referred to in your quote is that it would represent knowledge about how the world is, yet knowledge that is not subject to the Cartesian doubt that goes with sensory experience.

Certainly, if you want 'synthetic a priori' to mean something else, then you can. There is nothing to stop you! After all, Kant had a quite alternative understanding of it. But then, if you allow that there might be alternative understandings of 'synthetic a priori', how does that fit with the enormous generalisations about what those 'empiricists' believe to be 'true'! Why aren't they allowed similar subtleties of argument? If the claim is reduced to something like 'empiricists think they have a justifiable belief in thinking that you can't have a justifiable belief', then yes; they would be very silly, but is that really what we think they are saying?

But these side arguments about 'empiricists' or their 'justifiable beliefs' are just smoke and mirrors. Let us return to the quote (post 199):

'Consider empiricists who claim to know this to be true: 'There is no synthetic a priori knowledge.'

Look at that poor tortured language! In the opening sentence, the subject seems to be 'empiricists'. We then have the curious and clumsy construction 'who claim to know this is true'. Then the statement 'There is no synthetic a priori knowledge.'

By constructing it in this convoluted way, it creates a confusion of subject. Is we saying it is 'true' that empiricists think this way? Or that what they think is 'true'?

This confusion carries on the the end. 'So the empiricists' claim would be synthetic a priori knowledge—the very thing it rejects." Once again; are we saying that the empiricists' state of mind on the issue is 'synthetic a priori' knowledge. Well - obviously it isn't. So why keep bringing them in?

Instead, let's cut out all that verbiage about the mental state of those empiricists and just stick to the 'synthetic a priori'

Would the existence of a 'synthetic a priori' be an example of a 'synthetic a priori'? Yes, it would.

Would the non-existence of a 'synthetic a priori' be an example of a 'synthetic a priori'? No, it wouldn't.

Posted: **May 23rd, 2014, 8:55 am**

Londoner wrote:Consul…

Please include my member name in each quote box containing statements of mine (even if you quote me more than once in the same post)! That is, not

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but

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Posted: **May 23rd, 2014, 2:14 pm**

Think of Priori Knowledge as being Proprietary Knowledge.

Posted: **May 23rd, 2014, 2:53 pm**

Londoner wrote:
Consul wrote:What about convincing examples of synthetic knowledge a priori? Well, it turned out that such examples are very hard to come by....

I don't know why you are telling me this; that was my point, except that rather than examples of 'synthetic knowledge a priori' being hard to come by, I don't know of any.

I presented (what I think are) two examples in my previous post:
* "Dogs aren't numbers."
* "Holes don't have holes."
Two more:
* "Coloured things are extended."
* "Three-legged tables don't wobble."

Can you transform these into explicit logical truths and thereby show that they are analytic rather than synthetic?

Londoner wrote:As for your distinctions between 'a priori', 'analytic' and the rest, it is no good insisting on such definitions in an argument where some of the participants deny that that a priori/a posteriori or an analytic/synthetic distinction exists at all! Again, I make the point that although you may agree with those definitions - and you may have excellent arguments for doing so - the subject in this case is what 'empiricists' think.

As for the a priori/a posteriori distinction, I don't know any philosophers who reject it as ill-defined (do you?); but there are quite a few philosophers (Quine being the most famous) who reject the analytic/synthetic distinction as ill-defined. If it is, then the distinction between moderate and radical empiricism collapses, and empiricism is simply the view that experience is the only source of our knowledge. And then one can soundly argue again that this very proposition is itself not empirically knowable, so that if empiricism is true, it cannot be known to be true.

Londoner wrote:It isn't like two football teams. We can try to lump together groups of philosophers, saying 'they seem to have certain ideas in common', but it doesn't follow they must share the same position. For example, they may reach similar conclusions via quite different - and contradictory - arguments. They will agree in one area but differ in another.

I know that disagreement is ubiquitous in philosophy.

Londoner wrote:So why not be specific? Which philosopher do you think is both an empiricist and would agree that their assertion 'there are no synthetic a prioris' is to give an example of a synthetic a priori'? I think that as soon as we even consider linking that simplistic claim to the depth of arguments deployed by somebody like Russell we will realise we are way out of our depth.

Let me put it this way: I don't know any philosophers who assert that the statement "There is no synthetic a priori knowledge" is analytic and knowable a priori, or that it is synthetic and knowable a posteriori. They all seem to see that such an assertion would be indefensible.

"If empiricism is true, it cannot be known to be true. According to empiricism, all evidence is perceptual evidence. But it cannot be known through perception that perception is a source of knowledge. Witnesses cannot self-corroborate.
One perception can surely provide support for one another. I can have a tactile perception that confirms a visual perception. While establishing the veridicality of my visual perception relative to the assumption that my tactile assumption is correct, this does nothing to justify the presumption that perception is a source of knowledge.
That presumption can be justified, but not on strictly empirical grounds, The justification for it is indirect. We must first establish that an operation known as 'inductive inference' yields knowledge.
Suggestively, inductive inference is another casualty of empiricism a source of knowledge that empiricism claims not to be a source of knowledge. The same empiricist strictures that invalidate inductive inference are those that invalidate perception, and the very arguments that re-validate the one re-validate the other. The belief that there is an external world is itself known through inductive inference: hence the points just made."

(Kuczynski, John-Michael. Empiricism and the Foundations of Psychology. Philadelphia, PA: John Benjamins, 2012. p. 243)

"…what I shall call 'the empiricist hypothesis', namely that what we know without inference consists solely of what we have experienced (or, more strictly, what we are experiencing) together with the principles of deductive logic. But we cannot know the empiricist hypothesis to be true, since that would be knowledge of a sort that the hypothesis itself condemns. This does not prove the hypothesis to be false, but it does prove that we have no right to assert it. Empiricism may be a true philosophy, but if it is it cannot be known to be true; those who assert that they know it to be true contradict themselves."

(Russell, Bertrand. Human Knowledge: Its Scope and Limits. 1948. Reprint, Abingdon: Routledge, 2009. p. 161)

"EMPIRICISM, RUSSELL ON. Empiricism is a school of thought represented in Great Britain in the writings of John Locke, George Berkeley, and David Hume. It is the view that knowledge is entirely derived from sense-experience, or more exactly, from sensation and introspection, and that ideas are built up out of sensations and introspected experiences according to psychological laws of the association of ideas. Claims that purport to go beyond what can be experienced are rejected by empiricists as falsely metaphysical and meaningless. Likewise, empiricists reject the realist assertion of the extra-mental reality of universals, seeing these as produced by a psychological ability to abstract general ideas from the experience of particular instances.

Empiricists hold that what we experience are not things but our ideas or sensations caused by things, and it follows from their epistemology that knowledge is representational, and that a proposition, by consisting of ideas, is a mental representation of what is real. If what we know are our own ideas, it is not clear how there can be knowledge of the external world, that is, the world outside the mind, or whether anything exists apart from and corresponding to our
ideas. As a result, despite its emphasis on sense-experience, empiricism gives rise to various forms of idealism, the doctrine that what are ultimately real are not things, but ideas.

In The Principles of Mathematics (1903), Russell opposes empiricism largely on metaphysical grounds. For example, he rejects Ernst Mach’s view that propositions about the universe being other than it is can have no meaning, since no other universe exists. Such a view unduly confines propositions to what is in existence, according to Russell; in his nonempiricist conception, propositions are complex objects that either exist and are true or subsist and are false. This doctrine does justice, he thinks, to the fact that what we know are things, not our ideas of them; hence it allows for direct, nonrepresentational knowledge of the world. Russell’s insistence on the reality of universals is also nonempiricist.

In A History of Western Philosophy (1945), Russell is sympathetic to the empiricist contention that all human knowledge is uncertain, inexact, and partial. Yet he views the claim that all knowledge is derived from experience as inadequate to a theory of knowledge, even if less so than any other philosophy. Against empiricism, he thinks it necessary for the very possibility of objective knowledge to permit knowledge to rest in part on nonempirical, unverifiable propositions. For instance, principles of inductive inference cannot be justified inductively from experience—such an argument would be circular—so they must be accepted without justification. Empiricism itself must thus rest on nonempirical propositions, so the chief inadequacy of empiricism, he says, is that it is self-refuting. Since empiricism must thus accept one principle without empirical justification, a critic may wonder on what grounds other nonempirical principles are excluded. Russell is therefore willing to accept induction as involving a nonempirical logical principle, since without it, science is impossible.

Despite his discontent with it, Russell’s work is in many ways congenial to empiricism, or to that part of it that consists in establishing that knowledge derives from direct experience according to certain logical rules. In works like Our Knowledge of the External World (1914), 'The Relation of Sense-Data to Physics' (1914), Analysis of Matter (1927), and Human Knowledge: Its Scope and Limits (1948), Russell attempts to ground knowledge in experience of sense data by employing a technique of logical construction that defines suppositious entities in terms of those sense data. And in the 1930s and 1940s, his study of how certain extra-linguistic experiences give rise to linguistic ones (e.g., how the sight of butter causes someone to assert ‘this is butter’) is compatible with empiricism as a claim about the basis of knowledge.

Though Russell’s middle and late work is therefore empiricist in regard to method and in holding that experience is the ultimate basis of knowledge, he remains a realist with respect to universals and a rationalist in his belief that some general propositions must be known independently of experience. Moreover, in the 1940s, even as Russell defends the study of language as an empirical phenomenon, he is increasingly hostile toward Rudolf Carnap’s work and logical positivism, in part for dismissing talk about the world as metaphysical nonsense, not a subject of legitimate philosophical study. In this regard, even Russell’s late work is unabashed in making the kind of metaphysical utterances antithetic to empiricism and logical positivism."

(Carey, Rosalind, and John Ongley. Historical Dictionary of Bertrand Russell's Philosophy. Lanham, MD: Scarecrow Press, 2009. pp. 62-4)

Londoner wrote:What empiricist, or anyone else, would claim that we can't - or don't - have justified (though inconclusively) beliefs?

Radical skeptics do.

Londoner wrote:The reason we are interested in a 'synthetic a priori' in the sense referred to in your quote is that it would represent knowledge about how the world is, yet knowledge that is not subject to the Cartesian doubt that goes with sensory experience.

The rationalist belief in synthetic knowledge a priori doesn't entail the belief in its infallibility! That is, it's one thing to say that rational intuition is a source of knowledge (and belief-justification), and another to say that rational intuition is infallible. Moderate rationalists do not maintain it is.

"To insist that a priori justification requires a genuine rational insight…would make it impossible to tell whether a given claim was justified in this way or not without knowing independently whether or not the claim of necessity was correct—thus making the appeal to rational insight entirely useless as an independent and self-contained basis for justification. Thus, I suggest, a moderate rationalism that abandons the indefensible claim of infallibility should hold instead that, subject to certain further conditions…, it is apparent rational insight (and, correlatively, apparent self-evidence) that provides the basis for a priori epistemic justification. Such justification will thus, in common with all or virtually all other kinds of justification, be fallible, since it will be possible that the apparent insight that justifies a particular claim is not genuine. The moderate rationalist's main thesis is that such an apparent insight still yields a reason, albeit a fallible one, for thinking that the proposition in question is true."

(BonJour, Laurence. In Defense of Pure Reason: A Rationalist Account of A Priori Justification. Cambridge: Cambridge University Press, 1998. p. 113)

Londoner wrote:Certainly, if you want 'synthetic a priori' to mean something else, then you can. There is nothing to stop you! After all, Kant had a quite alternative understanding of it. But then, if you allow that there might be alternative understandings of 'synthetic a priori', how does that fit with the enormous generalisations about what those 'empiricists' believe to be 'true'!

What alternative understandings of "synthetic a priori" are there?

Londoner wrote:But these side arguments about 'empiricists' or their 'justifiable beliefs' are just smoke and mirrors. Let us return to the quote (post 199):
'Consider empiricists who claim to know this to be true: 'There is no synthetic a priori knowledge.'
Look at that poor tortured language! In the opening sentence, the subject seems to be 'empiricists'. We then have the curious and clumsy construction 'who claim to know this is true'. Then the statement 'There is no synthetic a priori knowledge.'
By constructing it in this convoluted way, it creates a confusion of subject. Is we saying it is 'true' that empiricists think this way? Or that what they think is 'true'?
This confusion carries on the the end. 'So the empiricists' claim would be synthetic a priori knowledge—the very thing it rejects." Once again; are we saying that the empiricists' state of mind on the issue is 'synthetic a priori' knowledge. Well - obviously it isn't. So why keep bringing them in?

Now you're confusing me. As I showed you, there's a sound argument to the effect that empiricists cannot non-self-contradictorily claim to know that empiricism is true—full stop.

Londoner wrote:Instead, let's cut out all that verbiage about the mental state of those empiricists and just stick to the 'synthetic a priori'
Would the existence of a 'synthetic a priori' be an example of a 'synthetic a priori'? Yes, it would.
Would the non-existence of a 'synthetic a priori' be an example of a 'synthetic a priori'? No, it wouldn't.

Again, the point is that if, as the empiricists claim, all synthetic knowledge is grounded in experience, they cannot know and therefore cannot justifiably claim to know that this is true, because this knowledge claim would go beyond what is empirically justifiable.

Posted: **May 23rd, 2014, 6:03 pm**

Consul wrote: I presented (what I think are) two examples in my previous post:
* "Dogs aren't numbers."
* "Holes don't have holes."
Two more:
* "Coloured things are extended."
* "Three-legged tables don't wobble."

Can you transform these into explicit logical truths and thereby show that they are analytic rather than synthetic?

(Note: all further quotes are also yours.)

It is hard to tell what any of them mean because they are too brief. This makes writing out explanations tiresome because I would have to give several alternatives in the attempt to guess your meaning. To take the first as an example, if you are saying that the word we use to describe four legged animals is a different word to that which we use to describe the abstract quality of quantity, then I would say that this is an observation about the meaning of words. But you might have something else in mind.

'Holes don't have holes' doesn't make sense because our understanding of 'hole' is that it represents a void in a thing, and a void isn't a thing. But again, you might have your own understanding of what 'hole' means.

'Two more' lacks a subject.

'Three legged tables don't wobble' might be a generalisation made from observation, in which case it is subject to the same sort of doubt as all such generalisations involving induction and arising from experience.

Now, having written all that, if you wish to call them 'synthetic a priori' propositions then fine. But if those were examples of 'synthetic a priori propositions' as referred to in your quote, why do you think all those empiricist philosophers, who you must admit seem to be reasonably thoughtful persons, could think such things don't exist when you have no problem coming up with so many examples?

It seems to me that either these philosophers were very stupid - or they had something different in mind.

(I don't know why you feel it is relevant to add all the stuff about the a priori/a posteriori distinction and those vast copy-pastes about empiricism and Russell etc. What point are you trying to make? I am the one who has been saying that it is iffy to just talk about 'empiricists' as if that was a clear description and as if philosophers fell neatly into such categories, then you produce a vast quotes that prove the point.)

Me: What empiricist, or anyone else, would claim that we can't - or don't - have justified (though inconclusively) beliefs?

Radical skeptics do.

They think that certainty is never justified. To say we have 'justified (though inconclusively) beliefs' does not claim certainty. I think we have some justification for a belief the the earth orbits the sun. But there is always the possibility of doubt. Are you saying empiricists wouldn't agree with that? If not, then what was your point?

The rationalist belief in synthetic knowledge a priori doesn't entail the belief in its infallibility! That is, it's one thing to say that rational intuition is a source of knowledge (and belief-justification), and another to say that rational intuition is infallible. Moderate rationalists do not maintain it is.

Once again, didn't I say that? Yes, philosophers now understand 'synthetic a priori' in this - and other - ways. That is because they all came to the conclusion that 'synthetic a priori' in the sense of something that could overcome Cartesian doubt is out of reach.

But I ask again, if in your original quote 'empirical a priori', that only meant statements like "Three-legged tables don't wobble" and examples of other 'fallible beliefs', do you honestly think any Empiricists ever denied that such notions were possible?

Again, the point is that if, as the empiricists claim, all synthetic knowledge is grounded in experience, they cannot know and therefore cannot justifiably claim to know that this is true, because this knowledge claim would go beyond what is empirically justifiable.

You still have to insert this 'claim to know that this is true' phrase in order to muddy the waters. Anyone with Google will quickly find a well-known on-line site that tells us that Empiricism says that knowledge arises only or primarily from experience. And as a consequence, 'knowledge is tentative and probabilistic, subject to continued revision and falsification'. So note - they are talking about 'knowledge' meaning those things we take to be true. So they don't 'claim to know this is true' in the sense of claiming they have access to a metaphysical 'truth' beyond experience.

Before I gave you the example of the atheist. The atheist does not believe in God. Why? Because they see neither evidence for him, not any other compelling argument for believing he exists. That is not the same as claiming that they 'know that this is true' in the sense that they have an indisputable proof that God does not exist, because that would require the omniscience of God.

Similarly, I could give the scientific proposition; 'the earth orbits the sun'. We think it is true in the context of what counts as evidence in science. Adding the comment 'scientists 'know that this is true'' to such propositions only serves to falsely suggest that the scientists are claiming that they know the truth of scientific propositions independently from the scientific evidence. They make no such claim.

'Know that this is true' is essentially a form of ad hominen. To insert it is to accuse empiricists, atheists, scientists and anyone else of believing something without reason.

('Know that this is true' has a vaguely Biblical feel. That figures, because religion is the one context where that strange phrase really is at home; that of telling others of a faith, 'knowledge' that you recognise is not based on evidence. Like: 'I know it is true that Jesus is my saviour')

Posted: **May 23rd, 2014, 7:24 pm**

Stepping out; Man, having recognized the Nature of Individuality, became a Human Being the Moment he became convinced that his personal, Proprietary, Priori, Self Knowledge had greater value that Empirical Knowledge; the Moment man recognized the fact that he was Naked; covering himself, hiding the bushes at the first sign of danger without actually being endangered; Priori Knowledge, hearsay, not being fact, is born of Man's Feminine Side; it being Woman's Nature to be Arbitrary, Flighty, to be easily Beguiled; Priori Knowledge being born of that which is Above, the Mind, Man's Helpmate, savior, Priori Knowledge being born of Rationalization, Femininity, wishful thinking, It being the Feminine Way to believe that One might be able to foretell the Future.

Priori Knowledge allowing man to have Knowledge of a forth coming event before said event is experienced thus allowing Man to avoid a harm, allowing man to take advantage of the Priori Knowledge of a forth coming beneficial event.

By recognizing that he was born Bare, less than a mere Animal, man realized that in order to survive(99 % of every species to have ever lived on the Planet Earth now Extinct, being born of the competitive Spirit) Man reasoned that he must become more than a mere Animal.

Being Born Bare, Less than a Mere Animal, without specification, incomplete, Flawed, born Boundless, without the Limitation of (Reason allowing Man to step out of the Ways of the Empirical, Material, World of Reality, the Dominance of Mother Nature) the Empirical World of Reality Dominated by the Laws of Nature; born of the dust of the ground, Flesh and Bone, Man's destiny being predetermined for him, Man being born to Die, become Extinct; by overcoming the Fear in his Mind born of Ignorance, Man has become the Ultimate Survivor. Man's only Salvation being Priori Knowledge born of Reason; the only problem being that Priori Knowledge may be Absolutely Bad Knowledge. Man being totally dependent upon Reason, which if carried to an Extreme, totally ignoring Empirical Knowledge, the Priori Knowledge born of Rationalization gives birth to Absolutely Bad Knowledge; Absolutely Bad Knowledge having a Dual Quality, Absolutely Bad Knowledge, pseudo, quasi- Knowledge, being mistaken to be Absolutely Good Knowledge, the Knowledge of Good and Evil, Priori Knowledge, Illusion, being the Greatest cause of all Unnecessary Suffering.

Bound by the Laws of Nature, the Empirical World of Reality, cause and effect, suffering born of Mother Nature is never judge to be Evil.

Bound by the Rational Mind, Suffering born of Priori Knowledge when carried to an extreme by totally ignoring Empirical Knowledge, Rationalization, is deemed to be unnecessary, is Evil.

Posted: **May 24th, 2014, 11:44 am**

Londoner wrote:
Consul wrote:I presented (what I think are) two examples in my previous post:
* "Dogs aren't numbers."
* "Holes don't have holes."
Two more:
* "Coloured things are extended."
* "Three-legged tables don't wobble."
Can you transform these into explicit logical truths and thereby show that they are analytic rather than synthetic?

(Note: all further quotes are also yours.)

[The respective member names should be included in each and every quote box, even if you quote the same member more than once in the same post! That is, there should be no nameless quote boxes! Thanks!]

Londoner wrote:It is hard to tell what any of them mean because they are too brief. This makes writing out explanations tiresome because I would have to give several alternatives in the attempt to guess your meaning. To take the first as an example, if you are saying that the word we use to describe four legged animals is a different word to that which we use to describe the abstract quality of quantity, then I would say that this is an observation about the meaning of words. But you might have something else in mind.

Come on, my examples are readily comprehensible to every English-speaking person.

Londoner wrote:'Holes don't have holes' doesn't make sense because our understanding of 'hole' is that it represents a void in a thing, and a void isn't a thing. But again, you might have your own understanding of what 'hole' means.

No, I use "hole" in its ordinary-language sense. "Holes don't have holes" is a meaningful and true statement (why it is true is another question), and the question is whether it is analytic or synthetic. If the former, then it is equivalent to a tautology (logical truth). But to which one?

Londoner wrote:'Three legged tables don't wobble' might be a generalisation made from observation, in which case it is subject to the same sort of doubt as all such generalisations involving induction and arising from experience.

No, that three-legged tables don't wobble is not an inductive generalization based on observation, because it follows from a fact of analytic geometry, namely that three points are always on the same plane. This is knowable a priori, and it is arguably a synthetic truth (the name "analytic geometry" notwithstanding). I do not have to observe and check any three-legged tables in order to be able to know that they can't wobble. (This is not to say that they cannot topple over. They can and do, depending on where their mass centre is.)

Londoner wrote:Now, having written all that, if you wish to call them 'synthetic a priori' propositions then fine. But if those were examples of 'synthetic a priori propositions' as referred to in your quote, why do you think all those empiricist philosophers, who you must admit seem to be reasonably thoughtful persons, could think such things don't exist when you have no problem coming up with so many examples?
It seems to me that either these philosophers were very stupid - or they had something different in mind.

Empiricists would try to explain away the apparent syntheticity of my examples by arguing either that they are actually analytic or that they are actually only empirically knowable. But there are cases which seem to defy their attempts to transform all the allegedly synthetic statements into tautologies. If you disagree with me, then show me that my examples are actually equivalent to tautologies by presenting the corresponding tautologies! For example, of which logical truth is "Coloured things are extended" an instance?

Londoner wrote:(I don't know why you feel it is relevant to add all the stuff about the a priori/a posteriori distinction and those vast copy-pastes about empiricism and Russell etc. What point are you trying to make? I am the one who has been saying that it is iffy to just talk about 'empiricists' as if that was a clear description and as if philosophers fell neatly into such categories, then you produce a vast quotes that prove the point.)

There are two kinds of empiricism (about knowledge and justification):
* radical empiricism = the view that all knowledge is (ultimately) grounded in experience, i.e. that there is no knowledge a priori.
* moderate empiricism = the view that all synthetic knowledge is (ultimately) grounded in experience, i.e. that there is no synthetic knowledge a priori.

These definitions are sufficiently precise for our discussion.

Londoner wrote:
Consul wrote:
(Nested quote removed.)

Radical skeptics do.

They think that certainty is never justified. To say we have 'justified (though inconclusively) beliefs' does not claim certainty. I think we have some justification for a belief the the earth orbits the sun. But there is always the possibility of doubt. Are you saying empiricists wouldn't agree with that? If not, then what was your point?

Epistemological Skepticism is the denial of knowability, the attainability of certainty, or the justifiability of belief with regard to propositions. There are global and local skepticisms. For example, one can be a local skeptic about a priori knowledge but a nonskeptic about a posteriori knowledge.
We have skepticism about
1. knowledge: There is no and can be no knowledge.
2. certainty: There is and can be no (objectively) certain knowledge.
3. justification: There is no and can be justification of belief.

To be skeptical about a proposition p is
1. to deny that p is knowable, or
1.1 to deny that it is knowable whether p is knowable, or
2. to deny that p is knowable for certain, infallibly knowable, or
3. to deny that belief in p is justifiable.

The basic definition of empiricism as the view that all (synthetic) knowledge/belief-justification is empirical/a posteriori is neutral between fallibilism and infallibilism.

Of course, if you stipulate that only objectively certain, i.e. infallible, knowledge/belief-justification is real knowledge/belief-justification, and perception and introspection are fallible, then there is and can be no empirical knowledge/belief-justification. But this point is irrelevant to the definition of empiricism, because "All (synthetic) knowledge is empirical" doesn't imply "There is empirical (synthetic) knowledge" but only "If there is (synthetic) knowledge, it is empirical".

Londoner wrote:
Consul wrote:The rationalist belief in synthetic knowledge a priori doesn't entail the belief in its infallibility! That is, it's one thing to say that rational intuition is a source of knowledge (and belief-justification), and another to say that rational intuition is infallible. Moderate rationalists do not maintain it is.

Once again, didn't I say that? Yes, philosophers now understand 'synthetic a priori' in this - and other - ways. That is because they all came to the conclusion that 'synthetic a priori' in the sense of something that could overcome Cartesian doubt is out of reach.

Again, the question of a priori knowledge in general and of synthetic a priori knowledge in particular is one thing, and the question of objectively certain, infallible a priori knowledge in general and of objectively certain, infallible synthetic a priori knowledge in particular is another.

But if mathematical and particularly geometrical truths are synthetic truths, then they are rationally indubitable. How could they be false?

Londoner wrote:But I ask again, if in your original quote 'empirical a priori', that only meant statements like "Three-legged tables don't wobble" and examples of other 'fallible beliefs', do you honestly think any Empiricists ever denied that such notions were possible?

"Empirical a priori"? – That's a contradiction in terms!
You should know by now that empiricists do not only reject the notion of infallible synthetic a priori knowledge but of synthetic a priori knowledge simpliciter, be it fallible or infallible.

Londoner wrote:Anyone with Google will quickly find a well-known on-line site that tells us that Empiricism says that knowledge arises only or primarily from experience. And as a consequence, 'knowledge is tentative and probabilistic, subject to continued revision and falsification'. So note - they are talking about 'knowledge' meaning those things we take to be true. So they don't 'claim to know this is true' in the sense of claiming they have access to a metaphysical 'truth' beyond experience.

To say that empiricism isn't knowable is not to say that it isn't credible or plausible.

You are not an empiricist if you merely believe that knowledge arises primarily from experience. For empiricism is not just the view that some or most knowledge arises from experience, but that all knowledge does. Moderate rationalists certainly don't deny that some truths are only empirically knowable.

Per se, the basic assumption of empiricism is compatible both with fallibilism and with infallibilism. An empiricist could consistently (but unconvincingly) claim that perception and introspection are infallible sources of knowledge.

Londoner wrote: Before I gave you the example of the atheist. The atheist does not believe in God. Why? Because they see neither evidence for him, not any other compelling argument for believing he exists. That is not the same as claiming that they 'know that this is true' in the sense that they have an indisputable proof that God does not exist, because that would require the omniscience of God.

Empiricists don't lack a belief like the (negative) atheists, they hold one. But it is true that belief doesn't entail (subjective) certainty. So believing that p is not the same as claiming to know that p.

Londoner wrote: Similarly, I could give the scientific proposition; 'the earth orbits the sun'. We think it is true in the context of what counts as evidence in science. Adding the comment 'scientists 'know that this is true'' to such propositions only serves to falsely suggest that the scientists are claiming that they know the truth of scientific propositions independently from the scientific evidence. They make no such claim.
'Know that this is true' is essentially a form of ad hominen. To insert it is to accuse empiricists, atheists, scientists and anyone else of believing something without reason.
('Know that this is true' has a vaguely Biblical feel. That figures, because religion is the one context where that strange phrase really is at home; that of telling others of a faith, 'knowledge' that you recognise is not based on evidence. Like: 'I know it is true that Jesus is my saviour')

When a theist says "I don't believe that God exists, I know he does", then he is wrong firstly because knowledge entails belief, and secondly because his claim to knowlegde is nothing more than an expression of subjective certainty, of the absence of doubt: "I am certain/do not doubt that God exists."

Of course, scientific knowledge and scientific claims to knowledge are and have to be based on empirical evidence. The question is still whether or not the evidence must be conclusive, i.e. whether or not beliefs and knowledge claims must be justified infallibly in order to be epistemologically kosher. Am I ever justified in believing or claiming to know that p if my evidence for p doesn't eliminate the possibility that p is false?

Posted: **May 24th, 2014, 12:17 pm**

Bound by the Rational Mind, Suffering born of Priori Knowledge when carried to an extreme by totally ignoring Empirical Knowledge, Rationalization, is deemed to be unnecessary, is Evil.

Insane, Irrational!

-- Updated May 24th, 2014, 11:24 am to add the following --

Consul #214 " I presented (what I think are) two examples in my previous post: * "Dogs aren't numbers." * "Holes don't have holes." Two more: * "Coloured things are extended." * "Three-legged tables don't wobble."

Can you transform these into explicit logical truths and thereby show that they are analytic rather than synthetic?"

Wayne wrote:

Hell no, there is nothing analytic about those statements, No Logic what so ever, Totally Irrational.

Posted: **May 25th, 2014, 7:27 am**

Consul Since you prefer it, I have labelled every quote with your name.

Consul: Come on, my examples are readily comprehensible to every English-speaking person....

Really? Like "Coloured things are extended" ?

And I didn't say they were incomprehensible, I said they could be comprehended in more than one way, which is a problem if I supposed to analyse them

Consul: No, I use "hole" in its ordinary-language sense. "Holes don't have holes" is a meaningful and true statement (why it is true is another question), and the question is whether it is analytic or synthetic. If the former, then it is equivalent to a tautology (logical truth). But to which one?

I don't think "Holes don't have holes" has an ordinary-language sense - and since you neglect to tell me what was wrong with my last interpretation I am reluctant keep on guessing what you think it might be.

But for fun, let's try another definition of 'hole'. If by 'hole' you meant a discontinuity in something considered in two dimensions, then I can think of examples of holes having holes. Imagine an area of dry land. There is a hole in that dry land containing water (also known as a 'lake'). The lake has a hole in it consisting of dry land (also known as an 'island'). That island would be a hole in a hole.

Consul: I do not have to observe and check any three-legged tables in order to be able to know that they can't wobble.

Yes you do. If the three-legged table is situated on a tightrope it won't be stable. If the three legs are placed in a line it won't be stable. And so on.

If by three-legged table you mean a real object, then you have to have knowledge of the object to know it is stable. If you mean some geometrical concept, then its stability will be a result of its definition. You can remove the instability of my versions of the table by adding to your definition, but when you have defined away all the circumstances that might apply to real tables then the stability of your table becomes a tautology.

Consul: Empiricists would try to explain away the apparent syntheticity of my examples by arguing either that they are actually analytic or that they are actually only empirically knowable. But there are cases which seem to defy their attempts to transform all the allegedly synthetic statements into tautologies. If you disagree with me, then show me that my examples are actually equivalent to tautologies by presenting the corresponding tautologies! For example, of which logical truth is "Coloured things are extended" an instance?

As ever, I cannot tell exactly what you might mean by Coloured things are extended

If I guess that by 'extended' you mean it in the Cartesian sense of having more than one dimension, then to have extension is a necessary part of being a 'thing' (assuming by 'thing' you mean an object).

So your example reduces to saying 'Coloured things'. As such it is neither true or false because it doesn't assert anything.

But I'm not going to keep guessing. You need to be precise. But in my opinion, to be precise would be fatal to your examples.

Consul: But if mathematical and particularly geometrical truths are synthetic truths, then they are rationally indubitable.

The argument is that they are not synthetic because the predicate is contained in the subject. Two plus two equal four because (amongst other things) 'four' means 'two plus two'. (Nor does the truth of 2+2=4 derive from experience.)

Kant thought otherwise, but from the perspective that the truths of maths etc. are 'exhibited in intuition'. To put it another way, they 'flow' from 'pure concepts of the understanding'. So since to Kant, we have no access or knowledge to 'things in themselves' but only to them as they are manifested as objects of understanding, then the idea of the 'synthetic' can only have meaning if it is applied, not to 'things', but to us, meaning those intuitive categories we require to make sense of anything.

Now you can either take the first version, in which case maths isn't synthetic, or the Kantian version. But the Kantian version doesn't work with your 'three-legged tables' examples. Nor is it that claim of metaphysical certainty suggested in the quote in your post 199, which we are supposed to be discussing.

Consul: Of course, scientific knowledge and scientific claims to knowledge are and have to be based on empirical evidence. The question is still whether or not the evidence must be conclusive, i.e. whether or not beliefs and knowledge claims must be justified infallibly in order to be epistemologically kosher. Am I ever justified in believing or claiming to know that p if my evidence for p doesn't eliminate the possibility that p is false?

Not infallibly in an absolute, metaphysical sense. As with the science and empiricism and everything else, you only believe/know conditionally, within a particular context. You have used the symbol 'P'. In logic we have to start out with 'assume P' and recognise that all our subsequent conclusions will hang on that assumption being correct. So it is with everything.

Posted: **May 25th, 2014, 12:30 pm**

Londoner wrote:Consul Since you prefer it, I have labelled every quote with your name.

Thanks, that's one step forward; but you still don't use the quote function correctly.
NOT

Code: Select all

[quote]NAME: TEXT[/quote]

BUT

Code: Select all

[quote="NAME"]TEXT[/quote]

Londoner wrote:
Consul wrote:Come on, my examples are readily comprehensible to every English-speaking person....

Really? Like "Coloured things are extended" ?
And I didn't say they were incomprehensible, I said they could be comprehended in more than one way, which is a problem if I supposed to analyse them.

There's nothing ambiguous about the simple statement that coloured things are extended.

Londoner wrote:
Consul wrote:No, I use "hole" in its ordinary-language sense. "Holes don't have holes" is a meaningful and true statement (why it is true is another question), and the question is whether it is analytic or synthetic. If the former, then it is equivalent to a tautology (logical truth). But to which one?

I don't think "Holes don't have holes" has an ordinary-language sense - and since you neglect to tell me what was wrong with my last interpretation I am reluctant keep on guessing what you think it might be.

The noun "hole" is part of ordinary language, and every normal person understands it and the sentence in question.

Londoner wrote:But for fun, let's try another definition of 'hole'. If by 'hole' you meant a discontinuity in something considered in two dimensions, then I can think of examples of holes having holes. Imagine an area of dry land. There is a hole in that dry land containing water (also known as a 'lake'). The lake has a hole in it consisting of dry land (also known as an 'island'). That island would be a hole in a hole.

No, it wouldn't. Even if a mass of water can properly be said to have holes, an island is not a hole but a hole-filler, with hole-fillers not being holes. So an island is a nonhole in a hole. (You cannot fill a hole with another hole.) A lake is a hole-filler too: it fills a hole in the soil.
For instance, you could say that a fish in the water fills a hole in the water, but the fish itself is certainly not a hole.

Note that by arguing that the sentence "Holes don't have holes" is a synthetic truth, I am by no means implying that the questions whether there really are holes, and if there are, what they really are aren't ontologically puzzling. See: http://plato.stanford.edu/entries/holes/

Londoner wrote:
Consul wrote:I do not have to observe and check any three-legged tables in order to be able to know that they can't wobble.

Yes you do. If the three-legged table is situated on a tightrope it won't be stable. If the three legs are placed in a line it won't be stable. And so on.
If by three-legged table you mean a real object, then you have to have knowledge of the object to know it is stable. If you mean some geometrical concept, then its stability will be a result of its definition. You can remove the instability of my versions of the table by adding to your definition, but when you have defined away all the circumstances that might apply to real tables then the stability of your table becomes a tautology.

I already said that to say that three-legged tables cannot wobble is not to say that they cannot topple over and be unstable in this sense. Nonetheless, a three-legged table which stands upright doesn't wobble, which fact is provable a priori by means of analytic geometry. And I doubt that the principles of analytic geometry are reducible to tautologies. I may be wrong, but if you think I am, it's up to you to show me I am!

Londoner wrote:As ever, I cannot tell exactly what you might mean by Coloured things are extended
If I guess that by 'extended' you mean it in the Cartesian sense of having more than one dimension, then to have extension is a necessary part of being a 'thing' (assuming by 'thing' you mean an object). So your example reduces to saying 'Coloured things'. As such it is neither true or false because it doesn't assert anything. But I'm not going to keep guessing. You need to be precise. But in my opinion, to be precise would be fatal to your examples.

I thought it was obvious that "Coloured things are extended" means "Coloured things are spatially extended". By "thing" I mean "object", but it is not true by definition that all objects are spatially extended. For example, numbers and sets are objects, but they are abstract objects, which are unextended by definition. Space/spacetime-points and point-particles are concrete objects, but they are unextended too. Immaterial souls are concrete but unextended objects.
(Note that I do not mean to say that all these kinds of objects exist. In the Cartesian sense, all material/physical objects are spatially extended; and so zero-dimensional point-particles are ruled out by definition.)

If you believe that "Coloured objects are spatially extended" is implicitly tautologous and thereby analytic, I defy you to show me the explicit tautology to which it is equivalent! (It's not "Coloured extended objects are extended"!)

Londoner wrote:
Consul wrote:But if mathematical and particularly geometrical truths are synthetic truths, then they are rationally indubitable.

The argument is that they are not synthetic because the predicate is contained in the subject. Two plus two equal four because (amongst other things) 'four' means 'two plus two'. (Nor does the truth of 2+2=4 derive from experience.)

You're right insofar as mathematical truths are knowable a priori, but you're wrong insofar as "4" doesn't mean "2+2". "4" and "2+2" (which are names rather than predicates/concepts) are coreferential—they refer to the same number—but not synonymous. To use a famous example, "the evening star" and "the morning star" refer to the same thing but they do not have the same meaning.

Londoner wrote:Kant thought otherwise, but from the perspective that the truths of maths etc. are 'exhibited in intuition'. To put it another way, they 'flow' from 'pure concepts of the understanding'. So since to Kant, we have no access or knowledge to 'things in themselves' but only to them as they are manifested as objects of understanding, then the idea of the 'synthetic' can only have meaning if it is applied, not to 'things', but to us, meaning those intuitive categories we require to make sense of anything.
Now you can either take the first version, in which case maths isn't synthetic, or the Kantian version. But the Kantian version doesn't work with your 'three-legged tables' examples. Nor is it that claim of metaphysical certainty suggested in the quote in your post 199, which we are supposed to be discussing.

First of all, I should mention that I haven't yet formed a firm opinion on whether or not all mathematical and geometrical propositions are analytic. At least, I tend to believe that this is not the case.

Let's not confuse the question of a-priority with the question of analyticity/syntheticity!
You may explain the possibility of a priori knowledge in terms of conceptual intuition, and conceptual intuition as an unmysterious manifestation of logico-linguistic competence and intelligence.
If, as the logical empiricists hold, conceptual intuition cannot reveal anything more than analytic truths, then the belief in mathematical and geometrical knowledge a priori is defensible only if all propositions of mathematics and geometry can be shown to be analytic. Frege with his logicist programme tried to do so (with regard to arithmetics), and he almost succeeded—almost.

"It seems clear that epistemological considerations in part motivated Frege's work on the foundations of mathematics. It is well documented that Frege had the following goal, namely, to explain our knowledge of the basic laws of arithmetic by giving an answer to the question “How are numbers ‘given’ to us?” without making an appeal to the faculty of intuition. If Frege could show that the basic laws of number theory are derivable from analytic truths of logic, then he could argue that we need only appeal to the faculty of understanding (as opposed to some faculty of intuition) to explain our knowledge of the truths of arithmetic. Frege's goal then stands in contrast to the Kantian view of the exact mathematical sciences, according to which general principles of reasoning must be supplemented by a faculty of intuition if we are to achieve mathematical knowledge. The Kantian model here is that of geometry; Kant thought that our intuitions of figures and constructions played an essential role in the demonstrations of geometrical theorems. (In Frege's own time, the achievements of Frege's contemporaries Pasch, Pieri and Hilbert showed that such intuitions were not essential.)
…Frege's strategy then was to show that no appeal to intuition is required for the derivation of the theorems of number theory. This in turn required that he show that the latter are derivable using only rules of inference, axioms, and definitions that are purely analytic principles of logic. This view has become known as ‘Logicism’."

http://plato.stanford.edu/entries/frege-theorem/

Remark: Frege was wrong insofar as an appeal to intuition is required for the justification of the belief in the principles of logic.

"Logic, mathematics, and mathematical geometry had traditionally seemed to be confirmationally “different”. Indeed it is hard to indicate any conditions under which any parts of them would be disconfirmed. Leibniz had called them truths of reason. Hume said that they represented relations of ideas. Kant had held that the truths in these areas were a priori. Mathematics and geometry were not analytic for Kant, but logic was. Kant had two criteria of analyticity, apparently thinking them equivalent. First, in subject-predicate sentences, an analytic sentence is one in which the concept of the predicate is contained in that of the subject. Second, an analytic sentence is one whose denial is self-contradictory. This seems to include not only the sentences whose surface logical form would be of the required sort but also those that can be got from such logical truths by making substitutions that were conceptually equivalent. The more modern rough analog of this is to say that the analytic sentences are those that are true in virtue of logic and definition.
Frege certainly developed logic beyond that which was available to Kant, but he did not think of himself as changing the analytic status of it. Logic is after all the only avenue we have for giving meaning to the notion of (logical) contradiction. Of course Frege also attempted to reduce mathematics to logic (including both first and second order logic), and insofar as that reduction was successful it would have implied that mathematics was analytic as well. Frege said little of geometry, but for him it was synthetic a priori.
Carnap had not only studied with Frege, but like many of the logical empiricists he had started out as a neo-Kantian as a well. So especially in view of Russell's relatively more successful attempt at reducing mathematics to logic, it was perhaps natural that Carnap would consider both mathematics and logic as analytic. Geometry could be handled in several different ways that we will not discuss here. But from fairly early on there was widespread agreement among the logical empiricists that there was no synthetic a priori, and that logic and mathematics and perhaps much else that seemed impervious to empirical disconfirmation should be thought of as analytic."

http://plato.stanford.edu/entries/logical-empiricism/

Londoner wrote:As with the science and empiricism and everything else, you only believe/know conditionally, within a particular context. You have used the symbol 'P'. In logic we have to start out with 'assume P' and recognise that all our subsequent conclusions will hang on that assumption being correct. So it is with everything.

Of course, the (degree of) justification of beliefs inferred from other beliefs depends on the (degree of) justification of the beliefs from which they have been inferred. And rational persons proportion the strength of their beliefs to the strength of the evidence they have for them.

Posted: **May 25th, 2014, 1:06 pm**

Consul wrote:

No, that three-legged tables don't wobble is not an inductive generalization based on observation, because it follows from a fact of analytic geometry, namely that three points are always on the same plane. This is knowable a priori, and it is arguably a synthetic truth (the name "analytic geometry" notwithstanding). I do not have to observe and check any three-legged tables in order to be able to know that they can't wobble. (This is not to say that they cannot topple over. They can and do, depending on where their mass centre is.)

Then 'a priori' means that if one knows plane geometry one necessarily knows every fact into which plane geometry can be analysed. However plane geometry (or its finite body of facts , or axioms and theorems as they are called) is known a posteriori i.e. after the initial axioms have been taught; the axioms necessarily imply the theorems. For instance when one has observed that a three legged table has all its legs on the same plane the axioms and all the theorems of the whole of plane geometry necessarily follow. Therefore plane geometry, although its analysis yields a priori knowledge, must be learned by way of at least one observed fact. We cannot know plane geometry unless we have observed at least one fact about three dimensional space.

All so-called a priori knowledge which is known from analysing some finite body of knowledge is not open -ended, creative or infinite (i.e. synthetic)knowledge about the world but is knowledge about a measuring or categorising system . Measuring or categorising systems don't contain signs of reality they contain symbols for selected aspects of reality.

To possess the skill to manipulate symbols hardly merits the name of knowledge. To know something is to recognise signs of reality, despite the problem of induction.

Posted: **May 26th, 2014, 5:24 am**

Consul

Thanks, that's one step forward; but you still don't use the quote function correctly.

And thank you for the continued instruction, but I'm afraid I have decided you will have to accept my style as I accept yours. If I tell you now that all the quotes below are from your most recent post, surely that shouldn't cause any problems to someone who is at home with the complexities of Frege, Russell and co!

And I doubt that the principles of analytic geometry are reducible to tautologies. I may be wrong, but if you think I am, it's up to you to show me I am!

I wrote something about that in my last post and Belinda has covered it.

I'm not going to keep chasing all your examples any more as you decline to clarify what you mean. Just telling me that normal English speakers would understand isn't helpful. As any casual reader of this thread would confirm, it does not resemble any normal English converstaion.

By "thing" I mean "object", but it is not true by definition that all objects are spatially extended. For example, numbers and sets are objects, but they are abstract objects, which are unextended by definition.

If you choose to call numbers objects, then fine, but since you said "Coloured things are spatially extended" and you say numbers aren't extended, by 'things' you can't have been talking about numbers, so what is the relevance?

If you believe that "Coloured objects are spatially extended" is implicitly tautologous and thereby analytic, I defy you to show me the explicit tautology to which it is equivalent!

You did not read my answer last time!

You're right insofar as mathematical truths are knowable a priori, but you're wrong insofar as "4" doesn't mean "2+2". "4" and "2+2" (which are names rather than predicates/concepts) are coreferential—they refer to the same number—but not synonymous. To use a famous example, "the evening star" and "the morning star" refer to the same thing but they do not have the same meaning.

Again, I think you are wandering from the subject at issue, not that all this stuff isn't interesting in its own right.

So I will focus by returning to the quote in post 199 at which I entered this exchange. You say:

Of course, the (degree of) justification of beliefs inferred from other beliefs depends on the (degree of) justification of the beliefs from which they have been inferred. And rational persons proportion the strength of their beliefs to the strength of the evidence they have for them.

So - by inserting the quite unnecessary phrase in Post 199 'know that this is true' into an account of the Empiricist position on the 'synthetic a priori' the writer wrongly asserted a claim of metaphysical certainty that was not there.

On that topic, that will do, as far as I am concerned.

Posted: **May 26th, 2014, 9:14 am**

Londoner wrote:And thank you for the continued instruction, but I'm afraid I have decided you will have to accept my style as I accept yours.

Name- or sourceless quotations are a plague in internet forums. The author or source of a quotation must be directly and clearly identifiable! My style is the standard style! Your refusal to adopt it is an expression of laziness and unfriendliness that I do not accept.

Londoner wrote:I'm not going to keep chasing all your examples any more as you decline to clarify what you mean. Just telling me that normal English speakers would understand isn't helpful. As any casual reader of this thread would confirm, it does not resemble any normal English converstaion.

You're being evasive! My examples do not come from a textbook in quantum mechanics.

Posted: **July 20th, 2014, 6:33 pm**

Kant's division into analytic and synthetic is well grounded--his argument according to his Transcendental Aesthetic is that the a priori concepts of space and time lie at the basis of all of our a posteriori knowledge, they make experience of phenomenon possible (as all experience takes place in space and over time). This is fundamental to Kant's critical philosophy.

An easy way to define the separate nature of the a priori and the a posteriori is given in this example: Throw a brick at a window. Is it a priori certain that the window will break? No, it is not a priori certain. Of course, while one might with good reason judge that the window will break, it is not necessarily true that the window will break. Maybe it will be the case that the window will stay intact because the brick was not thrown with sufficient force.

However, it one draws an arc on a one dimensional piece of paper and continues to extend the line of this arc then it follows that the line will eventually return upon itself to form a circle. This conclusion is necessary and a priori certain and the proof for the conclusion does not depend on experience. We do not need to repeatedly extend the line of the arc to see if it returns upon itself to form a circle. We can know that it will form a circle independently of experience and completely through the use of pure reason.

Empiricists who deny such a priori knowledge may as well deny the existence of mathematics or theoretical physics which are just as Kant would argue, founded upon a priori reasoning. He makes this point in both his Critique of Pure Reason and his Prolegomena to Any Future Metaphysics.

Posted: **July 20th, 2014, 10:56 pm**

Soylent. Although I agree with most of what you say I would dispute your assertion that theoretical physics is founded on a priori reasoning. I only wish it were and then it might make some sense. The spacetime paradigm, for instance is founded on a conclusion extrapolated from observation, a process Herr Kant would sniff at in haughty contempt.

Regards Leo

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