Apparently, Parsons leaves the epistemological status of intuitive knowledge eventually unaccounted for. He categorises it as `intuitively evident’ but this turns out to be a vacuous category.
In view of this unsatisfactory result I must go beyond what is developed in the book, to finally account for the epistemological status of intuitive knowledge. It seems to me still sufficiently faithful to Parsons’ project although it does not fit perfectly into his epistemological categories. The outlet suggests itself if one recalls that intuitive knowledge is grounded in intuition-of, which Parsons again thinks of as quasi-perception. The nearby answer to the epistemological status of intuitive knowledge would therefore be to give it the evidential status of quasi-perception.
On this view, the axioms of intuitive arithmetic would not fall into the intrinsically plausible anymore. The category of intrinsic plausibility could then be left to self-evident, holistic and supposedly analytic truths. Thus, the epistemology of Parsons’ arithmetic would sufficiently differ from rationalist, Quinean and logicist accounts. Moreover, presuming that Parsons’ bridge from genuine to quasi-perception is strong enough to preserve evidence, intuitive knowledge would inherit the exceptional epistemic status of perception, in accord with Parsons’ talk of arithmetic’s high evidential status [2008, p.333].
This simple solution faces various obstacles. Most saliently, it contradicts to Parsons’ explicit categorisation of arithmetic as intrinsically plausible [2008, p.332 ]
Undoubtedly the axioms of arithmetic are intrinsically plausible
Considering how permissive Parsons tends to be with his terms I would not consider this difference unsurmountable. The text does not give compelling reason why perceptual evidence could not fulfil the function required from intuitive arithmetical knowledge. Because perception in general is of buck-stopping quality, it would certainly provide the uncontested principles required for arithmetic reasoning.
It may be demurred, however, whether the quasi-perception Parsons establishes in Chapter 5 falls under what he calls `perception’ when developing his categories. I do not, however, insist on this but would introduce a fourth class of buck-stopping principles. Thus, intuitive arithmetic would fall into a epistemological category of its own genuine kind. This would not, however, collapse again into a vacuous category, because what is intuively known is merely a subclass of what is intuited on the basis of quasi-perception.
