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Dictum De Omni Et Nullo
In Aristotelian logic, ''dictum de omni et nullo'' (Latin: "the maxim of all and none") 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''. ''Dictum de omni'' ''Dictum de omni'' (sometimes misinterpreted as universal instantiation) is the principle that whatever is universally affirmed of a kind is affirmable as well for any subkind of that kind. Example: (1) Dogs are mammals. (2) Mammals have livers. Therefore (3) dogs have livers. Premise (1) states that "dog" is a subkind of the kind "mammal". Premise (2) is a (universal affirmative) claim about the kind "mammal". Statement (3) concludes that what is true of the kind "mammal" is true of the subkind "dog". ''Dictum de nullo'' ''Dic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Organon
The ''Organon'' ( grc, Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logical analysis and dialectic. The name ''Organon'' was given by Aristotle's followers, the Peripatetics. The six works are as follows: Constitution of the texts The order of the works is not chronological (which is now hard to determine) but was deliberately chosen by Theophrastus to constitute a well-structured system. Indeed, parts of them seem to be a scheme of a lecture on logic. The arrangement of the works was made by Andronicus of Rhodes around 40 BC. Aristotle's ''Metaphysics'' has some points of overlap with the works making up the ''Organon'' but is not traditionally considered part of it; additionally, there are works on logic attributed, with varying degrees of plausibility, to Aristotle that were not known to the Peripatetics. # The ''Categories'' (Latin: ) introduces Aristotle's 10-fold classification of that which exists: s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class (set Theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Classes act as a way to have set-like collections while differing from sets so as to avoid Russell's paradox (see ). The precise definition of "class" depends on foundational context. In work on Zermelo–Fraenkel set theory, the notion of class is informal, whereas other set theories, such as von Neumann–Bernays–Gödel set theory, axiomatize the notion of "proper class", e.g., as entities that are not members of another entity. A class that is not a set (informally in Zermelo–Fraenkel) is called a proper class, and a class that is a set is sometimes called a small class. For instance, the class of all ordinal numbers, and the class of all sets, are proper classes in many formal systems. In Quine's set-theoretical writing, the phrase "ultimate class" is often used in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin Logical Phrases
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the Roman Republic it became the dominant language in the Italian region and subsequently throughout the Roman Empire. Even after the fall of Western Rome, Latin remained the common language of international communication, science, scholarship and academia in Europe until well into the 18th century, when other regional vernaculars (including its own descendants, the Romance languages) supplanted it in common academic and political usage, and it eventually became a dead language in the modern linguistic definition. Latin is a highly inflected language, with three distinct genders (masculine, feminine, and neuter), six or seven noun cases (nominative, accusative, genitive, dative, ablative, and vocative), five declensions, four verb conjuga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prior Analytics
The ''Prior Analytics'' ( grc-gre, Ἀναλυτικὰ Πρότερα; la, Analytica Priora) is a work by Aristotle on 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 term ''analytics'' comes from the Greek words ''analytos'' (ἀναλυτός, 'solvable') and ''analyo'' (ἀναλύω, 'to solve', literally 'to loose'). However, in Aristotle's corpus, there are distinguishable differences in the meaning of ἀναλύω and its cognates. There is also the possi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Downward Entailing
In linguistic semantics, a downward entailing (DE) propositional operator is one that constrains the meaning of an expression to a lower number or degree than would be possible without the expression. For example, "not," "nobody," "few people," "at most two boys." Conversely, an upward-entailing operator constrains the meaning of an expression to a higher number or degree, for example "more than one." A context that is neither downward nor upward entailing is ''non-monotone'', such as "exactly five." A downward-entailing operator reverses the relation of ''semantic strength'' among expressions. An expression like "run fast" is semantically ''stronger'' than the expression "run" since "John ran fast" entails "John ran," but not conversely. But a downward-entailing context reverses this strength; for example, the proposition "At most two boys ran" entails that "At most two boys ran fast" but not the other way around. An upward-entailing operator preserves the relation of semantic st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type (metaphysics)
Type may refer to: Science and technology Computing * Typing, producing text via a keyboard, typewriter, etc. * Data type, collection of values used for computations. * File type * TYPE (DOS command), a command to display contents of a file. * Type (Unix), a command in POSIX shells that gives information about commands. * Type safety, the extent to which a programming language discourages or prevents type errors. * Type system, defines a programming language's response to data types. Mathematics * Type (model theory) * Type theory, basis for the study of type systems * Arity or type, the number of operands a function takes * Type, any proposition or set in the intuitionistic type theory * Type, of an entire function ** Exponential type Biology * Type (biology), which fixes a scientific name to a taxon * Dog type, categorization by use or function of domestic dogs Lettering * Type is a design concept for lettering used in typography which helped bring about modern textual printin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Kind
"Natural kind" is an intellectual grouping, or categorizing of things, in a manner that is reflective of the actual world and not just human interests. Some treat it as a classification identifying some structure of truth and reality that exists whether or not humans recognize it. Others treat it as intrinsically useful to the human mind, but not necessarily reflective of something more objective. Candidates examples of natural kinds are found in all the sciences, but the field of chemistry provides the paradigm example of elements. John Dewey held a minority view that belief in unconditional natural kinds is a mistake, a relic of obsolete scientific practices. W. V. O. Quine and Hilary Kornblith held the majoirity view that natural kinds are the unchanging structure of truth and reality. Hilary Putnam rejects descriptivist approaches to natural kinds with semantic reasoning. Hasok Chang and Rasmus Winther hold the emerging view that natural kinds are useful and evolving scientific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class (philosophy)
A class is a collection whose members either fall under a predicate or are classified by a rule. Hence, while a set can be extensionally defined only by its elements, a class has also an intensional dimension that unite its members. When the term 'class' is applied such that it includes those sets elements of which are intended to be collected without a common predicate or rule, the distinction can be indicated by calling such sets "improper class." Philosophers sometimes distinguish classes from types and kinds. We can talk about the ''class'' of human beings, just as we can talk about the ''type'' (or ''natural kind''), human being, or humanity. How, then, might classes differ from types? One might well think they are not actually different categories of being, but typically, while both are treated as abstract objects, classes are not usually treated as universals, whereas types usually are. Whether natural kinds ought to be considered universals is vexed; see natural ki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the Roman Republic it became the dominant language in the Italian region and subsequently throughout the Roman Empire. Even after the fall of Western Rome, Latin remained the common language of international communication, science, scholarship and academia in Europe until well into the 18th century, when other regional vernaculars (including its own descendants, the Romance languages) supplanted it in common academic and political usage, and it eventually became a dead language in the modern linguistic definition. Latin is a highly inflected language, with three distinct genders (masculine, feminine, and neuter), six or seven noun cases (nominative, accusative, genitive, dative, ablative, and vocative), five declensions, four verb conjuga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Term Logic
In philosophy, 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. Term logic revived in medieval times, first in Islamic logic by Alpharabius in the tenth century, and later in Christian Europe in the twelfth century with the advent of new logic, remaining dominant until the advent of predicate logic in the late nineteenth century. However, even if eclipsed by newer logical systems, term logic still plays a significant role in the study of logic. Rather than radically breaking with term logic, modern logics typically expand it, so to understand the newer systems, one must be acquainted with the earlier one. Aristotle's system Aristotle's logical work is collected in the six texts that are collectively known as the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of philosophy within the Lyceum and the wider Aristotelian tradition. His writings cover many subjects including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, meteorology, geology, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be a subject of contemporary philosophical discussion. Little is known about his life. Aristotle was born in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
