Mathematical Logical Fallacies: Definitions and Examples

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Mathematical

Missteps involving probability, statistics, scope, quantity, or numerical expectations.

How to spot it

11 fallacies in this category.

What numbers, rates, or probabilities are being ignored or mishandled?

Examples in this category

Appeal to probability Base rate fallacy Broken window fallacy Conjunction fallacy Ecological fallacy

+6 more listed below.

Category vs. family

A category is a diagnostic lens, so a fallacy may appear in more than one category. A family is the broader umbrella that gives the fallacy its single main home.

Appeal to probability

Occurs when someone assumes that because something could happen, it is therefore likely or inevitable that it will happen.

Mathematical

Advanced Advanced undergraduate

Appeal to probability companion poster in a retro mid-century editorial cartoon style, illustrating occurs when someone assumes that because something could happen, it is therefore likely or inevitable that it will happen.

Base rate fallacy

Occurs when someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question.

Mathematical

Intermediate Intro college

Base rate fallacy companion poster in a retro mid-century editorial cartoon style, illustrating occurs when someone judges how likely a case is by focusing on vivid case-specific evidence while ignoring the underlying frequency of the thing in question.

Broken window fallacy

Occurs when destruction or forced replacement is treated as an economic gain because the visible spending is counted while the unseen losses and forgone alternatives are...

EvidentialMathematical

Intermediate Intro college

Broken window fallacy companion poster in a retro mid-century editorial cartoon style, illustrating occurs when destruction or forced replacement is treated as an economic gain because the visible spending is counted while the unseen losses and forgone alternatives are ignored.

Conjunction fallacy

Occurs when a more detailed scenario is treated as more probable than a less detailed scenario that already contains it.

ConceptualMathematical

Advanced Advanced undergraduate

Conjunction fallacy companion poster in a retro mid-century editorial cartoon style, illustrating occurs when a more detailed scenario is treated as more probable than a less detailed scenario that already contains it.

Ecological fallacy

Occurs when statistics about a group are used to draw conclusions about particular individuals in that group.

MathematicalConceptual

Advanced Advanced undergraduate

Ecological fallacy companion poster in a retro mid-century editorial cartoon style, illustrating occurs when statistics about a group are used to draw conclusions about particular individuals in that group.

Gambler's fallacy

Occurs when someone thinks past outcomes of independent events make a future independent outcome more or less likely than it really is.

MathematicalCausal

Advanced Advanced undergraduate

Gambler's fallacy companion poster in a retro mid-century editorial cartoon style, illustrating occurs when someone thinks past outcomes of independent events make a future independent outcome more or less likely than it really is.

Hasty generalization

Occurs when someone draws a broad conclusion from too little evidence, too small a sample, or a badly skewed sample.

EvidentialMathematical

Intermediate Intro college

Hasty generalization companion poster in a retro mid-century editorial cartoon style, illustrating occurs when someone draws a broad conclusion from too little evidence, too small a sample, or a badly skewed sample.

Linearity fallacy

Occurs when someone assumes that doubling the input will double the output even though the system has thresholds, saturation, feedback loops, or diminishing returns.

ConceptualMathematical

Advanced Intro college

Linearity fallacy companion poster in a retro mid-century editorial cartoon style, illustrating occurs when someone assumes that doubling the input will double the output even though the system has thresholds, saturation, feedback loops, or diminishing returns.

Prosecutor's fallacy

Occurs when a low probability of a false match is confused with a low probability that a matched person is innocent.

Mathematical

Advanced Advanced undergraduate

Prosecutor's fallacy companion poster in a retro mid-century editorial cartoon style, illustrating occurs when a low probability of a false match is confused with a low probability that a matched person is innocent.

Regression fallacy

Occurs when movement back toward a normal range after an extreme result is credited to some intervention that may have had little or nothing to do with it.

CausalMathematical

Advanced Intro college

Regression fallacy companion poster in a retro mid-century editorial cartoon style, illustrating occurs when movement back toward a normal range after an extreme result is credited to some intervention that may have had little or nothing to do with it.

Survivorship bias

Occurs when conclusions are drawn from the visible successes that made it through a filter while the failures, dropouts, or non-survivors are ignored.

MathematicalEvidential

Advanced Advanced undergraduate

Survivorship bias companion poster in a retro mid-century editorial cartoon style, illustrating occurs when conclusions are drawn from the visible successes that made it through a filter while the failures, dropouts, or non-survivors are ignored.