A priori synthetic statements

[Paul C. Anagnostopoulos]

What is an a priori synthetic statement? I bring this up as an offshoot of the "Must a skeptic also be an atheist" thread.
Here it says:

Now we are in a position to appreciate what 'a priori synthetic' claims are. 'A priori synthetic' refers to a class of claims which we can make quite independently of our experiences, but which are not true in virtue of definitions alone. That is to say, they are not trivial statements like 'all bachelors are unmarried', but are ones (for Kant) that say substantial things. For Kant, this includes talk of our intuitions of space and time, and the concepts of causation and substance. What he is saying is that I do not form my idea of space from the experience of space; it is a priori just to the extent that the existence of space is presupposed in my experience. And claims like 'All things occur in space' are clearly not analytic, but synthetic and substantial. So they are a priori, but this does not affect their status as synthetic.

I sense we could argue this definition incessantly.

~~ Paul

 

[UndercoverElephant]

Hi Paul

I sense we could argue this definition incessantly.

Why?

Can you give a clearer description of what you think the argument would be about?



Geoff

NB: Yeah, we could probably argue. Analytic a posteriori statements are quite fun too, especially since Kant claimed there weren't any.

And this thread is in the wrong forum. It should be in philosophy.

 

[UndercoverElephant]

OK, since this a side-thread I ought to respond to this post by Stimpy:

Please note that I am not claiming that a priori synthetic judgments cannot be meaningful. I am just saying that I cannot think of any way they could be.

They are meaningfull because they are neccesarily true for us to be able to experience anything at all.

"All events have a cause."

Perhaps I can explain my point this way.

One thing I agree with the positivists about is that the meaning of a statement is precisely the set of necessary and sufficient conditions by which the statement is true.

The neccesary and sufficient conditions for the above statement to be true is that we are experiencing being in a world.

If we are experiencing being in a world, then that statement must be true. According to Kant, that is.

In other words, when I make a statement, the meaning which I am conveying is nothing more and nothing less than that the necessary and sufficient conditions for that statement to be true, have been met.

This means that for a statement to be meaningful, it must be known what those conditions for it to be true are.

The conditions are that we are experiencing being in a world.

In the case of analytic statements, this is trivial. The conditions are stipulated by the logical framework from which the terms being used are defined. Thus such statements can be meaningful.

Now a positivist would claim that for synthetic statements, then only way that we can possibly know what the conditions are for which the statement is true, is if the statement is expressed entirely in terms of empirical observations, in which case, the truth of the statement will be verifiable.

Note that the claim is not that verifiability is what makes the statement meaningful. That is a common misconception. The claim is that being expressed entirely in terms of empirical observations is what makes the statement meaningful. The fact that such statements are also empirically verifiable is just a true fact about such statements.

Of course it follows from the above that a positivist will claim that a priori synthetic statements are meaningless.

Yes, seems so.

Now I don't go quite that far. I will not claim that the only way a synthetic statement can be meaningful is if it is expressed entirely in terms of empirical observations (in other words, that it is a posteriori statement). What I will say is that posteriori synthetic statements can be meaningful, and that their meaning is simply that the predicted observations will be observed under the conditions stipulated by the statement.

Furthermore, I will say that I know of no way to determine the meaning of an a priori synthetic statement.

"Every event has a cause"?

Are you saying that you don't know what this statement means, that you don't know how to verify it's truth conditions, or that it is not an a priori synthetic statement?

As regards the stuff about science and maths, I'll leave that for later.

 

[Drooper]

In a word

a cliche

 

[Stimpson J. Cat]

JustGeoff,

They are meaningfull because they are neccesarily true for us to be able to experience anything at all.

Could you give an example of such a statement? If I am guessing correctly, I think that what you are talking about are actually posteriori synthetic statements.

"All events have a cause."

???? Is this meant to be an example of such a statement? If so, then I don't see how it qualifies. It seems likely that it isn't even true.

Perhaps I can explain my point this way.

One thing I agree with the positivists about is that the meaning of a statement is precisely the set of necessary and sufficient conditions by which the statement is true.

The necessary and sufficient conditions for the above statement to be true is that we are experiencing being in a world.

Actually, that would only be a necessary condition, but I don't see your point.

If we are experiencing being in a world, then that statement must be true. According to Kant, that is.

I am confused. Which statement?

In other words, when I make a statement, the meaning which I am conveying is nothing more and nothing less than that the necessary and sufficient conditions for that statement to be true, have been met.

This means that for a statement to be meaningful, it must be known what those conditions for it to be true are.

The conditions are that we are experiencing being in a world.

Which statement is this the conditions for?

Furthermore, I will say that I know of no way to determine the meaning of an a priori synthetic statement.

"Every event has a cause"?

Are you saying that you don't know what this statement means, that you don't know how to verify it's truth conditions, or that it is not an a priori synthetic statement?[/quote]
I would say that it is not an a priori synthetic statement. I know what it means, and the evidence seems to pretty clearly indicate that it is not true. That is, unless you mean something different by "cause" than I think you do. Are you talking about causality in the sense of all events being determined by prior events (temporal determinism)? Or are you talking about more general determinism?

If the latter, then I would have to ask what the necessary and sufficient conditions for it to be true would be. It certainly is not necessary for us to be "experiencing being in a world".


Incidentally, You seem to be saying that any statement about the world which must be true in order for us to be able to be able to experience the world, is an a priori synthetic statement. I disagree. Remember that we are talking about a priori and posteriori in the sense of epistemology here. So what is at issue is not why something is true, but how we know that it is true.

Take, for example, the statement "I exist". This statement must clearly be true for it to be possible for me to experience the world. Does that make it an a priori synthetic statement? Not in the epistemological sense.

How do I know that I exist? Simple. First, I believe that I exist. In order for it to be possible for me to believe that I exist, I must exist (I think therefore I am). Thus I can conclude that my belief that I exist is justified (I know that I exist). So I have inferred the truth of the statement "I exist" from the observation that I believe that I exist. That is an example of a posteriori synthetic statement.

In general, for any statement about the world which must be true in order for us to be experiencing, we infer the truth of that statement from the observation that we are, in fact, experiencing a universe. Therefore they are posteriori synthetic statements. Epistemologically speaking, this is no different than any other case of logically concluding that X is true because !X is not logically consistent with our observations.


Dr. Stupid

 

[Paul C. Anagnostopoulos]

Geoff said:
Can you give a clearer description of what you think the argument would be about?

Among other things, I think we would argue about what is analytic. Is "2 + 3 = 5" analytic or synthetic?

And claims like 'All things occur in space' are clearly not analytic, but synthetic and substantial.

I'd say it depends on one's definition of space.

~~ Paul

 

[Dr Adequate]

A synthetic a priori statement would be a tautology with empirical content --- which would be a contradiction in terms, since we cannot give any example of an observation that would tend to confirm or deconfirm a tautology.

 

[UndercoverElephant]

OK folks....rewind...

Kant is trying to determine the neccesary conditions for any knowledge at all, particularly whether any of these neccesary conditions come from the mind itself. His strategy is to try to show that the universal and neccesary (hence a priori) claims of maths and metaphysics owe their special status to the fact that certain conditions, which are neccesary for knowledge in general, lie a priori in the mind and enable it to deal with sensory experience.

His conclusion is that some claims of metaphysics, science and maths are universally true of all the objects of which we can have any knowledge, because those claims reflect the way our minds work - and must work - if we are going to be able to have any knowledge at all based on the evidence presented to our senses.

The standard view in epistemology is that our knowledge claims can be vindicated only by showing that our thoughts about objects confoirm to what the objects themselves are like. Kant wants us to consider vindicating our knowledge claims by inquiring whether the objects of which we can have knowledge must conform to our ways of knowing.

Now, I suspect by this point that Kant and Stimpson J Cat are already on a collision course because Stimpsons definition of what a statement means is incompatible with what I have already written about Kant.

If so, the answer to Pauls question is probably "yes". We could indeed argue about this for a very long time.

 

[Kevin_Lowe]

OK folks....rewind...

Kant is trying to determine the neccesary conditions for any knowledge at all, particularly whether any of these neccesary conditions come from the mind itself. His strategy is to try to show that the universal and neccesary (hence a priori) claims of maths and metaphysics owe their special status to the fact that certain conditions, which are neccesary for knowledge in general, lie a priori in the mind and enable it to deal with sensory experience.

His conclusion is that some claims of metaphysics, science and maths are universally true of all the objects of which we can have any knowledge, because those claims reflect the way our minds work - and must work - if we are going to be able to have any knowledge at all based on the evidence presented to our senses.

Some examples of such claims would help enormously. Could you throw out a few such claims for us?

 

[Interesting Ian]

What is an a priori synthetic statement? I bring this up as an offshoot of the "Must a skeptic also be an atheist" thread.
Here it says:

I sense we could argue this definition incessantly.

~~ Paul

They are something we know to be true independently of experience. Like everything has a cause. Time is absolute.

Of course one can deny we do know any such things.

 

[Interesting Ian]

Cat
In the case of analytic statements, this is trivial. The conditions are stipulated by the logical framework from which the terms being used are defined. Thus such statements can be meaningful.

Now a positivist would claim that for synthetic statements, then only way that we can possibly know what the conditions are for which the statement is true, is if the statement is expressed entirely in terms of empirical observations, in which case, the truth of the statement will be verifiable.

Note that the claim is not that verifiability is what makes the statement meaningful. That is a common misconception. The claim is that being expressed entirely in terms of empirical observations is what makes the statement meaningful. The fact that such statements are also empirically verifiable is just a true fact about such statements.

Of course it follows from the above that a positivist will claim that a priori synthetic statements are meaningless.

No, no one can say they are meaningless. Merely that they aren't any.

 

[Interesting Ian]

Geoff
"All events have a cause."
--------------------------------------------------------------------------------

Cat
???? Is this meant to be an example of such a statement? If so, then I don't see how it qualifies. It seems likely that it isn't even true.

In that case the statement is false, not meaningless.

 

[UndercoverElephant]

Some examples of such claims would help enormously. Could you throw out a few such claims for us?

http://www.nutters.org/docs/kant-sap

But do synthetic a priori judgments exist, and when (if at all) are we actually justified in calling them "knowledge"? Indeed, they do exist; it's not unreasonable to say that all the really "interesting" judgments are exactly of this kind. "Every event has a cause" is an example — one that is immediately recognisable as the kind of judgment accepted as knowledge by the rationalists (although they failed to recognise it as synthetic). But the antithesis, "no event has a cause", is also a synthetic a priori judgment: the fact that I can phrase it negatively without producing a contradictory or meaningless statement is sufficient to demonstrate that it is synthetic, and its claims to universality and necessity preclude it from being determined empirically.

How do we determine which (if either) of these can be considered knowledge? What are our grounds? Kant says that, whereas we can appeal to experience in the case of empirical judgments, we need some substitute source of appeal, "X", in the case of synthetic a priori judgments, since ordinary experience can no longer help us. That the need for this mysterious "X" has not been recognised in the past, says Kant, was the cause of many long and fruitless speculative arguments and investigations.[7]

Other examples of fields containing synthetic a priori judgments include pure mathematics and pure science. Pure science might raise an eyebrow at first, given as how it is firmly rooted in the empirical, but scientific laws like Newton's laws of mechanics are synthetic a priori judgments: they make necessary and universal claims (thus a priori) which are more than simple logical imperatives (thus synthetic). And mathematics, although rich with logic and proof-by-contradiction (and thus apparently analytic, as supposed by Hume), is ultimately synthetic at its roots, and thus synthetic at its leaves (since it is not possible to arrive at an analytic result from a synthetic base, even when each step along the way is analytic). That mathematics is ultimately synthetic is by no means obvious, but Kant's stance on the matter seems to have been vindicated with time; if my (admittedly naïve) understanding is correct, Gödel's incompleteness theorem has demonstrated that no fully satisfactory purely analytic account of mathematics can ever be forthcoming.

Similarly, all the important statements of metaphysics are synthetic a priori propositions.[8] When viewed this way, the problem of metaphysics becomes one of determining how to make synthetic a priori judgments in that domain. Given the success of mathematics and natural science, which also deal with synthetic a priori judgments, there seems cause to hope for at least some semblance of real progress in the field when the appropriate rules of the game are recognised.

These "appropriate rules", says Kant, must arise from reason itself, but not unbridled reason, free to speculate as it pleases. That, presumably, would be no better than a kind of natural science which operates speculatively from an armchair and never goes out of doors for a reality check. But metaphysics has no access to the great outdoors in the way that the natural sciences do (or else rationalism would have been less problematic). So the best "reality check" we can offer on reason is reason itself: reason scrutinising itself; a critique of pure reason.

 

[Stimpson J. Cat]

JustGeoff,

Kant is trying to determine the neccesary conditions for any knowledge at all, particularly whether any of these neccesary conditions come from the mind itself. His strategy is to try to show that the universal and neccesary (hence a priori) claims of maths and metaphysics owe their special status to the fact that certain conditions, which are neccesary for knowledge in general, lie a priori in the mind and enable it to deal with sensory experience.

His conclusion is that some claims of metaphysics, science and maths are universally true of all the objects of which we can have any knowledge, because those claims reflect the way our minds work - and must work - if we are going to be able to have any knowledge at all based on the evidence presented to our senses.

The standard view in epistemology is that our knowledge claims can be vindicated only by showing that our thoughts about objects confoirm to what the objects themselves are like. Kant wants us to consider vindicating our knowledge claims by inquiring whether the objects of which we can have knowledge must conform to our ways of knowing.

Now, I suspect by this point that Kant and Stimpson J Cat are already on a collision course because Stimpsons definition of what a statement means is incompatible with what I have already written about Kant.

Well, more to the point I do not think that what Kant is calling "metaphysical claims" are claims which are not either analytically derivable, or empirically verifiable, so I see no reason to label them as "metaphysical", and do not understand why they do not qualify as either a priori analytic statements, or posteriori synthetic statements. Could you give a specific example of a statement which whose truth value can neither be derived from the definitions of the terms in the statement, nor empirically verified? Can you then explain to me what that statement means?

As I mentioned before, it seems to me that any synthetic statement which must be true in order for us to be able to have synthetic knowledge at all, must be a posteriori statement, because the fact that our synthetic beliefs which our epistemological system is claiming are justified, accurately describe our empirical observations, is itself empirical evidence that those beliefs are justified. Thus we have empirical verification of the fact that we have synthetic knowledge.

I guess it really comes down to what constitutes "justification" for a synthetic belief. Some people seem to want their epistemological system to have justification for synthetic beliefs somehow come from something other than empirical observations. This makes no sense to me. Ultimately the justification comes down to a question of utility. Does the model accurately describe our observations? If so, then the model can be considered to be synthetic knowledge.


Ian,

They are something we know to be true independently of experience. Like everything has a cause. Time is absolute.

Of course one can deny we do know any such things.

I certainly deny it. Not only do I not know that the above are true, but I don't even believe that they are. Furthermore I cannot imagine how you could claim to know these independently of experience? What is your justification for these beliefs? If they are not justified beliefs, then they are not things which you "know". They are just things you believe.

Of course it follows from the above that a positivist will claim that a priori synthetic statements are meaningless.

No, no one can say they are meaningless. Merely that they aren't any.

What I meant is that they will say that the statements which Geoff is claiming are a priori synthetic statements, are actually meaningless statements. Of course this means that they are not actually a priori synthetic statements at all.

???? Is this meant to be an example of such a statement? If so, then I don't see how it qualifies. It seems likely that it isn't even true.

In that case the statement is false, not meaningless.

I did not say it was meaningless. On the contrary, I think that it is a false posteriori synthetic statement.


Dr. Stupid

 

[Interesting Ian]

Could you give a specific example of a statement which whose truth value can neither be derived from the definitions of the terms in the statement, nor empirically verified? Can you then explain to me what that statement means?

Physical laws are univeral. That is to say they have always applied, they will always apply, and they apply wherever you are. Now this is certainly not true by definition. Nor can it be established empirically since we would need to rely on induction. But assuming the inductive principle obviously begs the question.

--------------------------------------------------------------------------------
They are something we know to be true independently of experience. Like everything has a cause. Time is absolute.

Of course one can deny we do know any such things.
--------------------------------------------------------------------------------


I certainly deny it. Not only do I not know that the above are true, but I don't even believe that they are.

Neither do I.

 

[UndercoverElephant]

Originally posted by Stimpson J. Cat

I guess it really comes down to what constitutes "justification" for a synthetic belief.

Probably does, yes.

Some people seem to want their epistemological system to have justification for synthetic beliefs somehow come from something other than empirical observations.

Well, yes - they are the ones that allow us to make empirical observations in the first place - according to Kant.

Could we make empirical observations if we did not experience linear time? I think the answer is no. This observation is not a posteriori, because it is universally and neccesarily true. By the time we experience anything at all, it already must be true. And it's certainly not analytic. It's metaphysical because it's about how the world has to be. We couldn't have minds if it wasn't.

This makes no sense to me. Ultimately the justification comes down to a question of utility. Does the model accurately describe our observations?

Kant isn't talking about judgements that reuiqre observations to have been taken already. Therefore you can't ask the question "Does the model accurately describe the observations", because anything that already requires observations and models must be a posteriori. This stuff appeared in a book called "Critique of pure reason". It is reasoning about reasoning. That's how it manages to be both a priori and synthetic. How do you assess it's true? Using pure reason, I guess. Not comparing models and observations.

Can we, using pure reason, establish synthetic truths about the nature of minds and of experience - and therefore about the nature of the world, which are neccesarily true?

 

[Kevin_Lowe]

I was hoping you could provide us with examples in your own words.

"All things have a cause" looks to me like a claim that must be based on some empirical experience of things and causes, and it is certainly not a belief that is necessarily true because we are experiencing the world.

Is there a better example to be had?

 

[UndercoverElephant]

I was hoping you could provide us with examples in your own words.

I'd rather stick to examples given by others. I'm not sure I can think of any better ones. Kant gives lots of others, but in order to explain them I'd need to write an essay rather than make a post. So I am giving the simple examples that come up in books trying to explain what Kant meant. Sorry if that's not helpful, but Critique of Pure Reason is full of all sorts of jargon which I can't use without explaining what it means, and explaining what it means requires starting from the beginning of Kant and trying to explain pretty much all of it. Which is beyond me.

"All things have a cause" looks to me like a claim that must be based on some empirical experience of things and causes, and it is certainly not a belief that is necessarily true because we are experiencing the world.

Well, QM has thrown a spanner in the works of this example. An interesting spanner - since the very thing which seems to now be suggesting that maybe there are acausal events is itself deeply controversial on the grounds that it appears to be impossible to provide an account of what it means which is free from metaphysical elements. In order to use QM to claim that there are acausal events, you have to pick a specific interpretation of QM, and in doing so you have no choice but to introduce metaphysics.

I think that in order for us to have experiences, our minds must be structured in such a way that we experience linear time where it appears to us that all events have causes. Whether they really do all have causes, whether there are acausal quantum events, or whether there is a seperate form of "quantum causality" which is hidden from us rather depends on which metaphysics you attach to the maths of QM.

 

[Interesting Ian]

I was hoping you could provide us with examples in your own words.

"All things have a cause" looks to me like a claim that must be based on some empirical experience of things and causes, and it is certainly not a belief that is necessarily true because we are experiencing the world.

Is there a better example to be had?

This is a good example although perhaps less than ideally expressed. Experience doesn't tell you that all things have a cause because we have not experienced all possible things. We infer that all things have a cause from induction. But the validity of induction itself is a priori synthetic premise.

So I would express it as the universality of physical laws.

 

[Kevin_Lowe]

I'd rather stick to examples given by others. I'm not sure I can think of any better ones. Kant gives lots of others, but in order to explain them I'd need to write an essay rather than make a post. So I am giving the simple examples that come up in books trying to explain what Kant meant. Sorry if that's not helpful, but Critique of Pure Reason is full of all sorts of jargon which I can't use without explaining what it means, and explaining what it means requires starting from the beginning of Kant and trying to explain pretty much all of it. Which is beyond me.

Surely if you understand this jargon you can translate it into regular expressions for us? I find that when I am grappling with a tricky bit of philosophy it often helps to try to put it in the simplest possible terms, so it might well be good for you as well as good for us if you gave it a go.

Well, QM has thrown a spanner in the works of this example. An interesting spanner - since the very thing which seems to now be suggesting that maybe there are acausal events is itself deeply controversial on the grounds that it appears to be impossible to provide an account of what it means which is free from metaphysical elements. In order to use QM to claim that there are acausal events, you have to pick a specific interpretation of QM, and in doing so you have no choice but to introduce metaphysics.

If events that are acausal in the relevant sense are observable fact, I do not see how you need to invoke metaphysics to disprove the claim that "everything has a cause".

I think that in order for us to have experiences, our minds must be structured in such a way that we experience linear time

I am not sure what you might mean by non-linear time, so I am not sure whether this is a meaningful claim or a meaningless claim.

where it appears to us that all events have causes.

To the extent that's true it's only true in the same sense that it appears to us that all psychics are frauds, which is the sense in that we have looked and we haven't found a counterexample yet. We don't know a priori that no counterexample exists or has ever existed.

Whether they really do all have causes, whether there are acausal quantum events, or whether there is a seperate form of "quantum causality" which is hidden from us rather depends on which metaphysics you attach to the maths of QM.

It seems to me that this is the same argument as "doubting religion is a religious belief". I we accept that questioning the value of a claimed bit of metaphysics is in itself metaphysics, then it's tautologically true that we all engage in metaphysics. I don't think we should accept that premise though.