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Type of logical argument that applies deductive reasoning
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive
Syllogism
Logical rule of inference
syllogism (historically known as modus tollendo ponens (MTP), Latin for "mode that affirms by denying") is a valid argument form which is a syllogism
Disjunctive_syllogism
Reasoning pattern that links beliefs to actions through a conclusion
The practical syllogism is an instance of practical reasoning which takes the form of a syllogism, where the conclusion of the syllogism is an action.
Practical_syllogism
Type of logical fallacy
The politician's syllogism, also known as the politician's logic or the politician's fallacy, is a logical fallacy of the form: We must do something.
Politician's_syllogism
Form of argument to test if an act is lawful
Legal syllogism is a legal concept concerning the law and its application, specifically a form of argument based on deductive reasoning and seeking to
Legal_syllogism
Syllogism with conditional premise(s)
In classical logic, a hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises
Hypothetical_syllogism
A statistical syllogism (or proportional syllogism or direct inference) is a non-deductive syllogism. It argues, using inductive reasoning, from a generalization
Statistical_syllogism
Prosleptic syllogisms (/prəˈslɛptɪk/; from Greek πρόσληψις proslepsis "taking in addition") are a class of syllogisms that use a prosleptic proposition
Prosleptic_syllogism
British mathematician and logician (1806–1871)
De Morgan (1850) "On the syllogism, No. II". De Morgan (1858) "On the syllogism, No. III". De Morgan (1863) "On the syllogism, No. V". De Morgan 1860.
Augustus_De_Morgan
Formal fallacy that occurs when a syllogism has four (or more) terms
that occurs when a syllogism has four (or more) terms rather than the requisite three, rendering it invalid. Categorical syllogisms always have three terms:
Fallacy_of_four_terms
Categorical syllogism
Quasi-syllogism is a categorical syllogism where one of the premises is singular, and thus not a categorical statement. For example: All men are mortal
Quasi-syllogism
In logic, a type of syllogistic fallacy
affirmative premises is a syllogistic fallacy committed when a categorical syllogism has a negative conclusion yet both premises are affirmative. The inability
Negative conclusion from affirmative premises
Negative_conclusion_from_affirmative_premises
Type of rhetorical deductive argument
is taken to be common sense. However, where the general premise of a syllogism is supposed to be true, making the subsequent deduction necessary, the
Enthymeme
Approach to logic
Aristotle identifies valid and invalid forms of arguments called syllogisms. A syllogism is an argument that consists of at least three sentences: at least
Term_logic
Scientific work by Aristotle
definition, and scientific knowledge. The demonstration is distinguished as a syllogism productive of scientific knowledge, while the definition marked as the
Posterior_Analytics
Sequence of propositions which constitute a sequence of overlapping syllogisms
of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise
Polysyllogism
Form of reasoning
There are no clouds in the sky. Thus, it is not raining. A hypothetical syllogism is an inference that takes two conditional statements and forms a conclusion
Deductive_reasoning
In Reformed theology, the practical syllogism (Latin: syllogismus practicus) is a concept relating assurance of salvation to evidence in a person's life
Practical syllogism (theology)
Practical_syllogism_(theology)
Graphical set representation involving overlapping shapes
measuring instrument for logic). Weigel was the first to prove all valid syllogisms with the aid of shapes in a two-dimensional plane. In the case of generally
Euler_diagram
Mathematical logical symbol of 3 dots
generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is
Therefore_sign
Logical fallacy
categorical syllogism is not distributed in either the minor premise or the major premise. It is thus a syllogistic fallacy. In classical syllogisms, all statements
Fallacy of the undistributed middle
Fallacy_of_the_undistributed_middle
syllogisms as formulated in Aristotle's Categories, De interpretatione and Prior Analytics. In the spirit of Aristotle, they considered the syllogism
Logic_in_Islamic_philosophy
Ancient Greek philosopher and polymath (384–322 BC)
relations in On Interpretation, to the study of more complex forms, namely, syllogisms and demonstration (in the Analytics) and dialectics (in the Topics and
Aristotle
that occur in categorical syllogisms. Affirmative conclusion from a negative premise (illicit negative) – a categorical syllogism has a positive conclusion
List_of_fallacies
Ancient philosophy
other, the third thema, was a cut rule by which chain syllogisms could be reduced to simple syllogisms.[e] The importance of these rules is not altogether
Stoicism
Logical fallacy in syllogisms
exclusive premises is a syllogistic fallacy committed in a categorical syllogism that is invalid because both of its premises are negative. E Proposition:
Fallacy_of_exclusive_premises
syllogistic logic, there are 256 possible ways to construct categorical syllogisms using the A, E, I, and O statement forms in the square of opposition.
List_of_valid_argument_forms
Method of deriving conclusions
different patterns of valid arguments, such as modus tollens, disjunctive syllogism, constructive dilemma, and existential generalization. Rules of inference
Rule_of_inference
Totality of psychological phenomena
249, 290 Ball 2013, pp. 739–740 Nunes 2011, p. 2066 Groarke, § 9. The Syllogism Ball 2013, pp. 739–740 Bernstein & Nash 2006, p. 254 Chowdhary 2020, p
Mind
Branch of logic
First-order equational logic consists of quantifier-free terms of ordinary first-order logic, with equality as the only predicate symbol. The model theory
Equational_logic
Rule of logical inference
Therefore, Q must also be true." Modus ponens is a mixed hypothetical syllogism and is closely related to another valid form of argument, modus tollens
Modus_ponens
Mathematical logic concept
Hypothetical syllogism (HS2) ( p → q ) → ( ( q → r ) → ( p → r ) ) {\displaystyle (p\to q)\to ((q\to r)\to (p\to r))} - another form of Hypothetical syllogism. We
Contraposition
Logical fallacy
implies the negation of the consequent. It is a type of mixed hypothetical syllogism that takes on the following form: If P, then Q. Not P. Therefore, not
Denying_the_antecedent
Propositional logic theorem
(r\to q)} by φ0. We also use repeatedly the method of the hypothetical syllogism metatheorem as a shorthand for several proof steps. (1) φ 0 {\displaystyle
Double_negation
Theorem in formal logic
true, i.e., unicorns exist (this inference is known as the disjunctive syllogism). The procedure may be repeated to prove that unicorns do not exist (hence
Principle_of_explosion
Informal fallacy involving falsely limited alternatives
the constructive dilemma, the destructive dilemma or the disjunctive syllogism. False dilemmas are usually discussed in terms of deductive arguments
False_dilemma
Rule of logical inference
argument form and a rule of inference. Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q. Therefore, not P." It is
Modus_tollens
2008 video game
Trism is a puzzle game for the Apple iPhone developed by American developer Demiforce, notable for his work on the widely acclaimed Mother 3 fan translation
Trism
Romanian philosopher, aphorist, and essayist (1911–1995)
décomposition ("A Short History of Decay"), Gallimard 1949 Syllogismes de l'amertume (literally "Syllogisms on Bitterness"; tr. "All Gall Is Divided"), Gallimard
Emil_Cioran
Works by Aristotle
location"). Though the Topics, as a whole, does not deal directly with syllogism, clearly Aristotle contemplates the use of topics as places from which
Topics_(Aristotle)
Work by Georg Wilhelm Friedrich Hegel
unity. Science of Logic also incorporates the traditional Aristotelian syllogism: it is conceived as a phase of the "original unity of thought and being"
Science_of_Logic
5th-century BC Greek mathematician
considerations that can produce only belief." His account of the syllogism is as follows: Bryson's syllogism on the squaring of the circle was of this sort, it is
Bryson_of_Heraclea
Work of Aristotle pertaining to logic
gives an account of deductions in general narrowed down to three basic syllogisms while Posterior Analytics deals with demonstration. In the first book
Prior_Analytics
1323 textbook on logic by William of Ockham
of the Aristotelian Predicables, Categories, terms, propositions, and syllogisms. These headings, though often given in a different order, represent the
Sum_of_Logic
Steps in reasoning
reaching such a conclusion. Ancient Greek philosophers defined a number of syllogisms, correct three part inferences, that can be used as building blocks for
Inference
Work of dramatic theory by Aristotle
Category of being Future contingents Genus–differentia Irrelevant conclusion Syllogism Physics accident Active intellect Antiperistasis Essence Eternity of the
Poetics_(Aristotle)
Attempt to persuade or to determine the truth of a conclusion
do not entail it. Forms of non-deductive logic include the statistical syllogism, which argues from generalizations true for the most part, and induction
Argument
Logical fallacy
illicit negative, is a formal fallacy that is committed when a categorical syllogism has a positive conclusion and one or two negative premises. For example:
Affirmative conclusion from a negative premise
Affirmative_conclusion_from_a_negative_premise
System of enforceable rules
and methods of interpreting (construing) the law. The former are legal syllogism, which holds sway in civil law legal systems, analogy, which is present
Law
Incorrect proposition that forms the basis of an argument
premise is an incorrect proposition that forms the basis of an argument or syllogism. Since the premise (proposition, or assumption) is not correct, the conclusion
False_premise
Work of literature by Aristotle
there are three: ethos, pathos, and logos. He introduces paradigms and syllogisms as means of persuasion. Chapter Three Aristotle introduces the three genres
Rhetoric_(Aristotle)
Judging arguments by the plausibility of their conclusion
conditional reasoning, relation reasoning and transitive reasoning. A syllogism is a kind of logical argument in which one proposition (the conclusion)
Belief_bias
Study of correct reasoning
2015, 4. Categorical Syllogisms; Copi, Cohen & Rodych 2019, 6. Categorical Syllogisms. Groarke; Hurley 2015, 4. Categorical Syllogisms; Copi, Cohen & Rodych
Logic
Book by Francis Bacon
treatise on logic and syllogism. In Novum Organum, Bacon details a new system of logic he believes to be superior to the old ways of syllogism. This is now known
Novum_Organum
Overview of and topical guide to logic
Disjunction introduction Disjunctive syllogism Double negation elimination Generalization (logic) Hypothetical syllogism Law of excluded middle Law of identity
Outline_of_logic
Topics referred to by the same term
that is applied to dates before its introduction Proleptic syllogism, a class of syllogism in logic This disambiguation page lists articles associated
Proleptic
Treatise by Aristotle
its properties and operations. It is like finding the middle term to a syllogism with a known conclusion. Therefore, we must seek out such operations of
On_the_Soul
Misleading use of a term with multiple meanings
not from the grammar or structure of the sentence. Equivocation in a syllogism (a chain of reasoning) produces a fallacy of four terms (quaternio terminorum)
Equivocation
Method of logical reasoning
of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. There are also differences
Inductive_reasoning
Work of political philosophy by Aristotle
Category of being Future contingents Genus–differentia Irrelevant conclusion Syllogism Physics accident Active intellect Antiperistasis Essence Eternity of the
Politics_(Aristotle)
Type of philosophical counseling
ordered in terms of a syllogism was in fact an insight of Aristotle, who called this kind of syllogism a "practical syllogism." The distinction is that
Logic-based_therapy
Formal fallacy about knowledge of objects
who Y is. Conclusion: Therefore, X is not Y. Note, however, that this syllogism happens in the reasoning by the speaker "I"; Therefore, in the formal
Masked-man_fallacy
Part of the mind that is not currently of focal awareness
(1963), Joseph Murphy likens the workings of the subconscious mind to a syllogism. Murphy states (p. 43), "whatever major premise your conscious mind assumes
Subconscious
Type of formal logic
disjunctive syllogism. From the perspective of dialetheism, it makes perfect sense that disjunctive syllogism should fail. The idea behind this syllogism is that
Paraconsistent_logic
Subfield of mathematics
emergence, logic was studied with rhetoric, with calculationes, through the syllogism, and with philosophy. The first half of the 20th century saw an explosion
Mathematical_logic
Topic in philosophy; something that is the opposite of something else
one simpler. Aristotle states that antithesis in rhetoric is similar to syllogism due to the presentation of two conclusions within a statement. Antitheses
Antithesis
American philosopher (1917–2002)
works Introduction to Logic (1953) Notable ideas Logical matrix Venn diagram method for syllogism testing Reverse truth table method for syllogism testing
Irving_Copi
Branch of logic
the binary connectives, and the rule reductio ad adbsurdum. Disjunctive Syllogism can be used as an easier alternative to the proper ∨-elimination, and
Propositional_logic
Problem or enigma that tests a person's ingenuity
Optical illusion Packing problems Paradox Problem solving Puzzlehunt Syllogism Tale Lists Impossible puzzles Maze video games Nikoli puzzle types Puzzle
Puzzle
Use of science to increase knowledge
fundamental to instances or implications of principles. The notion of syllogism, a means of deductive reasoning as proceeding from previously established
Scientific_study
Category of being Future contingents Genus–differentia Irrelevant conclusion Syllogism Physics accident Active intellect Antiperistasis Essence Eternity of the
Works_of_Aristotle
Symbolic logic system
disjunctive syllogism as in the next section. Practically, in the intuitionistic context, the principle of explosion enables proving the disjunctive syllogism in
Minimal_logic
Diagram that shows all possible logical relations between a collection of sets
their applications, he noted that a three-set diagram could show the syllogism: 'All A is some B. No B is any C. Hence, no A is any C.' Charles L. Dodgson
Venn_diagram
Aristotelian logic, baroco is a mnemonic word used to memorize a class of syllogism. Specifically, it has the first proposition universal and affirmative
Baroco
Ancient Indian philosophy
conditionally proven hypothesis is called a nigamana (conclusion). The syllogism of the Vaiśeṣika school was similar to that of the Nyāya school of Hinduism
Vaisheshika
Operation on binary relations
Beginning with Augustus De Morgan, the traditional form of reasoning by syllogism has been subsumed by relational logical expressions and their composition
Composition_of_relations
Topics referred to by the same term
traditional names for two of the syllogisms of Aristotelian logic A mnemonic poem by William of Sherwood listing the syllogisms A pseudonym of Andrew Abbott
Barbara_Celarent
Logical operation
Logical equivalence Consistency Equiconsistency Argument Soundness Validity Syllogism Square of opposition Venn diagram Propositional Boolean algebra Boolean
Negation
Basic framework of mathematics
a theorem that is proved from true premises by means of a sequence of syllogisms (inference rules), the premises being either already proved theorems or
Foundations_of_mathematics
Yes-or-no question that cannot ever be solved by a computer
Logical equivalence Consistency Equiconsistency Argument Soundness Validity Syllogism Square of opposition Venn diagram Propositional Boolean algebra Boolean
Undecidable_problem
Subfield of automated reasoning and mathematical logic
Logical equivalence Consistency Equiconsistency Argument Soundness Validity Syllogism Square of opposition Venn diagram Propositional Boolean algebra Boolean
Automated_theorem_proving
Philosophical argument for the existence of God
defended by William Lane Craig, is expressed in two parts, as an initial syllogism followed by further philosophical analysis. The Kalam cosmological argument
Kalam_cosmological_argument
Mathematical set containing no elements
the set of all opening moves in chess that involve a king." The popular syllogism Nothing is better than eternal happiness; a ham sandwich is better than
Empty_set
Greek Stoic philosopher (c.279–c.206 BC)
Aristotle – Theophrastus and Eudemus – had investigated hypothetical syllogisms, it was Chrysippus who developed these principles into a coherent system
Chrysippus
Type of fallacy in modal logic
two. A fallacy of necessity is an informal fallacy in the logic of a syllogism whereby a degree of unwarranted necessity is placed in the conclusion
Modal_fallacy
Epistemological view centered on reason
categorical syllogisms which consist of three categorical propositions in his work Prior Analytics. These included categorical modal syllogisms. Although
Rationalism
Class of formal logics
mathematical theorems rely on classical rules of inference such as disjunctive syllogism and the double negation elimination. The adjective "classical" in logic
Classical_logic
{\underline {\varphi \lor \psi }}} χ {\displaystyle \chi } Disjunctive syllogism φ ∨ ψ {\displaystyle \varphi \lor \psi } ¬ φ _ {\displaystyle {\underline
List_of_rules_of_inference
Various systems of symbolic logic
which excluded middle holds can be proven stable using the disjunctive syllogism, which is discussed more thoroughly below. The converse does however not
Intuitionistic_logic
Function that preserves distinctness
Logical equivalence Consistency Equiconsistency Argument Soundness Validity Syllogism Square of opposition Venn diagram Propositional Boolean algebra Boolean
Injective_function
Oral puzzle guessing game
Optical illusion Packing problems Paradox Problem solving Puzzlehunt Syllogism Tale Lists Impossible puzzles Maze video games Nikoli puzzle types Puzzle
Situation_puzzle
Treatise by Aristotle
Category of being Future contingents Genus–differentia Irrelevant conclusion Syllogism Physics accident Active intellect Antiperistasis Essence Eternity of the
Physics_(Aristotle)
Axiom that has everything has a reason
Hamilton 1860:241–242: “2°, "If the essential nature of an Hypothetical Syllogism consist in this, – that the subsumption affirms or denies one or other
Principle of sufficient reason
Principle_of_sufficient_reason
Statement regarding whether or not an item belongs to a category
predicate term). The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the
Categorical_proposition
Development of Indian logic
Classical logic. Nyāya (ni-āyá, literally "recursion", used in the sense of "syllogism, inference") is the name given to one of the six orthodox or astika schools
Indian_logic
Puzzle deriving from the mathematical field of deduction
list of premises and asked what can be deduced from them, are known as syllogisms.[citation needed] Dodgson goes on to construct much more complex puzzles
Logic_puzzle
Puzzle game involving sliding pieces
Optical illusion Packing problems Paradox Problem solving Puzzlehunt Syllogism Tale Lists Impossible puzzles Maze video games Nikoli puzzle types Puzzle
Sliding_puzzle
1969 non-fiction book by G. Spencer-Brown
of LoF shows how to translate traditional syllogisms and sorites into the primary algebra. A valid syllogism is simply one whose primary algebra translation
Laws_of_Form
Property that assigns truth values to k-tuples of individuals
ISBN 978-0201141924. De Morgan, A. (1966) [1858], "On the syllogism, part 3", in Heath, P. (ed.), On the syllogism and other logical writings, Routledge, p. 119 Halmos
Finitary_relation
Teacher
the Divine Scriptures declare, but strive laboriously after any form of syllogism which may be devised to sustain their impiety. And if any one brings before
Artemon
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