The method of Science

Hume's Problem of Induction

• The Two Pillars of Science
• Title: The Pillars of Scientific Knowledge
• Core Argument: Science rests on two foundational pillars:
• The Empirical Pillar: All knowledge originates in observation and experiment.
• The Logical Pillar: Scientists use rational inference to derive general conclusions from specific observations. The most crucial form of this is Inductive Reasoning.

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What is Inductive Reasoning?�

• Logical Form:
• Premise 1: Observed Swan 1 is white.
• Premise 2: Observed Swan 2 is white.
• ...
• Premise N: Observed Swan N is white.
• Conclusion: Therefore, All swans are white.
• Contrast with Deduction:
• Deduction: If premises are true, the conclusion is necessarily true. (It is truth-preserving).
• Induction: If premises are true, the conclusion is probably true. (It is ampliative - it expands our knowledge).
• Example: Every time I release an object, it falls. Therefore, the next object I release will fall. This prediction relies on induction.

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Hume's Question

• What is the rational, non-circular justification for using inductive inference?
• The Two Failed Justifications:
• Justification by "Causality": Hume argues we never perceive "causation," only "constant conjunction." Our belief in cause-and-effect is itself a product of induction.
• Justification by "Past Success": The argument "Induction has worked in the past, so it will work in the future" is itself an inductive argument. It presupposes the very principle it seeks to justify.
• Hume's Conclusion: Induction has no rational foundation. It is a product of custom and habit. We use it because we are psychologically hardwired to, not because it is logically sound.

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The Philosophical Consequences for science

• Title: The Aftermath: A Crisis of Justification
• The Threat to Science: If scientific laws are based on a non-rational habit, how is science objectively superior to superstition or faith?
• The Problem of the Uniformity Principle:
• The foundations of science appear to rely on the assumption that nature is uniform — that the future will resemble the past.
• To justify induction, we need to assume "Nature is uniform." But this principle cannot be proven without using induction (circularity) or by pure logic (it's not a logical truth).

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The Logical Positivist

Building the Fortress: The Logical Positivist Response in the early 20^th century

The Weapon Against Metaphysics

• The Criterion: The meaning of a (non-analytic) statement is its method of verification. A statement is cognitively meaningful if and only if it is, in principle, verifiable (or confirmable) through empirical observation.
• The Dichotomy of Propositions:
• Analytic Propositions: True or false by definition alone (e.g., "All bachelors are unmarried men"). They are tautologies and empty of factual content.
• Synthetic Propositions: Their truth depends on facts about the world (e.g., "The cat is on the mat").
• The Demarcation Criterion: Any statement that is neither analytic nor empirically verifiable is meaningless metaphysics. Examples: "The Absolute is perfect," "The monad is the true substance."

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"Solving" the Problem of Induction: Confirmation Theory

• The Strategic Retreat: Logical Positivists conceded that induction cannot prove a universal law to be true. However, observational evidence can confirm it, raising its probability or degree of confirmation.
• The Logic of Confirmation: Each positive instance (e.g., observing another white swan) increases the confirmation level of the universal hypothesis ("All swans are white").
• The Image of Science: Science is a system of hypotheses that asymptotically approach the truth through the gradual accumulation of confirming evidence.

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The Radical Worldview of Logical Positivism

• The New Map of Knowledge:
• Natural Sciences (Physics, Chemistry): The paradigm of meaningful discourse.
• Formal Sciences (Math, Logic): Analytic tools, not fact-stating.
• History, Geology: Empirical sciences based on evidence (documents, fossils).
• The Fate of Ethics and Aesthetics: Statements like "Murder is wrong" or "This painting is beautiful" are not truth-apt. They are emotive expressions ("Boo!" or "Hooray!") used to express feelings or persuade others. They have no cognitive meaning.
• The Exile of Metaphysics and Theology: All questions about "God," "the Absolute," or "the soul" are dismissed as meaningless pseudoproblems.

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The Peak: The Deductive-Nomological (DN) Model of Explanation

The Goal of Science: Explanation

• What is a Scientific Explanation?
• The Question: What does it mean to explain an event, rather than just describe or predict it?
• Hempel's Answer (The Covering Law Model): To explain an event is to show that it was to be expected by subsuming it under general laws. The event is "covered" by a universal regularity.

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The Deductive-Nomological Model

• The Explanans (解釋項)(That which does the explaining):
• L1, L2, ... Ln: One or more universal laws.
• C1, C2, ... Ck: Statements of antecedent (initial) conditions.
• The Explanandum (被解釋項)(That which is to be explained): A statement describing the phenomenon to be explained.
• The Logical Requirement: The explanandum (被解釋項)( must be the logical consequence of the explanans (解釋項)(. The argument must be deductively valid.

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DN Example I: The Metal Bar

• Explanans:
• Law (L1): All metals expand when heated. (Universal Law)
• Condition (C1): This bar is made of metal. (Specific Fact)
• Condition (C2): This bar was heated. (Specific Fact)
• ------------------------------------------------------------------------------
• Explanandum (E): This metal bar increased in length.
• Logical Deduction: From {L1, C1, C2}, E follows deductively.

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DN Example II: History and the Social Sciences

• Law (L1): Whenever a rising social class faces severe political and economic oppression by an entrenched aristocracy, a revolution is highly probable. (A sociological "law").
• Conditions (C1, C2...): The Bourgeoisie in 18th-century France was economically powerful but politically excluded. There was a famine. The monarchy was fiscally bankrupt, etc.
• ---------------------------------------------------------------------------------
• Explanandum (E): The French Revolution occurred.

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• Analysis: This structure demonstrates the Unity of Science thesis. The same logical model of explanation applies to history and social sciences as it does to physics. The difference is in the precision and universality of the laws, not the logical form.

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One Logic, Two Functions

• Symmetry Thesis of explanation and prediction(解釋-預測對稱論)
• The logical structure of a scientific explanation is identical to the structure of a scientific prediction.
• The Only Difference is Temporal:
• Explanation: Deduces the event after it has occurred. (Why did the bar expand? Because it was heated).
• Prediction: Deduces the event before it occurs. (We predict the bar will expand when we heat it).
• Significance: A good theory must be both explanatory and predictive. This symmetry was a cornerstone of the Logical Positivist ideal of science.

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Challenge I: The evolutionary

• The Asymmetry Problem: Some philosophers, such as Wesley Salmon, have noted that certain explanations, while explanatory, do not necessarily serve predictive purposes. For example, evolutionary theory can account for the historical development of species but struggles to provide precise predictions about future evolutionary trajectories.

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Challenge II: Asymmetry and Irrelevance

• We can explain the length of the shadow by citing the height of the flagpole and the laws of optics. This is a valid DN explanation.
• We can also deduce the height of the flagpole from the length of the shadow and the same laws. The logic is identical.
• The Problem: The second case is a calculation, not an explanation. The DN model cannot distinguish between the two because it ignores causal direction. The height causes the shadow length, not vice versa.

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Core Critique

• 1. Verification/Confirmation is too weak.
• Astrology can also find confirming instances.
• How about Fung Sui, Fortune telling as well?
• Freudian psychoanalysis? Is every human behavior based on sexual desire which is rooted in childhood experience?
• Karl Marx theory of social development? Is every social phenomena based on economic factor?
• Stock prediction based on chart structure?
• The yin yang five elements in Traditional Chinese Medicine (TCM)?

• 2. What is a universal law?
• In ancient astronomy, the “ad hoc theory” refers to the practice of adding arbitrary and complicated modifications, such as epicycles(本輪) and deferents(均輪), makes the theory very complicated
• Should we apply Ockham razor to this theory?
• Ockham razor = "Entities must not be multiplied beyond necessity" (“如無必要，勿增實體”): When you have competing explanations for the same phenomenon, prefer the one that makes the fewest assumptions or posits the fewest entities — i.e., the simplest explanation consistent with the evidence.