Against Pure A Priori-ism

In a recent article for Aeon magazine, Prof. Bruce Russell argues that all our justified beliefs ultimately rest on a priori justification. At first glance, this appears to be quite a claim, for surely some of our justification is a posteriori – how can empirical propositions such as, say, the sun will rise tomorrow, because it has risen in the past (the inductive proposition par excellence) turn out to be justified a priori? Russell argues that even induction is justified a priori – a contentious claim, to say the least, but not an indefensible one. The question of its viability, then, hinges on the quality of the arguments given in its defence. It is important to note at the outset and keep in mind Russell’s definition of a priori justification – this will prove significant later:


There is another kind of justification, that ultimately founds all of our justified beliefs. It is called a priori. What is your justification in believing that 2 + 2 = 4? You are justified because you understand the concepts involved. You understand what all the terms in that simple sum mean and that, as a result, the sum of two and two is four. Philosophers call that sort of justification a priori justification, and describe it as justification independent of experience.

Key to Russell’s position here is the idea of intuition – it would not be an overstatement to say that this is the axis on which his entire position turns:

If a proposition seems true to you simply on the basis of your understanding of it, and not on the basis of empirical evidence, testimony, memory or reasoning, then you are having an intuition in a philosophical sense that it is true. ‘Red is a colour’ seems true to you solely on the basis of your understanding that proposition. That seeming true is a philosophical intuition, and it is what justifies you in believing that red is a colour. Many, but not all, philosophers hold that a priori justification is based on philosophical intuitions.


From his explication of the idea of intuition Russell moves on to say that ‘You might think that a priori justification is limited to trivial propositions such as ‘red is a colour’ or ‘all bachelors are unmarried males’, or to mathematics, but that would be a mistake.’ Again, fairly uncontroversial. However, the next idea that Russell explicates is somewhat more controversial and is worth quoting in full:


I assume that everyone believes that the Sun will rise tomorrow, or more precisely, that the Earth will rotate on its axis once again. But that belief is based on a more basic assumption that often is not made explicit. One version of the principle of induction says: if all observed As have been Bs, then it is reasonable to believe that all As are Bs, and that the next A we observe will be a B. For many years, people have observed the Sun go down and then rise in the morning. So the principle of induction allows us to conclude that it is reasonable to believe that the Sun will rise tomorrow. But what justifies us in believing the principle of induction? Because we understand the concept justification, we have a philosophical intuition that it is true and that intuition provides the justification. So the principle of induction is justified a priori.


The argument appears to run something like this:


  1. A belief is justified when we have an intuition – when it ‘just seems’ that it’s true
  2. We have an intuition that induction is reasonable/true
  3. Therefore we are justified in accepting induction
  4. Induction is justified a priori


Astute readers will hopefully have an intuition that something, somewhere, is amiss here. I hope to show in the next few paragraphs where, exactly, something is amiss.


You are justified because you understand the concepts involved. You understand what all the terms in that simple sum mean and that, as a result, the sum of two and two is four. Philosophers call that sort of justification a priori justification, and describe it as justification independent of experience.


At first glance, what one notices is that this is only one aspect of being a priori: what we really have here is a definition of analyticity (and mathematics is strictly speaking not purely analytic: no analysis of the meanings of the terms in a given mathematical proposition [2+2=4], for example demonstrates the truth of that proposition), only taken to be the sum total of what it is to be a priori, and not all a priori concepts are analytic. Synthetic a priori propositions and assertions are, obviously enough, a priori and while not being analytic. Let’s take, however, this definition (problems and all) as being accurate for the sake of argument.


What follows from this, if intuitions-as-justification are, as they are by Russell’s examples and explication, purely analytic, then the only things we can intuit on this scheme are analytic propositions, because only analytic propositions are such that they can be seen as true in a ‘just seems’ sort of way. I can ‘just see’ that ‘all bachelors are unmarried males’, because I have grasped the meanings of the terms – it’s self-evident.


Now, traditional accounts of intuition relating to the a priori are quite strict in insisting that that intuiting only occurs if there is no mediation or sensory input of any kind – that is, the subject knows that p both immediately and without any of the five senses operating (hence the focus on propositions). This was roughly Kant’s position, and critics have pointed out that he never actually explained what he meant by ‘knowledge that is absolutely independent of all experience’. This is generally seen as too strict of a requirement on intuitions and has rightly been recognized as such. Russell, however, appears to want to go to the opposite extreme and make every empirical belief subject to a priori justification – and this seems to be just implausible. There are a number of propositions which can be easily seen to be intuited (or at least, can be argued coherently to be intuited) – analytic propositions, propositions of logic, things of that nature. Russell extends, however, the a priori justification of analytic propositions to non-analytic propositions and even things that aren’t propositions at all, such as induction noted above as well as the inference to the best explanation (IBE):


What justifies us in believing IBE? The same thing that justifies us in accepting the principle of induction. Because we understand the concept justification, we have a philosophical intuition that IBE is true and that intuition provides the justification. As with induction, if we were not justified in accepting IBE, we would not be justified in our beliefs that implicitly rely on it.


Induction and IBE, for Russell, comprise the only two methods there are for acquiring empirical knowledge, and since both methods are justified a priori, all empirical knowledge is justified a priori. This seems, however, quite implausible. Consider:


I am walking down the street, and see a tall man walking towards me. I form the belief ‘that is a tall man’.


What has happened here? I have taken up the propositional attitude ‘belief’ towards the proposition ‘that the tall man is walking towards me’, and take the proposition to be true. Is the justification for this a priori? It is difficult to see how. That the man is tall and walking towards me is itself, self-evident: I see him walking towards me and see that he is tall. The empirical proposition ‘that the tall man is walking towards me’ is itself not analytic proposition, but surely I am justified in believing it to be true, and not on the basis of induction or IBE. According to Russell’s criteria for justification, I am justified by a prioi reasons alone, and yet, there is no plausible way in which I am justified a priori in taking ‘that the tall man is walking towards me’ to be true.


The core of Russell’s argument comes down to this: ‘All of our justified everyday empirical and scientific beliefs are justified either because they rest on the principle of induction or on the principle of IBE.’ For Rusell, both induction and IBE are themselves justified a priori, so any belief we have by way of either is justified a priori. In order to show the falsity of Russell’s position, all that needs to be done is show that some empirical propositions are not acquired by either induction or IBE.


Here’s a more formal explication of my argument against Russell’s theory of a priori justification (R):


  1. Either every empirical belief is justified a priori or it is not
  2. On (R), for this to be true, every empirical belief is acquired either by induction IBE
  3. Not all empirical beliefs are acquired by induction or IBE
  4. Therefore, some empirical beliefs are not justified a priori
  5. Therefore, (R) is false

3 thoughts on “Against Pure A Priori-ism

  1. Rod Lampard June 2, 2018 / 9:42 pm

    When coming generations look back on our current age, they won’t flippantly say, “many THOUGHT (those things that were allowed) were a good idea at the time”, they’ll be forced by the constraint of reason, and conviction of faith, to say with brutal honesty, “many FELT that it was a good idea at the time, and left ALL THOUGHT behind.”


  2. robertleewhite August 21, 2020 / 2:15 pm

    Interesting post! I think I construct things differently than Russell… I’m not convinced we believe the sun will rise tomorrow because of induction, but something closer to an intuitive understanding of Occam’s razor, for instance. However I do think all of logic bottoms out in intuition (I describe this to a degree in this podcast episode of mine: ).
    Probably the first time I realized this was reading Godel, Escher, Bach, when Hofstadter points out that even the most basic principles of logic are ultimately intuitively grasped with no external justification. He gives the example of:
    Rule: If A then B
    Given: A
    Then: B
    Then, in the vignette, a second character asks, “but how do you know that’s the case?”
    So the first character then adds another rule that explicitly defines that basic rule of logic. The second character then asks, “but how do you know *that* rule?”…. ad infinitum.
    So it seems to me that everything going on in our heads can be broken down to:
    1) Sense perception
    2) Organizing and processing that sense perception which is done using, at bottom, intuitively-grasped rules of logic
    So doesn’t that mean intuition, indeed, is the foundation?
    P.S. I discovered this post from


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s