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Inductive reasoning guarantees the certainty of its conclusions if the premises are true.
Answer: False
Inductive reasoning yields conclusions that are probable, not certain, even when the premises are true. This contrasts with deductive reasoning, which guarantees certainty under such conditions.
Deductive reasoning aims for conclusions that are probable, based on evidence.
Answer: False
Deductive reasoning aims for conclusions that are logically certain if the premises are true, not merely probable. Inductive reasoning is the mode that seeks probable conclusions based on evidence.
In deductive reasoning, if the premises are true, the conclusion is only probable.
Answer: False
In deductive reasoning, if the premises are true, the conclusion is guaranteed to be true, not merely probable. This certainty is a defining characteristic of valid deduction.
Mathematical induction is considered a form of inductive reasoning because it relies on a finite number of observed instances.
Answer: False
Mathematical induction is considered a form of deductive reasoning because its structure provides a rigorous logical proof that guarantees the truth of the conclusion, unlike inductive reasoning which relies on observed instances for probability.
What is the fundamental difference in the certainty of conclusions between deductive and inductive reasoning?
Answer: Deductive reasoning yields certain conclusions if premises are true, while inductive reasoning yields probable conclusions.
The fundamental difference lies in certainty: deductive reasoning guarantees a true conclusion if its premises are true, whereas inductive reasoning provides conclusions that are probable but not guaranteed.
What is the primary characteristic of mathematical induction that makes it deductive?
Answer: It provides strict proofs guaranteeing the conclusion's truth.
Mathematical induction is deductive because its logical structure ensures that if the base case and inductive step are valid, the conclusion is guaranteed to be true, unlike probabilistic inductive methods.
An inductive argument is described as 'strong' if:
Answer: Its premises make the conclusion probable.
An inductive argument is considered 'strong' when its premises provide a high degree of probability for the conclusion, meaning that if the premises are true, the conclusion is likely to be true as well.
Inductive generalization proceeds from observations about a population to conclusions about a sample.
Answer: False
Inductive generalization proceeds from observations about a sample to draw conclusions about a larger population, not the other way around.
The strength of an inductive generalization is solely determined by the size of the population being considered.
Answer: False
The strength of an inductive generalization depends not only on the size of the population but also crucially on the size and representativeness of the sample drawn from that population.
Statistical generalizations are considered more reliable than anecdotal generalizations because they rely on statistically representative samples.
Answer: True
Statistical generalizations derive their reliability from the use of statistically representative samples, which aim to accurately reflect the characteristics of the population, unlike anecdotal generalizations based on isolated instances.
An inductive prediction concludes with a statement about the population as a whole, based on observed instances.
Answer: False
An inductive prediction focuses on the probability of a specific future instance possessing a certain attribute, based on observed patterns, whereas an inductive generalization concludes about the population as a whole.
A statistical syllogism moves from a conclusion about an individual member to a general statement about a group.
Answer: False
A statistical syllogism moves from a general statement about a group (e.g., 'most X are Y') to a conclusion about an individual member of that group (e.g., 'this X is probably Y').
Arguments from analogy infer shared properties based on the elimination of dissimilarities.
Answer: False
Arguments from analogy infer shared properties based on observed similarities between items, not primarily on the elimination of dissimilarities.
A significant pitfall of arguments from analogy is the failure to consider crucial dissimilarities between the compared items.
Answer: True
Arguments from analogy are vulnerable to the pitfall of overlooking significant dissimilarities between the items being compared, which can undermine the validity of the inferred shared property.
Causal inference in inductive reasoning establishes definitive, proven cause-and-effect relationships.
Answer: False
Causal inference in inductive reasoning aims to establish potential or probable cause-and-effect relationships, rather than definitive, proven ones, as absolute certainty is typically beyond its scope.
Enumerative induction constructs generalizations based on the variety of supporting instances.
Answer: False
Enumerative induction constructs generalizations based on the *quantity* or number of supporting instances, whereas eliminative induction focuses on the variety of instances and the elimination of alternative hypotheses.
The 'all swans are white' example demonstrates that enumerative induction guarantees certainty if enough confirming instances are found.
Answer: False
The 'all swans are white' example illustrates that enumerative induction, even with numerous confirming instances, does not guarantee certainty, as a single counter-example (a black swan) can falsify the generalization.
Which of the following is a type of inductive reasoning mentioned in the text?
Answer: Argument from analogy
Argument from analogy is identified as a key type of inductive reasoning, distinct from deductive forms like syllogistic reasoning or logical entailment.
An inductive generalization proceeds from observations about a sample to draw a conclusion about:
Answer: A larger population.
Inductive generalization involves inferring characteristics of a larger population based on observations made from a representative sample of that population.
Which factor is NOT mentioned in the text as influencing the strength of an inductive generalization?
Answer: The complexity of the conclusion.
The text identifies sample size, sample representativeness, and population size as factors influencing inductive generalization strength. The complexity of the conclusion is not cited as a direct factor.
What distinguishes a statistical generalization from an anecdotal generalization according to the text?
Answer: Statistical generalizations rely on statistically representative samples, while anecdotal ones do not.
Statistical generalizations are grounded in samples that are statistically representative of the population, allowing for quantifiable inferences, whereas anecdotal generalizations are based on non-statistical evidence, such as personal experiences, making them less reliable.
How does an inductive prediction differ from an inductive generalization?
Answer: A generalization concludes about the population, while a prediction concludes about a specific future instance.
An inductive generalization infers characteristics of a population from a sample, while an inductive prediction infers the likelihood of a specific future event or instance based on past observations.
What is identified as a significant pitfall of arguments from analogy?
Answer: Ignoring crucial dissimilarities while focusing on similarities.
A primary pitfall of arguments from analogy is the tendency to overemphasize similarities while neglecting potentially significant dissimilarities between the items being compared, which can lead to flawed inferences.
Causal inference in inductive reasoning aims to establish:
Answer: Potential or probable cause-and-effect relationships.
Causal inference in inductive reasoning seeks to identify potential or probable cause-and-effect relationships based on observed correlations and patterns, rather than establishing definitive proof.
Enumerative induction constructs generalizations based on:
Answer: The quantity of supporting instances.
Enumerative induction builds generalizations by relying on the quantity or number of observed instances that support a particular conclusion.
Francis Bacon's eliminative induction focuses on the number of supporting instances to strengthen a conclusion.
Answer: False
Francis Bacon's method of eliminative induction emphasizes the *variety* of instances and the systematic elimination of hypotheses inconsistent with observed evidence, rather than solely the number of supporting instances.
Baconian probability is expressed as the ratio of successful eliminations to the total number of potential claims identified as incompatible.
Answer: True
Baconian probability, within Bacon's framework of eliminative induction, is quantified as 'i out of n,' where 'n' represents the total number of incompatible hypotheses or claims, and 'i' represents those successfully eliminated by evidence.
Aristotle used the term *inductio* to describe the move from particular instances to universal principles.
Answer: False
Aristotle used the term *epagogé* for the process of moving from particular instances to universal principles, which was later translated into Latin as *inductio* by Cicero.
The ancient Pyrrhonists questioned the ability of inductive reasoning to provide absolute certainty.
Answer: True
The ancient Pyrrhonists were early proponents of skepticism who questioned whether inductive reasoning could establish absolute certainty, highlighting its reliance on unproven assumptions.
The Empiric school of Greek medicine relied heavily on broad generalizations and theoretical frameworks.
Answer: False
The Empiric school of Greek medicine emphasized 'epilogism,' a method of accumulating facts without broad generalizations or theoretical frameworks, and cautiously approached causal claims.
David Hume argued that our reliance on induction is primarily based on rational justification and logical proof.
Answer: False
David Hume argued that our reliance on induction, including the assumption of the uniformity of nature, is based not on rational justification or logical proof, but rather on habit, instinct, and custom.
Immanuel Kant proposed that the uniformity of nature is a synthetic a posteriori truth discovered through experience.
Answer: False
Immanuel Kant proposed that the uniformity of nature is a *synthetic a priori* truth, meaning it is a necessary condition for structuring experience itself, rather than a truth discovered solely through empirical observation.
Francis Bacon's approach to eliminative induction emphasizes:
Answer: The elimination of hypotheses inconsistent with observed variety.
Francis Bacon's eliminative induction prioritizes the systematic elimination of hypotheses that contradict the observed variety of evidence, thereby strengthening the remaining consistent explanations.
What did David Hume argue about the foundation of inductive reasoning?
Answer: It is a matter of habit and instinct, lacking a rational foundation.
David Hume argued that inductive reasoning lacks a firm rational foundation, asserting that our reliance on it stems from habit and instinct rather than logical proof or empirical justification.
Immanuel Kant proposed that principles like the uniformity of nature are:
Answer: Synthetic a priori truths necessary for structuring experience.
Immanuel Kant posited that principles such as the uniformity of nature are synthetic a priori truths, essential cognitive structures that the mind imposes on experience to make it intelligible.
According to the text, what did Francis Bacon criticize about early forms of induction?
Answer: Relying solely on experience and enumerative induction.
Francis Bacon criticized early forms of induction for relying too heavily on mere enumeration of instances and insufficient attention to the variety of evidence, advocating for a more systematic approach.
What was the contribution of the ancient Greek Empiric school regarding inductive reasoning?
Answer: They employed 'epilogism,' a theory-free method of accumulating facts.
The ancient Greek Empiric school contributed 'epilogism,' a method characterized by the accumulation of facts without extensive generalization or theoretical speculation, contrasting with the Dogmatic school's use of 'analogismos'.
What is the 'Problem of Induction' primarily concerned with?
Answer: The justification for inferring future events from past observations.
The 'Problem of Induction' fundamentally questions the logical justification for assuming that future events will resemble past observations, and how to establish the reliability of such inferences.
The 'uniformity of nature' is a key assumption in inductive arguments that suggests:
Answer: The future will resemble the past.
The principle of the 'uniformity of nature' posits that the regularities observed in the past will continue to hold true in the future, forming a foundational assumption for many inductive arguments.
Auguste Comte, a positivist, viewed enumerative induction as unreliable and rejected the scientific method.
Answer: False
Auguste Comte, a key figure in positivism, viewed enumerative induction as reliable and foundational to the scientific method, which he championed as the correct approach for societal progress.
William Whewell introduced the concept of 'consilience' to describe the invention of a new conception applied to facts.
Answer: False
William Whewell introduced the concept of 'superinduction' to describe the invention of a new conception applied to facts. 'Consilience' refers to the confirmation of a hypothesis by its successful application across diverse areas of evidence.
C. S. Peirce identified 'abduction' as a mode of inference that moves from a general law to a specific case.
Answer: False
C. S. Peirce identified 'abduction' (or retroduction) as a mode of inference that involves reasoning towards a hypothesis that best explains observed phenomena, distinct from deduction (general law to specific case) and induction (sample to population).
Bertrand Russell considered induction to be derivable from experience or other logical principles.
Answer: False
Bertrand Russell, influenced by Keynes, argued that induction is an independent logical principle, not derivable from experience or other logical principles, and its acceptance is crucial for avoiding Humean skepticism.
Gilbert Harman proposed that enumerative induction is a form of Inference to the Best Explanation (IBE).
Answer: True
Gilbert Harman proposed that enumerative induction can be understood as a form of Inference to the Best Explanation (IBE), suggesting that we induce conclusions because they provide the most plausible explanation for our observations.
Karl Popper argued that scientific progress relies on building general laws from numerous observations through induction.
Answer: False
Karl Popper argued that scientific progress does not rely on building general laws through induction from observations. Instead, he proposed that science advances through conjecture and refutation, where theories are tested and potentially falsified.
Bayesian inference treats induction not as a theory of belief itself, but as a method for rationally updating existing beliefs.
Answer: True
Bayesian inference frames inductive reasoning as a process for rationally updating beliefs based on new evidence, using prior probabilities and likelihoods to calculate posterior probabilities.
William Whewell used the term 'consilience' to describe:
Answer: A criterion for the accuracy of explanations across diverse areas.
William Whewell used 'consilience' to denote the convergence of evidence from multiple, diverse domains that supports a single hypothesis, serving as a strong indicator of its accuracy.
C. S. Peirce's concept of 'abduction' or 'retroduction' is best described as:
Answer: Reasoning towards a hypothesis that best explains observed phenomena.
Peirce's abduction, also known as retroduction or inference to the best explanation, is the process of forming a hypothesis that plausibly accounts for observed facts.
Gilbert Harman suggested that enumerative induction is essentially a disguised form of:
Answer: Inference to the Best Explanation (IBE).
Gilbert Harman proposed that enumerative induction is fundamentally a form of Inference to the Best Explanation (IBE), where the conclusion is accepted because it best explains the observed evidence.
Karl Popper addressed the problem of induction by arguing that:
Answer: Scientific progress occurs through conjecture and refutation.
Karl Popper proposed that scientific progress is driven by conjecture and refutation, where theories are rigorously tested and falsified, rather than by the inductive accumulation of observations.
Bayesian inference uses 'prior probabilities' and 'likelihoods' to:
Answer: Rationally update existing beliefs when presented with new evidence.
Bayesian inference employs prior probabilities and likelihoods to systematically and rationally update beliefs in light of new evidence, providing a framework for inductive reasoning.
Ray Solomonoff's contribution to inductive inference is considered a formalization of:
Answer: Occam's razor.
Ray Solomonoff's work on universal inductive inference provides a formal, mathematical framework that is considered a rigorous formalization of Occam's razor, favoring simpler explanations.
Auguste Comte's view of positivism suggested that:
Answer: The scientific method, using induction, is the correct approach for societal improvement.
Auguste Comte's positivism posited that the scientific method, which relies on induction, is the most reliable path to knowledge and the key to societal progress, moving beyond theological and metaphysical stages.
What did Bertrand Russell assert about the nature of induction?
Answer: It is an independent logical principle.
Bertrand Russell asserted that induction is an independent logical principle, not derivable from experience or other logical principles, and its acceptance is crucial for avoiding Humean skepticism.
A hasty generalization occurs when a conclusion is drawn from an overly large and diverse sample.
Answer: False
A hasty generalization is a fallacy that occurs when a conclusion is drawn from an inadequate or unrepresentative sample, not an overly large one.
Confirmation bias is a cognitive bias that leads individuals to seek evidence confirming their existing hypotheses, potentially distorting inductive reasoning.
Answer: True
Confirmation bias is indeed a cognitive bias where individuals favor information that confirms their pre-existing beliefs or hypotheses, which can distort the objective process of inductive reasoning.
The fallacy of 'hasty generalization' occurs when:
Answer: A conclusion is drawn from an inadequate sample size.
The fallacy of hasty generalization arises when a conclusion is reached based on insufficient evidence, typically due to an inadequate or unrepresentative sample size.
Which cognitive bias involves over-reliance on easily recalled information, potentially distorting inductive reasoning?
Answer: Availability heuristic
The availability heuristic is a cognitive bias where the ease of recalling information influences judgments, potentially leading to distorted inductive reasoning by overemphasizing readily available examples.