[hist-analytic] Frederick's conception of the A Priori

Danny Frederick danny.frederick at tiscali.co.uk
Mon Mar 30 11:26:19 EDT 2009

Hi Roger,

Sorry for the delay, but life got in the way.

You are right that I attempted to demarcate a priori from empirical
knowledge, rather than a priori from empirical propositions. That was
deliberate. The reasons are given in Popper's 'Logic of Scientific
Discovery.' Briefly, they are as follows (this is a free rendering and the
examples are mine - if anyone wants page references to what Popper actually
says, let me know, and I'll look them up).

The first step in Popper's discrimination of science from metaphysics, logic
and mathematics is to distinguish empirically falsifiable propositions from
the rest. A proposition is empirically falsifiable if it is inconsistent
with an inter-subjectively testable observation statement.

However, Popper points out that this does not give us a demarcation between
empirical and a priori propositions. For instance, 'All swans are white' is
empirically falsifiable because it is inconsistent with the (false)
observation statement 'There is a black swan sitting on Danny's lap.' But
Newton's first law is not falsifiable. It says (to put it simply) that any
body that is accelerating is being acted on by a force. To falsify this I
need a statement of the form 'This accelerating body is not being acted on
by a force.' But the latter is not an observation statement. The fact that
there is no observable force acting on the body (such as someone pushing it)
does not exclude there being a non-observable force (such as gravity) acting
on it. To put it another way: the observation statement, 'this body is not
being acted on by any observable force,' is not inconsistent with Newton's
first law; and nor is any other observation statement. (Remember here that
'observation statement' = statement that people can agree upon by making
inter-subjectively available observations.)

But if we combine Newton's first law with the rest of his theory, along with
other theories about initial conditions, we will get a system of statements
that is falsifiable. So a non-falsifiable proposition may be part of a
falsifiable system of statements; and it may thus be a part of science.

It follows from this, as Popper explains, that statements which are one day
regarded as metaphysical (because they are non-falsifiable) may at a later
date become part of empirical science. This will happen if the piece of
metaphysical speculation concerned gets linked up with other hypotheses so
that the overall set becomes falsifiable. This has happened many times in
the history of science. One example he gives is atomism.

If I remember right, Popper suggests that some bits of metaphysics are
destined to remain metaphysical, such as 'there is a God.' But if he does
suggest that, he seems to be mistaken. For I need only combine that
proposition with

'If there is a God, then all swans are white'

to get an empirically falsifiable statement.

So a general distinction between empirical and non-empirical propositions
does not make sense. But we can, I think, distinguish empirical and
non-empirical knowledge, in the ways I indicated before. That is, a piece of
knowledge is empirical if it is empirically falsifiable, otherwise it is
not. How do systems of statements become knowledge and thus become eligible
for being either empirical or a priori? Something becomes empirical
knowledge if it has survived severe empirical tests and gives a better
explanation than rival theories (and it holds this position only until a
better theory comes along). Popper, so far as I can recall at the moment,
offered no account of when something becomes a part of a priori knowledge.
It seems clear to me that an account would have be something along the
following lines. A priori knowledge is what is accepted by the experts in
the field as being one of the following:

.	intuitively self-evident;

.	provable (formally or informally) from propositions that are
intuitively self-evident;

.	one of a simple set of axioms from which a large number of
intuitively self-evident propositions can be proved;

.	something which can be proved (formally or informally) from such a
set of axioms.

Not entirely straightforward, I know; and no doubt I have left something
out; but it is just a first stab. The biggest problem with it is that it
does not demarcate acceptable groups of experts. Even if all mystics could
agree on the self-evidence of a set of fundamental mystical truths, those
propositions would not count as part of knowledge. The problem, I think, is
that not many of us trust the mystics; but most of us trust the
mathematicians. But try spelling that out!

I completely reject the idea that there is any connection between what a
proposition says and how it can be justified. First, because nothing can be
justified. Thus what is important is how a proposition can be TESTED. But,
second, because how a proposition can be tested depends upon what other
propositions you combine it with. One and the same proposition can be tested
in very different ways if we combine it with very different sets of
propositions. To take a trivial example, look again at the proposition
'There is a God.' We can combine it with 'If there is a God then all swans
are white,' in which case we start looking for non-white swans. Or we can
combine it with 'If there is a God then all emeralds are green,' in which
case we start looking for non-green emeralds. And so on. (The irrelevance of
God to the empirical propositions that do the work here is not important: I
choose this example for simplicity. I could instead have used Newton's first
law. In fact, I am sure that Popper gives scientific examples to illustrate
the point.)

So, you are right: there are substantial disagreements between us!

Finally, going back to Popper, I said that the first step in his demarcation
of empirical science was the notion of falsifiability as inconsistency with
some (true or false) observations statements. This distinguishes those
systems of statements which are candidates for empirical science from those
that, for the time being at least, are not (i.e., those which are logical,
mathematical or metaphysical). The second step is to distinguish science
from pseudo-science. This is a matter of procedures. Any theory can be saved
from falsification by amending the other statements used to derive empirical
predictions from it or by rejecting any conflicting observation statements.
Such procedures are the mark of pseudo-science, EXCEPT where the
modifications to background knowledge that are made to save a particular
theory themselves lead to novel predictions which survive severe testing.

I mention this because it is astounding that most commentators and critics
somehow fail to notice that Popper's demarcation of science from non-science
has these two components, one logical, the other procedural (and this is
spelt out clearly in 'The Logic of Scientific Discovery').

Best wishes,


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