Addison Ellis

What Is A Priori Knowledge

[W]e will understand by a priori cognitions not those that occur independently of this or that experience, but rather those that occur absolutely independently of all experience. Opposed to these are empirical cognitions, or those that are possible only a posteriori, i.e., through experience.... Experience teaches us, to be sure, that something is constituted thus and so, but not that it could not be otherwise. First, then, if a proposition is thought along with its necessity, then it is an a priori judgment;.... Second: Experience never gives its judgments true or strict but only assumed and comparative universality (through induction), so properly it must be said: as far as we have perceived, there is no exception to this or that rule. Thus if a judgment is thought in strict universality, i.e., in such a way that no exception is allowed to be possible, then it is not derived from experience, but is rather valid absolutely a priori.... Necessity and strict universality are therefore secure indicators (Kennzeichen) of an a priori cognition, and also belong together inseparably. But since in their use it is sometimes easier to show the empirical limitation in judgments than contingency in them, or is often more plausible to show the unrestricted universality that we ascribe to a judgment than its necessity, it is advisable to employ separately these two criteria, each of which is infallible.

Why Logic Must Be Transcendental

[The logic of the general use of the understanding] contains the absolutely necessary rules of thinking, without which no use of the understanding takes place, and it therefore concerns these rules without regard to the difference of the objects to which it may be directed.... Now general logic is either pure or applied logic. In the former we abstract from all empirical conditions under which our understanding is exercised.... A general but pure logic therefore has to do with strictly a priori principles, and is a canon of the understanding and reason, but only in regard to what is formal in their use, be the content what it may.... A general logic, however, is called applied if it is directed to the rules of the use of the understanding under the subjective empirical conditions that psychology teaches us.... In general logic the part that is to constitute the pure doctrine of reason must therefore be entirely separated from that which constitutes applied (though still general) logic. The former alone is properly science.... In this therefore logicians must always have two rules in view. 1) As general logic it abstracts from all contents of the cognition of the understanding and of the difference of its objects, and has to do with nothing but the mere form of thinking. 2) As pure logic it has no empirical principles, and thus draws nothing from psychology.... It is a proven doctrine, and everything in it must be completely a priori.

Philosophical Intuitions, Scientific Naturalism, and The Mathematico-Centric Predicament

[H]ow does mathematical language function? Does it relate the world in the same ways as the language of natural science? What happens when human beings come to understand mathematical theories? How does mathematics work in various kinds of applications? And so on. To answer these questions, [the scientific- naturalist philosopher of mathematics] must face many of the metaphysician’s concerns: do mathematical entities exist, and if so, what is the nature of that existence? Are mathematical claims true, and if so, how do humans come to know this? These are not detached, extra-scientific pseudo-questions, but straightforward components of our scientific study of human mathematical activity, itself part of our scientific investigation of the world around us.

The Benacerraf Dilemma Extended and Generalized

These considerations bring us up to the problem: In what sense is logic something sublime? For there seemed to pertain to logic a peculiar depth — a universal significance. Logic lay, it seemed, at the bottom of all the sciences. For logical investigation explores the nature of all things. It seeks to see to the bottom of things and is not meant to concern itself whether what actually happens is that or that. It takes its rise, not from an interest in the fact of nature, nor from a need to grasp causal connexions: but from an urge to understand the basic, or essence, of everything empirical.

Parsons, Kantian Structuralism, and Kantian Intuitionism

The question is how it is possible for a priori intuition to be “of” objects that are not given a priori. Kant’ own solution to the puzzle... appeals to the idea that a priori intuition contains only the form of our sensibility. This evidently removes the causal dependence of intuition on the object. It is a nice question what is left of the characterization of intuition that gives rise to the puzzle. Kant’ solution seems to allow the phenome- nological presence of an object to be preserved, but it is a further question whether what one has is a representation of a physical object, not individually identified and not really present, or a representation of a mathematical object. The former is not ruled out by the a priori character of pure intuition, as the “presence” might be that characteristic of imagination rather han sense. In fact, a number of passages in Kant indicate that just that is his position. Kant’ puzzle may have force for us, but we are not likely to accept the position that pure intuition contains only the form of sensibility, a central part of Kant’ transcendental idealism, at least not as Kant understood it.

Introduction: The Old Rationalism and the New Rationalism

The philosophical debate about the possibility of authentic a priori knowledge, that is, non-stipulative, non-trivial knowledge of the way the world necessarily is, obtained sufficiently independently of any and all sense-experiential episodes and/or contingent natural facts, is no less important today than it was when Plato posited in the Meno that we are able to have such knowledge owing to a pre-natal close encounter that our disembodied souls had with the Forms, and when Descartes posited in the Meditations on First Philosophy that such knowledge is infallible because guaranteed by a non-deceiving God. Of course, neither the platonic story nor the Cartesian story about our purported a priori abilities has many adherents today. Nevertheless, a large majority of philosophers (71.1 percent, according to a recent PhilPapers survey1) do indeed believe that a priori knowledge is really possible.

Rational Intuitions and the Irrelevance of Experimental Philosophy

Philosophical intuition. .. is e piste mo logically useless, since it can be calibrated only when it is not needed. Once we are in a position to identify artifacts and errors in intuition, philosophy no longer has any use for it. Moreover, the most plausible account of the origins of philosophical intuitions is that they derive from tacit theories that are very likely to be inaccurate. There is a sense, then, in which philosophical intuitions can always be “explained away”: when a dispute arises, I can always, with some plausibility, suppose your intuitions are the artifacts of bad tacit theory. This is a game everyone can play, and I think we should all play it. We should, that is, dismiss philosophical intuitions as epistemologically valueless.

What Are Intuitions

One apparently distinctive feature of current methodology in the broad tradition known as “analytic philosophy” is the appeal to intuition. Crude rationalists postulate a special knowledge- generating faculty of rational intuition. Crude empiricists regard “intuition” as an obscurantist term for folk prejudice, a psychological or social phenomenon that cannot legitimately constrain truth-directed inquiry. Linguistic or conceptual philosophers treat intuitions more sympathetically as the deliverances of linguistic or conceptual competence.... [T]he common assumption of philosophical exceptionalism is false. Even the distinction between the a priori and the a posteriori turns out to obscure underlying similarities. Although there are real methodological differences between philosophy and the other sciences, as actually practiced, they are less deep than is often supposed. In particular, so-called intuitions are simply [armchair] judgments (or dispositions to [armchair] judgment); neither their content nor the cognitive basis on which they are made need be distinctively philosophical.

Rationalism Lost: The Original Benacerraf Dilemma

I who erewhile the happy garden sung, By one man’s disobedience lost, now sing Recovered Paradise to all mankind, By one man’s firm obedience fully tried Through all temptation, and the Tempter foiled In all his wiles, defeated and repulsed, And Eden raised in the waste wilderness.