Problems for Popper

Outline 1. Induction 2. Probability

Problems for Popper I

Many “scientific hypotheses” are not falsifiable, not even in principle: every planet has a moon, ∀x (Px → ∃yMxy ). Another example: every person has a secret.

I

Falsifying consequences often indicate errors that lie elsewhere: errors of measurement, auxiliary hypotheses (physical auxiliaries when testing a chemical hypothesis)

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

Problems for Popper I

Many “scientific hypotheses” are not falsifiable, not even in principle: every planet has a moon, ∀x (Px → ∃yMxy ). Another example: every person has a secret.

I

Falsifying consequences often indicate errors that lie elsewhere: errors of measurement, auxiliary hypotheses (physical auxiliaries when testing a chemical hypothesis)

I

Pierre Duhem (1861-1916; The Aim and Structure of Physical Theory, 1914) and Willard Van Orman Quine (1908-2000): holism about confirmation (entails holism about meaning given verificationism about meaning)

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

Problems for Popper I

Many “scientific hypotheses” are not falsifiable, not even in principle: every planet has a moon, ∀x (Px → ∃yMxy ). Another example: every person has a secret.

I

Falsifying consequences often indicate errors that lie elsewhere: errors of measurement, auxiliary hypotheses (physical auxiliaries when testing a chemical hypothesis)

I

Pierre Duhem (1861-1916; The Aim and Structure of Physical Theory, 1914) and Willard Van Orman Quine (1908-2000): holism about confirmation (entails holism about meaning given verificationism about meaning)

I

...

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

End of Second Week

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

Hypothetico-deductivism

I

Idea: hypotheses that survive many and severe tests and hypotheses that make many and strong successful predictions seem to have a higher chance of being true

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

Hypothetico-deductivism

I

Idea: hypotheses that survive many and severe tests and hypotheses that make many and strong successful predictions seem to have a higher chance of being true

I

Evidence E HD-confirms hypothesis H relative to background assumptions B iff the conjunction of H and B, H ∧ B, logically implies E (in some suitable way)

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

Hypothetico-deductivism

I

Idea: hypotheses that survive many and severe tests and hypotheses that make many and strong successful predictions seem to have a higher chance of being true

I

Evidence E HD-confirms hypothesis H relative to background assumptions B iff the conjunction of H and B, H ∧ B, logically implies E (in some suitable way)

I

HD-confirmation satisfies Hempel’s CCC, but neither EntC nor SCC nor SConsC

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

Hypothetico-deductivism

I

Idea: hypotheses that survive many and severe tests and hypotheses that make many and strong successful predictions seem to have a higher chance of being true

I

Evidence E HD-confirms hypothesis H relative to background assumptions B iff the conjunction of H and B, H ∧ B, logically implies E (in some suitable way)

I

HD-confirmation satisfies Hempel’s CCC, but neither EntC nor SCC nor SConsC

I

...

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

Problems of Irrelevance I

Problem of irrelevant conjunction: if E HD-confirms H relative to B, then E HD-confirms H ∧ X relative to B, for any X . Proof: ...

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

Problems of Irrelevance I

Problem of irrelevant conjunction: if E HD-confirms H relative to B, then E HD-confirms H ∧ X relative to B, for any X . Proof: ...

I

Mercury’s anomalous 4300 arc second advance of its perihelion HD-confirms GTR, and so it also HD-confirms GTR ∧ X , X = There is life on Mars.

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

Problems of Irrelevance I

Problem of irrelevant conjunction: if E HD-confirms H relative to B, then E HD-confirms H ∧ X relative to B, for any X . Proof: ...

I

Mercury’s anomalous 4300 arc second advance of its perihelion HD-confirms GTR, and so it also HD-confirms GTR ∧ X , X = There is life on Mars.

I

Problem of irrelevant disjunction: if E HD-confirms H relative to B, then E ∨ X HD-confirms H relative to B, for any X . Proof: ...

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

Problems of Irrelevance I

Problem of irrelevant conjunction: if E HD-confirms H relative to B, then E HD-confirms H ∧ X relative to B, for any X . Proof: ...

I

Mercury’s anomalous 4300 arc second advance of its perihelion HD-confirms GTR, and so it also HD-confirms GTR ∧ X , X = There is life on Mars.

I

Problem of irrelevant disjunction: if E HD-confirms H relative to B, then E ∨ X HD-confirms H relative to B, for any X . Proof: ...

I

Mercury’s anomalous 4300 arc second advance of its perihelion ∨ X HD-confirms GTR, X = Luca lives on the second floor. Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

The limits of deductivism I

The prediction criterion, Hempel’s satisfaction criterion, Popper’s falsificationism, hypothetico-deductivism all employ (first-order) logic (with identity).

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

The limits of deductivism I

The prediction criterion, Hempel’s satisfaction criterion, Popper’s falsificationism, hypothetico-deductivism all employ (first-order) logic (with identity).

I

All sciences, whether natural sciences such as physics, chemistry, biology or social sciences such as economics, political science, sociology heavily draw on the resources of statistics and probability theory.

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

The limits of deductivism I

The prediction criterion, Hempel’s satisfaction criterion, Popper’s falsificationism, hypothetico-deductivism all employ (first-order) logic (with identity).

I

All sciences, whether natural sciences such as physics, chemistry, biology or social sciences such as economics, political science, sociology heavily draw on the resources of statistics and probability theory.

I

Statistical hypotheses do not logically imply anything (that is empirically accessible or observable).

Franz Huber

PHL 246: Probability and Inductive Logic

Outline 1. Induction 2. Probability

The limits of deductivism I

The prediction criterion, Hempel’s satisfaction criterion, Popper’s falsificationism, hypothetico-deductivism all employ (first-order) logic (with identity).

I

All sciences, whether natural sciences such as physics, chemistry, biology or social sciences such as economics, political science, sociology heavily draw on the resources of statistics and probability theory.

I

Statistical hypotheses do not logically imply anything (that is empirically accessible or observable).

I

Therefore all the deductive accounts we have come across so far miss an indispensable part of actual science.

Franz Huber

PHL 246: Probability and Inductive Logic