External links
- Undistributed Middle entry in The Fallacy Files
| Formal |
| ||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Informal |
| ||||||||||||||||||||||||||||||||||
The fallacy of the undistributed middle (Latin: non distributio medii) is a formal error occurring in a categorical syllogism. This fallacy is committed when the middle term, which serves to connect the major and minor terms, is not distributed in either the minor premise or the major premise. In essence, it results in a syllogistic fallacy where the logical structure fails due to the inadequate distribution of the middle term across the premises.
In classical syllogisms, statements follow the forms of "A" (all), "E" (none), "I" (some), or "O" (some not), each consisting of two terms. The first term is distributed in A statements, the second in O statements, both in E statements, and none in I statements.
The fallacy of the undistributed middle arises when the term connecting the two premises is never distributed. In this context, distribution is emphasized as follows:
In this invalid syllogism, the common term B (the middle term) is never distributed. Introducing a premise such as All B is Z or No B is Z would distribute B and validate the argument. - A related rule dictates that anything distributed in the conclusion must be distributed in at least one premise. For instance:
- Here, the middle term Z is distributed, but Y is distributed in the conclusion without being distributed in any premise, rendering this syllogism invalid.
The fallacy of the undistributed middle takes the following form:
In this structure, the middle term "B" is not distributed across the premises, leading to an invalid conclusion where Y is asserted to be Z without proper logical support.
Premises:
Conclusion:
Explanation: This is an example of the Fallacy of the Illict Major. The Middle Term is actually distributed here in both premises in which it occurs. "All smartphones" is distributed as the subject of a universal proposition. "aren't smartphones" is distributed as the premise of a negative proposition. "touchscreens" however is distributed in the conclusion as the premise of a negative proposition but undistributed as the predicate of an affirmative proposition in the first premise.
Premises:
Conclusion:
Explanation: In this case, the middle term "smartphones" is not distributed in the first premise because the premise is not making a statement about all smartphones. The first premise is a Particular Affirmative proposition and hence, neither the subject nor the predicate are distributed. If it had stated that 'All smartphones are waterproof' it would be a Universal Affirmative proposition and as such would (in this instance) be making a statement about ALL smartphones and therefore, the middle term would in fact be distributed. However, as the predicate of a negative proposition in the second premise, "smartphones" actually IS distributed therefore, this syllogism has the middle term distributed at least once and hence does not qualify as an example of the fallacy of the undistributed middle. It is a fallacy though. In this case, the Fallacy of the Illicit Major. This occurs when the major term (ie, the predicate of the conclusion) is not distributed in the premise in which it occurs. Stating, as the first premise does, that 'some smartphones are not waterproof' tells us nothing meaningful about either smartphones as an entire class, nor about the state of being waterproof. Neither the subject nor the predicate are distributed in this style of premise, (a Particular Affirmative). So, whilst "waterproof" is distributed in the conclusion (being the predicate of a negative proposition), it is not distributed in the premise in which it occurs. If we believe that the reason laptops are not waterproof is because they aren't smartphones, would we conclude that functional, well-maintained submarines are also not waterproof because they too are not smartphones?
Premises:
Conclusion:
Explanation: Again, this is an example NOT of the Undistributed Middle but of the Illicit Major. See the above examples for comparison.
The fallacy of the undistributed middle has made its mark in popular culture, often depicted in various forms of media and entertainment. One notable example can be found in the TV series "Logic Labyrinth," where a character erroneously connects unrelated categories, leading to comedic misunderstandings.
It highlights instances where the fallacy has been humorously portrayed, providing a cultural perspective on the misunderstanding of logical connections in the broader context of entertainment.
| Formal |
| ||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Informal |
| ||||||||||||||||||||||||||||||||||
A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among a number of alternatives must be true. This disjunction is problematic because it oversimplifies the choice by excluding viable alternatives, presenting the viewer with only two absolute choices when in fact, there could be many.
A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. it is impossible for the premises to be true and the conclusion to be false.
In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics. It was revived after the third century CE by Porphyry's Isagoge.
Affirmative conclusion from a negative premise is a formal fallacy that is committed when a categorical syllogism has a positive conclusion and one or two negative premises.
The fallacy of four terms is the formal fallacy that occurs when a syllogism has four terms rather than the requisite three, rendering it invalid.
Illicit major is a formal fallacy committed in a categorical syllogism that is invalid because its major term is undistributed in the major premise but distributed in the conclusion.
Illicit minor is a formal fallacy committed in a categorical syllogism that is invalid because its minor term is undistributed in the minor premise but distributed in the conclusion.
The fallacy of exclusive premises is a syllogistic fallacy committed in a categorical syllogism that is invalid because both of its premises are negative.
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category are included in another. The study of arguments using categorical statements forms an important branch of deductive reasoning that began with the Ancient Greeks.
In propositional logic, transposition is a valid rule of replacement that permits one to switch the antecedent with the consequent of a conditional statement in a logical proof if they are also both negated. It is the inference from the truth of "A implies B" to the truth of "Not-B implies not-A", and conversely. It is very closely related to the rule of inference modus tollens. It is the rule that
In philosophical logic, the masked-man fallacy is committed when one makes an illicit use of Leibniz's law in an argument. Leibniz's law states that if A and B are the same object, then A and B are indiscernible. By modus tollens, this means that if one object has a certain property, while another object does not have the same property, the two objects cannot be identical. The fallacy is "epistemic" because it posits an immediate identity between a subject's knowledge of an object with the object itself, failing to recognize that Leibniz's Law is not capable of accounting for intensional contexts.
In logic and philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a formal fallacy is a fallacy where deduction goes wrong, and is no longer a logical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic.
In Aristotelian logic, Baralipton is a mnemonic word used to identify a form of syllogism. Specifically, the first two propositions are universal affirmative (A), and the third (conclusion) particular affirmative (I)-- hence BARALIPTON. The argument is also in the First Figure, and therefore would be found in the first portion of the full mnemonic poem as formulated by William of Sherwood; later this syllogism came to be considered one of the Fourth Figure.
The False Subtlety of the Four Syllogistic Figures Proved is an essay published by Immanuel Kant in 1762.
A premise or premiss is a proposition—a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion. Arguments consist of a set of premises and a conclusion.
The politician's syllogism, also known as the politician's logic or the politician's fallacy, is a logical fallacy of the form:
Negative conclusion from affirmative premises is a syllogistic fallacy committed when a categorical syllogism has a negative conclusion yet both premises are affirmative. The inability of affirmative premises to reach a negative conclusion is usually cited as one of the basic rules of constructing a valid categorical syllogism.
