In Aristotelian logic, Baralipton (also Bamalip or Bramantip) 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 (the middle term is the subject of the first premise and the predicate of the second premise), 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.
Generally stated:
All M is P
All S is M
Therefore some P is S.
For example,
Every evil ought to be feared.
Every violent passion is an evil.
Therefore, some things that ought to be feared are violent passions.
In traditional Aristotelian logic, Baralipton is just a weakened form of Barbara (where the conclusion is also universal affirmative: AllS are P).
In propositional logic, modus ponens, also known as modus ponendo ponens or implication elimination or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "P implies Q.P is true. Therefore Q must also be true."
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.
In term logic, the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle making the distinction between two oppositions: contradiction and contrariety. However, Aristotle did not draw any diagram. This was done several centuries later by Apuleius and Boethius.
In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to logic that began with Aristotle and was developed further in ancient history mostly by his followers, the peripatetics, but largely fell into decline by the third century CE.
Inductive reasoning is a method of reasoning in which a body of observations is synthesized to come up with a general principle. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from deductive reasoning. If the premises are correct, the conclusion of a deductive argument is certain; in contrast, the truth of the conclusion of an inductive argument is probable, based upon the evidence given.
The fallacy of the undistributed middle is a formal fallacy that is committed when the middle term in a categorical syllogism is not distributed in either the minor premise or the major premise. It is thus a syllogistic fallacy.
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 Prior Analytics is a work by Aristotle on deductive reasoning, known as his syllogistic, composed around 350 BCE. Being one of the six extant Aristotelian writings on logic and scientific method, it is part of what later Peripatetics called the Organon. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by Jan Łukasiewicz of a revolutionary paradigm. His approach was replaced in the early 1970s in a series of papers by John Corcoran and Timothy Smiley—which inform modern translations of Prior Analytics by Robin Smith in 1989 and Gisela Striker in 2009.
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.
The fallacy of exclusive premises is a syllogistic fallacy committed in a categorical syllogism that is invalid because both of its premises are negative.
The Posterior Analytics is a text from Aristotle's Organon that deals with demonstration, definition, and scientific knowledge. The demonstration is distinguished as a syllogism productive of scientific knowledge, while the definition marked as the statement of a thing's nature, ... a statement of the meaning of the name, or of an equivalent nominal formula.
Early Islamic law placed importance on formulating standards of argument, which gave rise to a "novel approach to logic" in Kalam . However, with the rise of the Mu'tazili philosophers, who highly valued Aristotle's Organon, this approach was displaced by the older ideas from Hellenistic philosophy. The works of al-Farabi, Avicenna, al-Ghazali and other Persian Muslim logicians who often criticized and corrected Aristotelian logic and introduced their own forms of logic, also played a central role in the subsequent development of European logic during the Renaissance.
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 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, baroco is a mnemonic word used to memorize a syllogism. Specifically, it has the first proposition universal and affirmative, but the second and third particular and negative, and the middle term the attribute in the two first. For example,
The False Subtlety of the Four Syllogistic Figures Proved is an essay published by Immanuel Kant in 1762.
In Aristotelian logic, dictum de omni et nullo is the principle that whatever is affirmed or denied of a whole kind K may be affirmed or denied (respectively) of any subkind of K. This principle is fundamental to syllogistic logic in the sense that all valid syllogistic argument forms are reducible to applications of the two constituent principles dictum de omni and dictum de nullo.
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.
Logic is the study of correct reasoning or good arguments. It is often defined in a more narrow sense as the science of deductively valid inferences or of logical truths. In this sense, it is equivalent to formal logic and constitutes a formal science investigating how conclusions follow from premises in a topic-neutral way or which propositions are true only in virtue of the logical vocabulary they contain. When used as a countable noun, the term "a logic" refers to a logical formal system. Formal logic contrasts with informal logic, which is also part of logic when understood in the widest sense. There is no general agreement on how the two are to be distinguished. One prominent approach associates their difference with the study of arguments expressed in formal or informal languages. Another characterizes informal logic as the study of ampliative inferences, in contrast to the deductive inferences studied by formal logic. But it is also common to link their difference to the distinction between formal and informal fallacies.
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