Inductive reasoning forms conclusions based on evidence, but unlike deductive logic, these conclusions aren't guaranteed. It's used in everyday life and scientific inquiry to make educated guesses about the world around us.

This section explores different types of inductive arguments, like generalizations and analogies. It also looks at how we evaluate their strength and use them in science to form and test hypotheses.

Deductive vs Inductive Reasoning

Reasoning Process and Conclusion Certainty

• Deductive reasoning starts with premises and draws a logically certain conclusion
  • The conclusion is guaranteed to be true if the premises are true
• Inductive reasoning starts with observations or evidence and infers a likely or probable conclusion
  • The conclusion is not guaranteed to be true, even if the premises are true

Argument Evaluation Criteria

• Deductive arguments are either valid or invalid based on their logical structure
• Inductive arguments are evaluated as strong or weak based on the degree to which the premises support the conclusion

Information Content of Conclusion

• In a deductive argument, the conclusion contains no new information beyond what is stated in the premises
• In an inductive argument, the conclusion goes beyond the information given in the premises, inferring additional claims

Forms of Inductive Arguments

Generalization and Statistical Reasoning

• Inductive generalization argues from specific cases to a general rule or principle
  • It takes observed instances and projects that pattern more widely (e.g. observing that the sun has risen every day and concluding it will always rise)
• Statistical syllogism uses statistics or proportions to draw a conclusion about an individual case
  • It applies a general statistic to infer a specific instance (e.g. most birds can fly, therefore this particular bird can probably fly)

Arguments by Analogy and Causal Inference

• Arguments from analogy reason that because two things are similar in certain respects, they are likely similar in further respects
  • The strength depends on the relevance of the similarities (e.g. Earth and Mars are similar in size, location and composition, so Mars may also be able to support life)
• Causal inference argues from a perceived correlation or constant conjunction between two types of events to a causal relationship
  • It attributes a causal connection based on observing patterns of co-occurrence (e.g. concluding that smoking causes cancer after observing that most lung cancer patients are smokers)

Inference to the Best Explanation

• Inference to the best explanation, or abductive reasoning, compares competing hypotheses and argues for the one that would, if true, best explain the relevant evidence
  • It favors the hypothesis that makes the evidence most probable (e.g. inferring there was a fire because that best explains the observed smoke and ash)
• Abductive reasoning is used to infer probable causes, motives, or reasons that would explain established facts

Strength of Inductive Arguments

Factors Affecting Inductive Strength

• Sample size and selection are important factors in evaluating inductive arguments
  • In general, arguments based on larger and more representative samples are stronger (e.g. a poll of 1000 voters is stronger evidence than one of 10 voters)
• The strength of an inductive generalization depends on the number of instances observed
  • A higher proportion of observed instances strengthens the argument (e.g. observing 100 out of 100 ravens are black is stronger than 10 out of 10)
• Analogy arguments are stronger when the similarities are more relevant to the conclusion being drawn
  • Irrelevant similarities do not strengthen an argument from analogy

Limits on Certainty of Inductive Conclusions

• Conclusions of strong inductive arguments are probable or likely to be true, but never absolutely certain
  • There is always a possibility that new evidence could overturn an inductive conclusion
• Even the strongest inductive arguments are not immune to doubt, as the conclusion goes beyond the evidence given in the premises
  • No amount of evidence can eliminate the possibility of a contradictory case

Evaluating Inductive Inferences

• Causal inference is stronger when there are no plausible alternative explanations for the observed correlation
  • Controlled scientific experiments aim to rule out alternative causes
• The strength of an inference to the best explanation depends on considering all plausible hypotheses
  • It requires favoring the explanation that best accounts for all the available evidence over other candidate explanations

Induction in Scientific Reasoning

Forming Hypotheses and Theories

• Scientific inquiry relies on inductive reasoning to draw general conclusions from specific observations and evidence
  • Scientists use induction to formulate hypotheses, theories and laws
• Observing patterns and regularities can lead scientists to propose hypotheses and theories as potential explanations
  • These conjectures then need to be tested against further evidence (e.g. observing that gases expand when heated led to kinetic theory)

Inferring Causal Relationships

• Inferring causal relationships is a key part of scientific reasoning
  • Controlled experiments aim to isolate cause and effect by testing correlations (e.g. testing if a drug causes a health improvement by comparing treatment and control groups)
• Causal reasoning in science aims to find the best explanation for patterns in data
  • Alternative explanations and confounding factors must be controlled for or ruled out

The Nature of Scientific Theories

• Scientific theories are inductive generalizations that explain a wide range of phenomena
  • Theories are never fully proven, but can be supported by a convergence of evidence from many lines of inquiry (e.g. evolutionary theory is supported by evidence from fossils, genetics, comparative anatomy, etc.)
• Well-established scientific theories are very strongly supported by evidence, but are always open to revision if contradictory evidence is found
  • Scientific conclusions are reliable but provisional

Hypothetico-Deductive Method

• The hypothetico-deductive model describes a process of forming a hypothesis through inductive reasoning, deducing testable predictions, then using further inductive reasoning to confirm or disconfirm the hypothesis based on observational evidence
  • This interplay of induction and deduction is central to the scientific method
• Hypotheses are tested by deducing observable consequences and then checking these predictions against evidence
  • Confirmed predictions strengthen the hypothesis, while disconfirmed predictions weaken it