3.2 Theories of confirmation and evidence

Theories of confirmation and evidence are crucial for understanding how scientific knowledge is built and validated. These theories explore different approaches to assessing the strength of evidence supporting scientific hypotheses.

The chapter discusses various models, including the hypothetico-deductive method, Bayesian confirmation theory, bootstrapping, and inference to the best explanation. Each approach offers unique insights into how scientists evaluate evidence and confirm theories in practice.

Theories of Confirmation in Science

The Hypothetico-Deductive Model

Top images from around the web for The Hypothetico-Deductive Model

• 

  Chapter 3: Scientific Method – Introduction to History and Philosophy of Science View original

  Is this image relevant?

• 

  Sarnecka Lab Blog: May 2018 View original

  Is this image relevant?

• 

  Chapter 3: Scientific Method – Introduction to History and Philosophy of Science View original

  Is this image relevant?

• 

  Chapter 3: Scientific Method – Introduction to History and Philosophy of Science View original

  Is this image relevant?

• 

  Sarnecka Lab Blog: May 2018 View original

  Is this image relevant?

1 of 3

Top images from around the web for The Hypothetico-Deductive Model

• 

  Chapter 3: Scientific Method – Introduction to History and Philosophy of Science View original

  Is this image relevant?

• 

  Sarnecka Lab Blog: May 2018 View original

  Is this image relevant?

• 

  Chapter 3: Scientific Method – Introduction to History and Philosophy of Science View original

  Is this image relevant?

• 

  Chapter 3: Scientific Method – Introduction to History and Philosophy of Science View original

  Is this image relevant?

• 

  Sarnecka Lab Blog: May 2018 View original

  Is this image relevant?

1 of 3

• Proposes that scientific theories are confirmed by deriving testable predictions and checking those predictions against empirical evidence
• Theories that generate more successful predictions are considered better confirmed
• Example: Newtonian mechanics was confirmed by its accurate predictions of planetary motions
• Example: The theory of relativity was confirmed by predicting the bending of light during a solar eclipse

Bayesian Confirmation Theory

• Uses probability theory to quantify the degree to which evidence supports a hypothesis
• Prior probabilities are updated in light of new evidence using Bayes' theorem to yield posterior probabilities
• Example: A medical test's accuracy can be used to update the probability of a patient having a disease given a positive test result
• Incorporates background knowledge through the assignment of prior probabilities

Alternative Approaches

• Bootstrapping confirmation holds that hypotheses are confirmed by being part of a coherent explanatory system that fits well with empirical evidence
  • Confirmation is viewed as holistic rather than based on individual predictions
  • Example: The atomic theory of matter was confirmed by its ability to coherently explain a wide range of chemical phenomena
• Inference to the best explanation argues that we should infer the truth of the hypothesis that would, if true, provide the best explanation of the available evidence
  • Explanatory virtues like simplicity, scope, and consistency are considered key
  • Example: The theory of evolution by natural selection is inferred to be true because it best explains the diversity and adaptation of life

Assessing Evidential Support

Prediction-Based vs. Explanation-Based

• The hypothetico-deductive model and Bayesian confirmation theory are prediction-based, assessing hypotheses by how well they predict empirical data
• Bootstrapping and inference to the best explanation are explanation-based, assessing how well hypotheses cohere with and explain evidence
• Prediction-based approaches emphasize testable implications, while explanation-based approaches focus on explanatory power

Quantitative vs. Qualitative

• Bayesian confirmation and the hypothetico-deductive model are quantitative, aiming to precisely measure evidential support
  • Bayes' theorem provides a mathematical formula for updating probabilities
  • The hypothetico-deductive model can compare theories based on the number and variety of successful predictions
• Bootstrapping and inference to the best explanation are qualitative, relying on judgments of explanatory goodness
  • These approaches do not provide precise measures of evidential support
  • Assessments of coherence and explanatory virtue are more subjective and difficult to formalize

Holistic vs. Piecemeal

• Bayesian confirmation factors in background knowledge via prior probabilities, taking a more comprehensive view of evidence
• The hypothetico-deductive model considers predictions in isolation, assessing each one independently of the overall theoretical context
• Bootstrapping takes a holistic view of evidential support, considering how well hypotheses fit into a larger explanatory framework
• Inference to the best explanation falls somewhere in between, considering explanatory success for a particular set of evidence but not necessarily the entire theoretical system

Scope of Reasoning

• The hypothetico-deductive model only considers deductive reasoning from theories to predictions
  • Theories are confirmed when their deductive consequences are verified empirically
  • Example: The prediction that light would bend around the sun was a deductive consequence of general relativity
• Bayesian confirmation, bootstrapping, and inference to the best explanation allow for inductive and abductive reasoning
  • Inductive reasoning involves generalizing from instances to probabilistic conclusions
  • Abductive reasoning involves inferring the best explanation for a set of observations
  • Example: Inferring the existence of atoms based on the success of atomic theory in explaining chemical bonding

Bayesian Confirmation Theory

Formal Framework

• Bayesian confirmation provides a formal framework for understanding how evidence affects the probability of hypotheses
• It models scientific reasoning as updating probabilities in light of evidence
• The degree of confirmation is represented using conditional probabilities
  • $P(H|E)$ represents the probability of the hypothesis $H$ given evidence $E$
  • This is called the posterior probability and represents the updated degree of belief in $H$ after observing $E$

Bayes' Theorem

• Bayes' theorem shows how the probability of a hypothesis given evidence depends on the prior probability of the hypothesis and the likelihood of the evidence given the hypothesis and its negation
  • $P(H|E) = \frac{P(E|H)P(H)}{P(E)}$
  • $P(H)$ is the prior probability of the hypothesis before considering the evidence
  • $P(E|H)$ is the likelihood of observing the evidence if the hypothesis is true
  • $P(E)$ is the total probability of observing the evidence under all hypotheses
• The theorem captures the idea that surprising evidence is more informative
  • If the evidence is very likely under the hypothesis but unlikely otherwise, then observing the evidence will strongly increase the posterior probability of the hypothesis
  • Example: A precise prediction of the perihelion precession of Mercury was strong evidence for general relativity because it was very unlikely under Newtonian gravity

Combining Evidence

• Bayesian reasoning can model how different lines of evidence combine to support a hypothesis
• Multiple independent sources of evidence that are likely given a hypothesis can lead to high posterior probabilities
• The confirmatory power of evidence depends not just on the likelihood of the evidence under the hypothesis, but also its likelihood under alternative hypotheses
  • Evidence that is likely under the hypothesis but unlikely under alternatives provides strong confirmation
  • Evidence that is equally likely under competing hypotheses does not discriminate between them and provides little confirmation
• Example: The Copernican model of the solar system was strongly confirmed by the convergence of evidence from telescopic observations, phases of Venus, and stellar parallax

Explanatory Principles

• Bayesian principles like favoring hypotheses that make the evidence more probable help explain features of scientific reasoning
• Scientists tend to prefer hypotheses that make bold, testable predictions
  • Hypotheses that predict surprising or unlikely evidence gain more confirmation if that evidence is observed
  • Example: Einstein's prediction of the bending of starlight during a solar eclipse was a bold prediction that strongly confirmed general relativity when verified
• Scientists often seek out surprising or novel evidence rather than just confirming existing data
  • Surprising evidence can more dramatically shift probabilities and provide stronger confirmation
  • Example: The discovery of the cosmic microwave background radiation was surprising evidence that strongly confirmed the Big Bang theory over the steady-state model

Challenges and Limitations

• Specifying objective prior probabilities can be difficult, especially for hypotheses about which there is little background knowledge
  • The choice of priors can significantly influence the posterior probabilities
  • Example: The prior probability of a revolutionary new scientific theory might be hard to determine objectively
• Scientists rarely reason explicitly in Bayesian terms or calculate precise probabilities
  • Bayesian confirmation theory is a normative model of how scientists should reason, but may not always describe their actual reasoning process
  • Example: Scientists may rely more on qualitative judgments of evidential support rather than explicit probability estimates
• In some cases, Bayesian reasoning seems to give counterintuitive results
  • The "problem of old evidence" arises when evidence that was already known is treated as if it provides no additional confirmation
  • Example: The precession of Mercury's orbit was known before Einstein developed general relativity, but intuitively seems to support the theory

Strengths and Weaknesses of Confirmation Theories

Hypothetico-Deductive Model

• Strengths:
  • Fits well with many examples from the history of science where theories were tested by deriving and testing bold predictions
  • Provides a clear account of how theories are falsified when predictions fail to match observations
  • Example: Newtonian mechanics was confirmed by its accurate predictions of planetary orbits and tides
• Weaknesses:
  • Struggles to account for cases where theories are accepted without making novel predictions
  • Does not capture the role of auxiliary hypotheses in deriving predictions, which can make theories difficult to decisively falsify
  • Example: The theory of continental drift was initially rejected because it lacked a mechanism, even though it made successful predictions

Bayesian Confirmation Theory

• Strengths:
  • Provides a precise, quantitative way of understanding evidential support and how probabilities should be updated in light of evidence
  • Captures the idea that surprising or risky predictions provide stronger confirmation when verified
  • Example: The confirmation of the Higgs boson with properties matching the Standard Model's predictions was strong evidence because the predictions were highly specific and unlikely under alternative theories
• Weaknesses:
  • Faces challenges in specifying objective prior probabilities, especially for theories with little relevant background knowledge
  • Describes an idealized form of reasoning that may not match the actual process of scientific inference, which often relies on qualitative judgments
  • Example: Scientists' judgments about the plausibility of string theory are based more on theoretical virtues like elegance and unification than precise probability estimates

Bootstrapping Confirmation

• Strengths:
  • Better captures the interconnected structure of scientific theories, where hypotheses are supported by their fit with a larger explanatory framework
  • Recognizes the role of coherence and explanatory power in providing evidential support, beyond just predictive success
  • Example: The kinetic theory of gases was confirmed by its coherence with laws of thermodynamics and statistical mechanics
• Weaknesses:
  • Lacks a clear, precise account of when evidence fits with or contradicts a larger theoretical system
  • Risks making confirmation too easy by allowing ad hoc hypotheses to be incorporated into a theoretical web without independent testability
  • Example: Ptolemaic astronomy was able to accommodate a wide range of observations by adding epicycles, but this did not provide genuine confirmation

Inference to the Best Explanation

• Strengths:
  • Matches the explanatory focus of much scientific reasoning, which often involves abductive inference to the most plausible explanation of a set of data
  • Captures the role of explanatory virtues like simplicity, unification, and coherence in scientific theory choice
  • Example: Lavoisier's oxygen theory of combustion was accepted because it provided a better explanation of key observations than the phlogiston theory
• Weaknesses:
  • Does not provide a precise method for determining which explanation is best or how to weigh different explanatory virtues
  • There is disagreement about the nature and justification of explanatory virtues and whether they track truth rather than pragmatic usefulness
  • Example: Debates about the interpretations of quantum mechanics often invoke explanatory virtues like locality and determinism, but there is no consensus on which interpretation is best

General Challenges

• All of these confirmation theories face challenges in handling cases where social and pragmatic factors seem to influence scientific reasoning and theory choice beyond just evidential support
  • The role of values, power structures, and personal biases in science poses problems for purely logical accounts of confirmation
  • Example: The early 20th century debate between Mendelian genetics and biometric approaches was influenced by political views about race and eugenics
• Philosophers have raised questions about whether any purely formal account of confirmation can capture the complexities of actual scientific practice
  • Scientific reasoning may be more context-dependent and reliant on domain-specific background knowledge than general confirmation theories suggest
  • Example: The standards of evidence and statistical methods used in particle physics differ from those used in ecology or social science
• Combining insights from different confirmation theories may be necessary to fully capture the diversity of scientific reasoning
  • Pluralist approaches suggest that different theories of confirmation may be applicable in different domains or contexts of inquiry
  • Integrative approaches seek to unify the insights of different confirmation theories into a more comprehensive account
  • Example: Bayesian confirmation theory can be combined with inference to the best explanation by using explanatory considerations to inform the assignment of prior probabilities