The Intuition/Deduction Thesis

What’s that all about?

~ Rationalism vs. Empiricism / The Stanford Encyclopedia of Philosophy

The Intuition/Deduction Thesis

The Intuition/Deduction thesis claims that we can know some propositions by intuition and still more by deduction.

Many empiricists (e.g., Hume 1748) have been willing to accept the thesis so long as it is restricted to propositions solely about the relations among our own concepts.
We can, they agree, know by intuition that our concept of God includes our concept of omniscience.
Just by examining the concepts, we can intellectually grasp that the one includes the other.

The debate between rationalists and empiricists is joined when the former assert, and the latter deny, the Intuition/Deduction thesis with regard to propositions that contain substantive information about the external world.

Rationalists, such as Descartes, have claimed that we can know by intuition and deduction that God exists and created the world, that our mind and body are distinct substances, and that the angles of a triangle equal two right angles, where all of these claims are truths about an external reality independent of our thought.

One defense of the Intuition/Deduction thesis assumes that we know some substantive external world truths, adds an analysis of what knowledge requires, and concludes that our knowledge must result from intuition and deduction.

Descartes claims that knowledge requires certainty and that certainty about the external world is beyond what empirical evidence can provide.
We can never be sure our sensory impressions are not part of a dream or a massive, demon orchestrated, deception.
Only intuition and deduction can provide the certainty needed for knowledge, and, given that we have some substantive knowledge of the external world, the Intuition/Deduction thesis is true.
As Descartes tells us, “all knowledge is certain and evident cognition” (1628, Rule II, p. 1) and when we “review all the actions of the intellect by means of which we are able to arrive at a knowledge of things with no fear of being mistaken,” we “recognize only two: intuition and deduction” (1628, Rule III, p. 3).

This line of argument is one of the least compelling in the rationalist arsenal.

First, the assumption that knowledge requires certainty comes at a heavy cost, as it rules out so much of what we commonly take ourselves to know.
Second, as many contemporary rationalists accept, intuition is not always a source of certain knowledge.
The possibility of a deceiver gives us a reason to doubt our intuitions as well as our empirical beliefs.
For all we know, a deceiver might cause us to intuit false propositions, just as one might cause us to have perceptions of nonexistent objects.

Descartes’s classic way of meeting this challenge in the Meditations is to argue that we can know with certainty that no such deceiver interferes with our intuitions and deductions. They are infallible, as God guarantees their truth.

The problem, known as the Cartesian Circle, is that Descartes’s account of how we gain this knowledge begs the question, by attempting to deduce the conclusion that all our intuitions are true from intuited premises.
Moreover, his account does not touch a remaining problem that he himself notes (1628, Rule VII, p. 7): Deductions of any appreciable length rely on our fallible memory.

A more plausible argument for the Intuition/Deduction thesis again assumes that we know some particular, external world truths, and then appeals to the nature of what we know, rather than to the nature of knowledge itself, to argue that our knowledge must result from intuition and deduction. Leibniz (1704) tells us the following.

The senses, although they are necessary for all our actual knowledge, are not sufficient to give us the whole of it, since the senses never give anything but instances, that is to say particular or individual truths.
Now all the instances which confirm a general truth, however numerous they may be, are not sufficient to establish the universal necessity of this same truth, for it does not follow that what happened before will happen in the same way again. …
From which it appears that necessary truths, such as we find in pure mathematics, and particularly in arithmetic and geometry, must have principles whose proof does not depend on instances, nor consequently on the testimony of the senses, although without the senses it would never have occurred to us to think of them… (1704, Preface, pp. 150–151)

Leibniz goes on to describe our mathematical knowledge as “innate,” and his argument may be directed to support the Innate Knowledge thesis rather than the Intuition/Deduction thesis.

For our purposes here, we can relate it to the latter, however: We have substantive knowledge about the external world in mathematics, and what we know in that area, we know to be necessarily true.

Experience cannot warrant beliefs about what is necessarily the case.
Hence, experience cannot be the source of our knowledge. The best explanation of our knowledge is that we gain it by intuition and deduction.

Leibniz mentions logic, metaphysics and morals as other areas in which our knowledge similarly outstrips what experience can provide.

Judgments in logic and metaphysics involve forms of necessity beyond what experience can support.

Judgments in morals involve a form of obligation or value that lies beyond experience, which only informs us about what is the case rather than about what ought to be.

The strength of this argument varies with its examples of purported knowledge.

Insofar as we focus on controversial claims in metaphysics, e.g., that God exists, that our mind is a distinct substance from our body, the initial premise that we know the claims is less than compelling.

Taken with regard to other areas, however, the argument clearly has legs.

We know a great deal of mathematics, and what we know, we know to be necessarily true.
None of our experiences warrants a belief in such necessity, and we do not seem to base our knowledge on any experiences.
The warrant that provides us with knowledge arises from an intellectual grasp of the propositions which is clearly part of our learning.
Similarly, we seem to have such moral knowledge as that, all other things being equal, it is wrong to break a promise and that pleasure is intrinsically good.
No empirical lesson about how things are can warrant such knowledge of how they ought to be.

This argument for the Intuition/Deduction thesis raises additional questions which rationalists must answer.

Insofar as they maintain that our knowledge of necessary truths in mathematics or elsewhere by intuition and deduction is substantive knowledge of the external world, they owe us an account of this form of necessity.
Many empiricists stand ready to argue that “necessity resides in the way we talk about things, not in the things we talk about” (Quine 1966, p. 174).
Similarly, if rationalists claim that our knowledge in morals is knowledge of an objective form of obligation, they owe us an account of how objective values are part of a world of apparently valueless facts.
Perhaps most of all, rationalist defenders of the Intuition/Deduction thesis owe us an account of what intuition is and how it provides warranted true beliefs about the external world.
What is it to intuit a proposition and how does that act of intuition support a warranted belief?
Their argument presents intuition and deduction as an explanation of assumed knowledge that can’t — they say — be explained by experience, but such an explanation by intuition and deduction requires that we have a clear understanding of intuition and how it supports warranted beliefs.

Metaphorical characterizations of intuition as intellectual “grasping” or “seeing” are not enough, and if intuition is some form of intellectual “grasping,” it appears that all that is grasped is relations among our concepts, rather than facts about the external world.

Moreover, any intellectual faculty, whether it be sense perception or intuition, provides us with warranted beliefs only if it is generally reliable.

The reliability of sense perception stems from the causal connection between how external objects are and how we experience them.

What accounts for the reliability of our intuitions regarding the external world?
Is our intuition of a particular true proposition the outcome of some causal interaction between ourselves and some aspect of the world?
What aspect?
What is the nature of this causal interaction? That the number three is prime does not appear to cause anything, let alone our intuition that it is prime.

These issues are made all the more pressing by the classic empiricist response to the argument. The reply is generally credited to Hume and begins with a division of all true propositions into two categories.

All the objects of human reason or inquiry may naturally be divided into two kinds, to wit, “Relations of Ideas,” and “Matters of Fact.”
Of the first are the sciences of Geometry, Algebra, and Arithmetic, and, in short, every affirmation which is either intuitively or demonstratively certain.
That the square of the hypotenuse is equal to the square of the two sides is a proposition which expresses a relation between these figures.
That three times five is equal to half of thirty expresses a relation between these numbers.

Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would forever retain their certainty and evidence.

Matters of fact, which are the second objects of human reason, are not ascertained in the same manner, nor is our evidence of their truth, however great, of a like nature with the foregoing.

The contrary of every matter of fact is still possible, because it can never imply a contradiction and is conceived by the mind with the same facility and distinctness as if ever so conformable to reality. (Hume 1748, Section IV, Part 1, p. 40)

Intuition and deduction can provide us with knowledge of necessary truths such as those found in mathematics and logic, but such knowledge is not substantive knowledge of the external world. It is only knowledge of the relations of our own ideas.

If the rationalist shifts the argument so it appeals to knowledge in morals, Hume’s reply is to offer an analysis of our moral concepts by which such knowledge is empirically gained knowledge of matters of fact.

Morals and criticism are not so properly objects of the understanding as of taste and sentiment.

Beauty, whether moral or natural, is felt more properly than perceived.

Or if we reason concerning it and endeavor to fix the standard, we regard a new fact, to wit, the general taste of mankind, or some other fact which may be the object of reasoning and inquiry. (Hume 1748, Section XII, Part 3, p. 173)

If the rationalist appeals to our knowledge in metaphysics to support the argument, Hume denies that we have such knowledge.

If we take in our hand any volume — of divinity or school metaphysics, for instance — let us ask, Does it contain any abstract reasoning concerning quantity or number? No.
Does it contain any experimental reasoning concerning matter of fact and existence? No.
Commit it then to the flames, for it can contain nothing but sophistry and illusion. (Hume 1748, Section XII, Part 3, p. 173)

An updated version of this general empiricist reply, with an increased emphasis on language and the nature of meaning, is given in the twentieth-century by A. J. Ayer’s version of logical positivism.

Adopting positivism’s verification theory of meaning, Ayer assigns every cognitively meaningful sentence to one of two categories: either it is a tautology, and so true solely by virtue of the meaning of its terms and provides no substantive information about the world, or it is open to empirical verification. There is, then, no room for knowledge about the external world by intuition or deduction.

There can be no a priori knowledge of reality. For … the truths of pure reason, the propositions which we know to be valid independently of all experience, are so only in virtue of their lack of factual content … [By contrast] empirical propositions are one and all hypotheses which may be confirmed or discredited in actual sense experience. [Ayer 1952, pp. 86; 93–94]

The rationalists’ argument for the Intuition/Deduction thesis goes wrong at the start, according to empiricists, by assuming that we can have substantive knowledge of the external world that outstrips what experience can warrant.

We cannot.

This empiricist reply faces challenges of its own.

Our knowledge of mathematics seems to be about something more than our own concepts.
Our knowledge of moral judgments seems to concern not just how we feel or act but how we ought to behave.
The general principles that provide a basis for the empiricist view, e.g. Hume’s overall account of our ideas, the Verification Principle of Meaning, are problematic in their own right.
In various formulations, the Verification Principle fails its own test for having cognitive meaning.
A careful analysis of Hume’s Inquiry, relative to its own principles, may require us to consign large sections of it to the flames.

In all, rationalists have a strong argument for the Intuition/Deduction thesis relative to our substantive knowledge of the external world, but its success rests on how well they can answer questions about the nature and epistemic force of intuition made all the more pressing by the classic empiricist reply.

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