David Hume

David Hume's radical empiricism is constructed upon four core structural axioms:

• The Copy Principle: All ideas (concepts, reflections, abstract thoughts) are faint, secondary copies of primary, vivid impressions (sensory perceptions, direct emotions, visceral desires). Any philosophical term that cannot be traced back to an originating impression is semantically empty.
• Hume's Fork: All objects of human reason or inquiry divide exhaustively into two mutually exclusive domains: 1. Relations of Ideas: Intuitively or demonstratively certain propositions knowable a priori (geometry, algebra, logic). They express definitional identities and cannot be negated without contradiction, but convey no information about physical reality. 2. Matters of Fact: Empirical propositions knowable only a posteriori. Their contraries are always logically conceivable and imply no contradiction; their truth is established solely through experiential verification.
• The Psychological Genesis of Causality: Necessary connection is not an objective property observed in external matter. It is a subjective projection produced by psychological habituation (custom) arising from the observation of spatial contiguity, temporal priority, and constant conjunction.
• The Is-Ought Separation (Hume's Guillotine): Normative statements (ought) cannot be logically deduced from purely descriptive or factual statements (is).

                    [ SENSORY REALITY ]
                             |
                     [ IMPRESSIONS ] (Direct, Vivid)
                             |
                      (Copy Principle)
                             |
                       [ IDEAS ] (Faint Reflections)
                             |
             +---------------+---------------+
             |                               |
  [ Relations of Ideas ]             [ Matters of Fact ]
  (A priori, Analytic)               (A posteriori, Synthetic)
  - Math & Formal Logic              - Physics, History, Biology
  - Certain, Empty of Reality        - Probable, Empirical, Inductive

2.1 The Formalization of the Inductive Gap

Let an empirical observation sequence be denoted as: $$O = \{ (E_1, t_1), (E_2, t_2), \dots, (E_n, t_n) \}$$ where event $A$ is followed by event $B$ across all historical instances $t_1, \dots, t_n$.

Inductive inference posits the universal proposition: $$ orall t > t_n, \quad A(t) ightarrow B(t)$$

Hume demonstrates that this inference requires a mediating premise, the Principle of Uniformity of Nature ($PUN$): $$PUN: ext{The unobserved future will resemble the observed past.}$$

Formal justification of $PUN$: 1. $PUN$ cannot be demonstrated a priori, because $ eg PUN$ implies no logical contradiction: $$ ext{Conceivable}( eg PUN) = ext{True} \implies ext{Analytic}(PUN) = ext{False}$$ 2. $PUN$ cannot be demonstrated a posteriori, because any empirical argument for $PUN$ relies on the validity of induction itself: $$P(PUN \mid O) = f(PUN)$$ This constitutes circular begging of the question (petitio principii). Hence, induction lacks deductive or rational justification.

2.2 Epistemic Calculus of Miracles

In Enquiry Concerning Human Understanding (Section X), Hume formulates the rational criterion for evaluating testimony regarding miracles:

Let $M$ be a purported miraculous event that violates established laws of nature, and $T(M)$ be the testimony affirming $M$. By Bayes' theorem / likelihood ratio: $$ rac{P(M \mid T(M))}{P( eg M \mid T(M))} = rac{P(M)}{P( eg M)} \cdot rac{P(T(M) \mid M)}{P(T(M) \mid eg M)}$$

Because the uniform experience of humanity establishes the natural law $L$, the prior probability of its violation approaches zero: $$P(M) \ll \epsilon \quad (\epsilon o 0)$$

Hume's Maxim:

"No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous than the fact which it endeavors to establish."

$$ ext{Believe } M \iff P( ext{Deception or Error} \mid T(M)) < P(M)$$ Because human deception, perceptual error, and myth-making have high empirical frequency ($P( ext{Error}) \gg 0$), the rational agent must always proportion belief to the greater probability and reject the miracle.

3.1 The Bundle Theory of the Self (Deconstruction of the Cartesian Ego)

CARTESIAN RATIONALISM:
   [ Unified, Indivisible Thinking Substance: RES COGITANS ]
                         |
      +------------------+------------------+
      |                  |                  |
  [ Thought ]       [ Memory ]         [ Volition ]

HUMEAN RADICAL EMPIRICISM:
   ( No underlying substrate / No metaphysical ego )

   t0:  [ Perception 1: Flash of Red ]
   t1:  [ Perception 2: Sensation of Heat ]
   t2:  [ Perception 3: Auditory Tone ]  ===> Bound together solely by
   t3:  [ Perception 4: Memory of Pain ]      Imaginative Association
   t4:  [ Perception 5: Anticipation ]        (Resemblance, Contiguity)

3.2 Hume's Fork: The Bifurcation of Epistemic Justification

                      [ ALL INQUIRIES ]
                              |
       +----------------------+----------------------+
       |                                             |
[ RELATIONS OF IDEAS ]                      [ MATTERS OF FACT ]
- Geometry, Algebra, Logic                  - Physics, History, Chemistry
- Discovered by thought alone               - Dependent on sensory experience
- Negation = Formal Contradiction           - Negation = Logically Conceivable
- Axiomatically Certain                     - Intrinsically Probable
- Invariant across all worlds               - Grounded on Cause & Effect (Custom)

• Stimulation of Kantian Critical Philosophy: Directly spurred Immanuel Kant to author the Critique of Pure Reason (1781) to resolve the skeptical destruction of causality and synthetic a priori judgments.
• Foundation of Modern Bayesian Epistemology: Hume's analysis of testimony and probability laid the direct conceptual framework for Thomas Bayes' 1763 essay on inverse probability.
• Linguistic and Positivist Revolution: Served as the direct ancestor to the Logical Positivism of the Vienna Circle (Schlick, Carnap, Ayer), who formalized the Verification Principle directly from Hume's Fork.
• Anticipation of Cognitive Associationism: Established the three laws of psychological association (Resemblance, Contiguity in time and place, and Cause and Effect), which formed the bedrock of associationist psychology (James Mill, Alexander Bain).

5.1 The Threat of Paralyzing Epistemic Skepticism

By showing that induction has no rational justification, Hume's philosophy theoretically undermines the epistemic authority of empirical science. While Hume maintained that animal custom is sufficient for practical life, his framework struggles to provide a rational demarcation between scientific consensus and superstitious belief.

5.2 Psychologism and Semantic Reductionism

Under the strict Copy Principle, abstract mathematical entities (such as irrational numbers, imaginary numbers, or infinite sets) and theoretical physical constructs (such as unobservable quantum fields or gravitational curvature) risk being dismissed as meaningless fictions because they lack direct sensory impressions.

5.3 Over-Reduction of Value to Subjective Sentiment

By asserting that reason can never adjudicate ends, Hume's emotivist ethics struggles to account for objective moral progress or resolve systemic moral conflicts between competing societies whose subjective sentiments are diametrically opposed.

• A Treatise of Human Nature, 1739–1740. Hume's magnum opus: understanding, passions, morals.
• Essays, Moral and Political, 1741–1742. Essays on government, liberty, and human nature.
• An Enquiry Concerning Human Understanding, 1748. Refined presentation of empiricist epistemology, induction, and miracles.
• An Enquiry Concerning the Principles of Morals, 1751. Sentimentalist ethics and the psychology of benevolence.
• Political Discourses, 1752. Pioneering monetary economics and trade balance theory.
• The Natural History of Religion, 1757. Anthropological and psychological origin of polytheism and monotheism.
• Dialogues Concerning Natural Religion, 1779 (posthumous). Surgical demolition of the teleological argument from design.