11.1 Inductive reasoning and inductive logic
5 min read•august 15, 2024
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
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- 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 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)
- 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)
- 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
- Hypotheses are tested by deducing observable consequences and then checking these predictions against evidence
- Confirmed predictions strengthen the hypothesis, while disconfirmed predictions weaken it
Key Terms to Review (18)
Analogical reasoning: Analogical reasoning is a cognitive process where individuals draw comparisons between two different situations or concepts to infer similarities and make predictions. This type of reasoning helps people understand new ideas by relating them to familiar ones, often used in problem-solving, decision-making, and hypothesis formation.
Causal Inference: Causal inference refers to the process of determining whether a relationship between two variables is causal, meaning that changes in one variable directly cause changes in another. This concept is crucial for understanding patterns and making predictions based on data, allowing researchers to identify underlying mechanisms in complex systems. Establishing causality involves using various methods and statistical techniques to distinguish between correlation and true cause-and-effect relationships.
Counterexample: A counterexample is a specific instance or example that demonstrates the falsity of a general statement or proposition. It is crucial in evaluating the validity of logical arguments and proofs, as it provides concrete evidence that contradicts a given claim. By identifying a counterexample, one can show that a statement is not universally true, which is essential in formal reasoning and analysis.
David Hume: David Hume was an 18th-century Scottish philosopher, historian, and economist known for his influential contributions to empiricism and skepticism, particularly in relation to inductive reasoning. His work laid the groundwork for modern philosophical inquiry by challenging the certainty of knowledge derived from experience and highlighting the limitations of inductive logic, which argues from specific observations to general conclusions.
Deductive vs. Inductive: Deductive reasoning is a logical process where the conclusion necessarily follows from the given premises, leading to definitive outcomes. In contrast, inductive reasoning involves forming generalizations based on specific observations or evidence, which may not always guarantee a certain conclusion. Understanding the distinction between these two types of reasoning is crucial in grasping how we arrive at conclusions and the validity of arguments.
Generalization: Generalization is the process of forming broad conclusions based on specific instances or evidence. It involves taking particular observations and extrapolating them to create general rules or principles that can apply to a wider context. This is a key component of inductive reasoning, where conclusions are drawn from patterns observed in data or experiences.
Hasty Generalization: Hasty generalization is a logical fallacy that occurs when a conclusion is drawn from an insufficient or unrepresentative sample of data. This fallacy can lead to flawed reasoning because it overlooks the need for adequate evidence to support broader claims. Often, hasty generalizations can skew perceptions and promote stereotypes, making it crucial to evaluate the quality and quantity of evidence before reaching conclusions.
Hypothesis formation: Hypothesis formation is the process of creating a testable statement or prediction based on observations or existing knowledge. It serves as the foundation for further investigation, guiding research and experimentation by providing a clear focus and direction. A well-formed hypothesis not only identifies a relationship between variables but also allows for the exploration of causal connections through inductive reasoning and inductive logic.
Inductive strength: Inductive strength refers to the degree to which the premises of an inductive argument support the conclusion. It evaluates how likely it is that the conclusion is true based on the information provided in the premises. Strong inductive arguments make their conclusions probable, while weak inductive arguments fail to do so, highlighting the essential role of evidence and reasoning in forming conclusions.
John Stuart Mill: John Stuart Mill was a 19th-century English philosopher and political economist, best known for his contributions to utilitarianism and liberal thought. He made significant advancements in the field of inductive reasoning and inductive logic, emphasizing the importance of empirical evidence and observation in forming generalizations. His work laid the groundwork for modern scientific methods and rational discourse, influencing various domains such as ethics, economics, and social theory.
Observation: Observation refers to the process of gathering information through the senses to form a basis for knowledge and reasoning. In the context of inductive reasoning and inductive logic, observation is crucial because it provides the empirical evidence that helps in forming generalizations or hypotheses based on specific instances. Observations can lead to patterns that allow for predictions about future occurrences.
Probability: Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. It plays a crucial role in inductive reasoning, allowing individuals to make predictions and form conclusions based on patterns and observed data rather than absolute truths.
Sampling: Sampling is the process of selecting a subset of individuals or observations from a larger population to make inferences about that population. It is essential in inductive reasoning as it allows for conclusions to be drawn based on limited data, which can help predict or understand broader trends. The effectiveness of sampling relies on how representative the selected subset is of the entire population, influencing the validity of the conclusions drawn from it.
Scientific method: The scientific method is a systematic approach to inquiry that involves making observations, forming hypotheses, conducting experiments, and drawing conclusions based on empirical evidence. This process emphasizes the importance of inductive reasoning, allowing researchers to formulate general principles based on specific observations, which is a core aspect of inductive logic.
Slippery slope: A slippery slope is a logical fallacy that suggests if one event is allowed to happen, it will lead to a chain of related events culminating in significant and often negative consequences. This reasoning is often used in arguments to warn against initial actions, implying that they will inevitably lead to undesirable outcomes without providing sufficient evidence for such inevitability.
Statistical Syllogism: A statistical syllogism is a type of argument that draws a conclusion about an individual based on statistical evidence related to a group that the individual belongs to. This reasoning connects individual characteristics to general statistical trends, making it a key aspect of inductive reasoning and inductive logic. By using probabilistic information, it allows for conclusions that may not be certain but are reasonable based on the evidence available.
Strong vs. Weak Argument: A strong argument is one where the premises provide substantial support for the conclusion, making it likely to be true, while a weak argument has premises that do not adequately support its conclusion, making it less likely to be true. This distinction is crucial in evaluating inductive reasoning, as it helps to determine how persuasive and credible an argument is based on the evidence provided.
Supporting evidence: Supporting evidence refers to the information, data, or facts that back up a claim or argument, making it more persuasive and credible. This type of evidence plays a critical role in inductive reasoning, as it helps to establish generalizations based on specific observations or instances. Without supporting evidence, arguments can be weak and unconvincing, failing to provide a solid basis for the conclusions drawn.