Can what we know be reduced to the descriptions and explanations of the empirical sciences?
Another way to think of this: Is all human knowledge empirical? Of course, everything we can know about derives from contact with external reality. But knowledge only occurs in the brain’s emergent ordering of experience as ‘mind.’
Consider the argument:
All human knowledge is empirical, [because] it derives from contact with empirical reality.
All knowledge derives from contact with empirical reality;
what derives from contact with empirical reality is itself empirical;
All knowledge is empirical.
The first problem is terminological; the “empirical” describing reality is not the same “empirical” describing knowledge. Reality, just as such, is not ’empirical’ (or anything else), it is just what is.
The proper phrase here is “empirical contact with reality” (where “empirical” means ‘sensory experience’ of reality). But once we rephrase this, the problem becomes clear – whatever could we mean by “all knowledge is ‘sensory experience'”? Obviously what we want to say is that “all knowledge is derived from sensory experience,” but then the argument is a tautology:
All knowledge derives from sensory experience; whatever derives from sensory experience is (derived from) sensory experience;
therefore all knowledge is (derived from) sensory experience.
One way to see this problem is that the “empirical” of “all knowledge is empirical” is part of an assertion of empiricist epistemology, while the “empirical” of “contact-with-reality” is a common language description of experience with reality. So what we really want to say is, “all knowledge derives (originates from, is developed out of) sensory experience.” After this we can then make a case for empiricism; but that won’t get us a case that ‘all knowledge reduces to what can be described in the empirical sciences.’
Just as I can grant that mathematics originated from counting, I can grant that all knowledge originates from (in the sense that the questions developing knowledge begin with questions about) sensory experience. But as I’ve just made clear, this is not at all the same as saying that “all knowledge is [sensory experience].” That’s just silly. That knowledge originates in sensory experience (via questions about it) makes no claim at all on its later development.
Consider the origin of number, as derived from counting, e.g. “1+1=2.” I know some philosophers do go back to that – but as a problem. The problem is, how do we get from there to complex deductive mathematics? That answer is not at all clear. Algebra is the problem (let alone, for now, calculus, and higher order mathematics dealing with large numbers, or say, n-dimensional geometry), not simple addition. *
Talking about adding apples as a basis of higher math is like discussing Newton’s law of gravity in terms of an apple falling on his head.
Newton himself said that he deduced the law of gravity. And while the physical issue involved actual masses, e.g., the moon and the earth; and while, had the movements of these spheres not tallied with the law, the hypothesis would have been falsified; the mathematical deduction itself involves abstract conceptual entities, not empirical or physical spheres: “Every point mass attracts every single other point mass by a force pointing along the line intersecting both points.”
Now, physics seems to me to be a complex interweaving of mathematical deductions and empirical testing; that’s exactly one of the things that makes epistemology of science, and the philosophy of science in general, so fascinating. Some want deduction, empirical testing, knowledge about abstract entities, knowledge about physical entities, and the sometimes difficult trail that somehow connects them all, to reduce to the same basic stuff. I think they would need, at the very least, engage in the epistemological problems directly before making such a claim.
No science can survive productively on the basis of a primitive empiricism (which is really little different from naive Realism trashed by various philosophers during the Middle Ages).
Such labels are important as markers for positions in a field of competing claims. They help us understand what claims relate to others, and what their issues are. John Stuart Mill once claimed that all mathematics were reducible to counting (he was quite a sophisticated empiricist, but he didn’t understand mathematics). And Hegel also claimed that all knowledge was essentially acquired one way, through dialectics (through which he once deduced that there could be only seven planets in the solar system). Basically the claim that all knowledge reduces to the empirical is a variant (and reductive) Millsian position totalizing knowledge in a manner similar to Hegelian claims for the dialectic. I don’t think Mill would appreciate that (and I know Hegel wouldn’t).
It is sometimes claimed that our knowledge of reality is unified through the sciences, a seamless whole. What’s odd about this is that it is rarely argued, simply asserted or implied, in variant ways.
Mathematics is primarily a deductive reasoning. It is all in the mind. Even geometry: Two dimensional forms cannot (as far as we know) exist in the 3+1 dimensional reality in which we actually live. Their reality is entirely of human mental construction. Their measurements, and the various maths we use to describe these measurements, are also a matter of mental construction. That these mental constructions often overlap physical reality is fortuitous – but not necessary: either as point of origin or as final culmination. They are simply useful tools for understanding the world in which we live; they are not that world.
Because mathematicians deal with formulas (derived or posited deductively), and physicists also work with theoretical postulates (not axioms in the strict mathematical sense, BTW), in mathematical formulas, derived from previous hypothesis and empirical research, does not at all mean that mathematicians and physicists are doing the same things – it means precisely that they’re not.
So basically, in the claim that all knowledge reduces to description and explanation in the empirical sciences, we have an incomplete philosophical argument for a primitive empiricism offered as a totalization of knowledge based on shaky premises and lacking historical accountability or epistemological insight.
This is not convincing, I’m sorry.
* BTW, here’s another problem equating number with counting, and it is simpler, and more definitive, than the problem of higher mathematics: zero. Zero doesn’t count anything, it doesn’t even count ‘nothing.’ It can not be derived from sensory experience. [In fact it was derived from Hindu/Jainist metaphysics.] Yet it’s function in mathematics is undeniable. Problems such as this have to be accounted for, not “1+1=2” – in whatever universe we like to imagine.