CONCEIVABILITY AND MODAL KNOWLEDGE
Hume: “’Tis an establis’d maxim in metaphysics That whatever the mind clearly conceives
includes the idea of possible existence, or in other words, that nothing we imagine is absolutely
Samuel Clarke, accepted this maxim (What is conceivable, is possible) as did Richard Price, and
Christian Wolff, but they also accepted the principle that What is inconceivable, is impossible.
1. Hume’s Maxim Explained
• ‘Possibility’, in the Maxim, attaches primarily to statements or propositions, not to
objects. It is statements that are possible––or impossible (and hence the Maxim deals
with possibility de dicto).
• ‘Possibility’ is broadly logical possibility
• One conceives a statement, when one can depict to oneself a consistent and coherent
scenario in which that statement is true, or, alternatively, when one can tell to oneself a
consistent and coherent story in which it is true.
Hume’s maxim: if you can depict to yourself a consistent and coherent scenario in which
a certain proposition P is true, then you may infer that P is possible in the metaphysical
sense of ‘possible’.
The counter positive of Hume’s Maxim is A: What is impossible, is inconceivable.
Let us call the following principle B: What is inconceivable, is impossible. (This is the other
principle that Clarke, Price and Wolff accepted). The counter positive of this is principle C: What
is impossible is inconceivable.
2. Reid’s Official Criticism of the Maxim
(1) The Maxim can be explained in different ways:
M1 Every proposition of which one understands the meaning is possible.
M2 Every proposition one can conceive to be true, is possible.
M2a Every proposition one can believe, is possible.
M2b Every proposition one judges to be possible, is possible.
M2c Every proposition such that one can consistently and coherently depict to
oneself a scenario in which it is true, is possible.
(2) when we conceive a necessarily true proposition, we also conceive an impossible one, i.e.
one that is necessarily false. This means that we can, and in fact do, conceive impossible
propositions, which shows that the Maxim is false.
(3) In order to prove a theorem to be impossible, mathematicians must at least conceive the
theorem. Therefore, to conceive of a theorem doesn’t licence one to conclude that the theorem is
(4) The practise of Reductio arguments denies the Maxim.
We are able to understand the meaning of statements that express impossible propositions. But
the maxim, properly understood, doesn’t deny this. For what it says is that propositions such that
one can depict to oneself a scenario in which they are true, are possible.
3. Reid’s Actual Acceptance of the Maxim
In the chapter “Of Touch” in the Inquiry, Reid aks us to imagine a person who (a) is blind, (b)
has lost all the experience, habits and notions he had got by touch, i.e. he has no conception of
the extension of his own body, nor of any other, (c) has been stripped of all his ‘hardwiring’,
especially of that segment of his constitution that, upon his having tactile sensations, occasions
the conception of extension, and (d) has the faculty of reasoning. About this person, Reid asks: Is
it possible that this person is given his tactile sensations, and yet will not obtain the notion of
extension? Reid’s answer is clearly “Yes, that is possible.”
The passage suggests that Reid reasons as follows: “I cannot conceive how certain tactile
sensations convey the notion of extension”, therefore “It is impossible that those sensations
convey the notion of extension”. This is the Maxim applied!
4. Cases Where We Are Led Astray By the Maxim?
The fact that Reid’s criticisms against Hume’s maxim don’t cut ice, and that he himself employs
it, doesn’t, of course, imply that the maxim is sound. Many think it is not. Tamar Szabó Gendler
and John Hawthorne, for example, suggest that “it is uncontroversial that there are cases where
we are misled” by the application of the Maxim. They refer to
• Greek philosophers who found it conceivable that stars are holes in the sky
• George Berkeley who found it conceivable that the sun, the moon, mountains and all of
the rest of the furniture of the earth are mere bundles of ideas
• various mathematicians who have found it conceivable that Goldbach’s conjecture is
• various metaphysicians who have found it conceivable that the Morningstar is not the
Eveningstar, or that water is not H2O
5. The Limited but Real Value of the Maxim
Three different sorts of situations:
I: situations where it is clear that we can conceive a scenario in which a certain proposition p is
• William the Silent died of natural causes.
II: situation where it is clear that we cannot conceive of the truth of a certain statement, a
situation, that is, where it is clear that we cannot depict to ourselves a scenario in which it is true
• John is both taller and shorter than Jack.
• 3 is not prime.
III: situations where it is not clear whether we can conceive of a certain statement, unclear that
we can depict to ourselves situations in which a certain statement is true.
• Transparent iron exists.
• There is a time machine.
The maxim, therefore, is only a limited guide to the modally perplexed.