Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Introduction
- 1 The Principles of Leibnizian Metaphysics
- 2 Leibniz and “The Liar” Paradox
- 3 Hume and Conceivability
- 4 Hume and Rationality
- 5 The Rationale of Kantian Ethics
- 6 Kant on a Key Difference between Philosophy and Science
- 7 Pragmatic Perspectives
- 8 Wittgenstein’s Logocentrism
- 9 Did Leibniz Anticipate Gödel?
- 10 Quantum Epistemology
- 11 Constituting the Agenda of Philosophy
- 12 Philosophy of Science’s Diminished Generation
- 13 A Fallen Branch from the Tree of Knowledge: The Failure of Futurology
- Name Index
3 - Hume and Conceivability
Published online by Cambridge University Press: 10 January 2023
- Frontmatter
- Dedication
- Contents
- Preface
- Introduction
- 1 The Principles of Leibnizian Metaphysics
- 2 Leibniz and “The Liar” Paradox
- 3 Hume and Conceivability
- 4 Hume and Rationality
- 5 The Rationale of Kantian Ethics
- 6 Kant on a Key Difference between Philosophy and Science
- 7 Pragmatic Perspectives
- 8 Wittgenstein’s Logocentrism
- 9 Did Leibniz Anticipate Gödel?
- 10 Quantum Epistemology
- 11 Constituting the Agenda of Philosophy
- 12 Philosophy of Science’s Diminished Generation
- 13 A Fallen Branch from the Tree of Knowledge: The Failure of Futurology
- Name Index
Summary
Philosophers, even the best of them, sometimes take too much for granted and try to build ambitious structures on weak foundations. Purporting to secure their conclusions by rigorous reasonings, they actually take for granted far more than the available information warrants.
An instructive example of this is afforded by the following passage from David Hume's Dialogue Concerning National Religion:
I shall begin with observing, that there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no being, whose existence is demonstrable. I propose this argument as entirely decisive, and am willing to rest the whole controversy upon it. (Op. cit., Pt. 1.)
Close scrutiny shows that Hume's contention is very problematic.
To elucidate Hume's line of reasoning, let us press a few items of symbolic machinery into service for the sake of precision in formulation and analysis. Let “p,” “q,” etc., serve as propositional variables, let “∼” represent negation, “&” conjunction, “→” logical entailment, and let “ξ” represent the impossible (or self-contradictory). Furthermore, let “E (p)” serve as an abbreviation for “ ‘p’ asserts existence,” “C (p)” for “ ‘p’ is conceivable,” and “D (p)” for “ ‘p’ is demonstrable.” Hume's argument can now be formulated as follows:
Premiss 1: Nothing is demonstrable, unless the contrary implies a contradiction (i.e., is impossible).
(P1) D (p) → (∼p → ξ)
Premiss 2: Nothing, that is distinctly [coherently] conceivable, implies a contradiction (i.e., is impossible).
(P2) C (p) → (∼p → ξ)
Premiss 3: Whatever we conceive as existent, we can also conceive as nonexistent.
(P3) C (E (p)) → C (∼E (p))
Given these premisses, can one demonstrate Hume's thesis that there is no (coherently conceivable) being whose existence is demonstrable, namely:
(H) C (E (p)) → D (E (p))?
We now reason as follows.
By (P1) we have
∼(∼p → ξ) → ∼D (p)
By substituting E (p) for p, we obtain
(T1) ∼(∼E (p) → ξ) → ∼D (E (p))
To obtain Hume's conclusion (H ) it now suffices to show that:
C (E (p)) → ∼(∼E (p) → ξ)
But we already have
(P3) C (E (p)) → C (∼E (p))
So what still we need is:
(T3) C (∼E (p)) → ∼(∼E (p) → ξ)
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- Ventures in Philosophical History , pp. 29 - 34Publisher: Anthem PressPrint publication year: 2022