Can there be true and meaningful synthetic
a priori statements?
Haugeland's view about objective perception illuminates this question, I think. There was an interesting thread three months ago about Kant's
Prolegomena To Any Future Metaphysics. Let me quote this paragraph from Jamalrob:
A few words about a priori and a posteriori. These are about justification, i.e., how we come to know things, so they are epistemological concepts. In the CPR Kant says that “There can be no doubt that all knowledge begins with experience”, but that “although our knowledge begins with experience, it does not follow that it arises from experience.” What this means is that it is experience that calls forth knowledge, not that it is the source. For example, it is in experience that we come to know about cause and effect in the first place, but only because events must be experienced in terms of a prior, independent (pure) concept of the understanding. — jamalrob
This distinction between two ways in which knowledge relates to experience, here marked with the phrases "begins with" and "arises from" is interesting but puzzling. It seems clear that the first way for knowledge to relate to experience ("i.e. "begins with") characterizes this form of knowledge (expressible with
synthetic a priori statements) as a condition for the very possibility of empirical (i.e.
a posteriori) knowledge, and hence for meaningful and contentful "intuitions". Once the conditions for the possibility of such experiences are satisfied, then it is empirical knowledge of particular facts (and particular objects) that can "arise from" experience. This empirical knowledge is expressed with synthetic
a posteriori statements.
The sorts of
synthetic a priori statements that were centrally at issue, in the passages from the
Critique or Pure Reason quoted by Jamalrob above, were statements that express the content of the
pure concepts of the understanding, that is, the Kantian
categories. Those are
a priori concepts that purport to represent the form thought has in virtue of the fact that it relates essentially to intuition while abstracting from the specific empirical contents those intuitions provide. Whatever one might think of the feasibility of such an inquiry into the form of the
pure understanding -- and for a masterful defense and realization, one can refer to Sebastian Rödl's
Categories of the Temporal: An Inquiry into the Forms of the Finite Intellect, HUP, 2012 -- it may still sound incredible that there might be synthetic
a priori statements that aren't
pure in this sense, and that therefore express genuine knowledge about the empirical world, or, more precisely, about determinate domains of empirical objects.
Yet that is exactly what Haugeland's account of objectivity enables us to better understand. Wilfrid Sellars -- whose
Concepts as Involving Laws and Inconceivable Without Them gets credited by Haugeland as anticipatory of some of his own ideas (further developed in his
Truth and Rule Following) -- also defended a broader conception of (inpure)
synthetic a priori truths.
Here is a quote from
Willem A. DeVries' book on Sellars:
"Sellars believes that any conceptual framework,
necessarily, includes valid forms of material inferences. But synthetic
a priori truths are framework relative; there is no set of framework-independent synthetic
a priori truths. The structure of our conceptual framework, which is responsible for our
a priori knowledge and which we often take to reflect articulation of reality itself, is in fact mind-dependent to a significant degree."
The denial of framework independent synthetic
a priori truths is the denial of what Kant argues for, and Rödl seconds, but this isn't my concern here. What is rather interesting, for my present purpose, is the assimilation of
framework dependent synthetic
a priori truths with the expressions of valid forms of
material inferences.
Valid forms of material inferences are inferences that are warranted by the conceptual content of terms involved in the premises and conclusion, rather than being warranted by the (deductive) logical form of those statements alone. Hence, for instance, the truth that
(A) Montreal is north of New York City
can be validly (materially) inferred from the truth that
(B) New York City is south of Montreal.
This inference is materially rather than deductively valid. The inference is valid in virtue of a form of inference that can be made explicit with the use of the synthetic
a priori statement:
(M) "X is south of Y if and only if Y is north of X".
This synthetic
a priori statement is partially constitutive of the meanings (i.e. the conceptual contents) of the relational predicates "... is south of..." and "... is north of...". It may be worth noticing, also, that when this synthetic
a priori statement is furnished as an additional premise, then one
can logically (i.e. deductively) infer (B) from (A) and (M).
To be continued in my next post...