Hypostatic abstraction

Hypostatic abstraction in mathematical logic, also known as hypostasis or subjectal abstraction, is a formal operation that transforms a predicate into a relation; for example "Honey is sweet" is transformed into "Honey has sweetness". The relation is created between the original subject and a new term that represents the property expressed by the original predicate.

Hypostasis changes a propositional formula of the form X is Y to another one of the form X has the property of being Y or X has Y-ness. The logical functioning of the second object Y-ness consists solely in the truth-values of those propositions that have the corresponding abstract property Y as the predicate. The object of thought introduced in this way may be called a hypostatic object and in some senses an abstract object and a formal object.

The above definition is adapted from the one given by Charles Sanders Peirce (CP 4.235, "The Simplest Mathematics" (1902), in Collected Papers, CP 4.227–323). As Peirce describes it, the main point about the formal operation of hypostatic abstraction, insofar as it operates on formal linguistic expressions, is that it converts an adjective or predicate into an extra subject, thus increasing by one the number of "subject" slots—called the arity or adicity—of the main predicate.

The transformation of "honey is sweet" into "honey possesses sweetness" can be viewed in several ways:

Hypostasis-diagram

Hypostasis-diagram

The grammatical trace of this hypostatic transformation is a process that extracts the adjective "sweet" from the predicate "is sweet", replacing it by a new, increased-arity predicate "possesses", and as a by-product of the reaction, as it were, precipitating out the substantive "sweetness" as a second subject of the new predicate.

The abstraction of hypostasis takes the concrete physical sense of "taste" found in "honey is sweet" and gives it formal metaphysical characteristics in "honey has sweetness".

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Abstraction

Abstraction in its main sense is a conceptual process where general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods.

"An abstraction" is the outcome of this process—a concept that acts as a common noun for all subordinate concepts, and connects any related concepts as a group, field, or category.Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only the aspects which are relevant for a particular subjectively valued purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on general ball attributes and behavior, excluding, but not eliminating, the other phenomenal and cognitive characteristics of that particular ball. In a type–token distinction, a type (e.g., a 'ball') is more abstract than its tokens (e.g., 'that leather soccer ball').

Abstraction in its secondary use is a material process, discussed in the themes below.

Abstraction (disambiguation)

Abstraction is a process or result of generalization, removal of properties, or distancing of ideas from objects. Abstraction may also refer to:

Abstraction (art), art unconcerned with the literal depiction of things from the visible world

Abstraction (computer science), a process of hiding details of implementation in programs and data

Abstraction layer, an application of abstraction in computing

Hardware abstraction, an abstraction layer on top of hardware

Abstraction (linguistics), use of terms for concepts removed from the objects to which they were originally attached

Abstraction (mathematics), a process of removing the dependence of a mathematical concept on real-world objects

Hypostatic abstraction, a formal operation that transforms a predicate into a relation

Lambda abstraction, a definition of an anonymous function that produces a valid term in lambda calculus

Abstraction (sociology), a process of considering sociological concepts at a more theoretical level

Nucleophilic abstraction, a nucleophilic attack which causes part or all of a ligand to be removed from a metal

Water abstraction, the process of taking water from any source

Abstracting electricity, the crime of diverting electricity around an electricity meter and/or using it without paying for it

Aka Manah

Aka Manah is the Avestan language name for the Zoroastrian daeva "Evil Mind", "Evil Purpose", "Evil Thinking", or "Evil Intention". Aka Manah is the demon of sensual desire that was sent by Ahriman to seduce the prophet Zoroaster. His eternal opponent is Vohu Manah. Aka Manah is the hypostatic abstraction of accusative akem manah (akәm manah), "manah made evil". The objectification of this malign influence is the demon Aka/Akem Manah, who appears in later texts as Middle Persian Akoman and New Persian Akvan.

Categories (Peirce)

On May 14, 1867, the 27-year-old Charles Sanders Peirce, who eventually founded pragmatism, presented a paper entitled "On a New List of Categories" to the American Academy of Arts and Sciences. Among other things, this paper outlined a theory of predication involving three universal categories that Peirce continued to apply in philosophy and elsewhere for the rest of his life. In the categories one will discern, concentrated, the pattern which one finds formed by the three grades of clearness in "How to Make Our Ideas Clear" (1878 foundational paper for pragmatism), and in numerous other three-way distinctions in his work.

Charles Sanders Peirce

Charles Sanders Peirce (, PURSS; 10 September 1839 – 19 April 1914) was an American philosopher, logician, mathematician, and scientist who is sometimes known as "the father of pragmatism". He was educated as a chemist and employed as a scientist for thirty years. Today he is appreciated largely for his contributions to logic, mathematics, philosophy, scientific methodology, semiotics, and for his founding of pragmatism.

An innovator in mathematics, statistics, philosophy, research methodology, and various sciences, Peirce considered himself, first and foremost, a logician. He made major contributions to logic, but logic for him encompassed much of that which is now called epistemology and philosophy of science. He saw logic as the formal branch of semiotics, of which he is a founder, which foreshadowed the debate among logical positivists and proponents of philosophy of language that dominated 20th century Western philosophy. Additionally, he defined the concept of abductive reasoning, as well as rigorously formulated mathematical induction and deductive reasoning. As early as 1886 he saw that logical operations could be carried out by electrical switching circuits. The same idea was used decades later to produce digital computers.In 1934, the philosopher Paul Weiss called Peirce "the most original and versatile of American philosophers and America's greatest logician". Webster's Biographical Dictionary said in 1943 that Peirce was "now regarded as the most original thinker and greatest logician of his time." Keith Devlin similarly referred to Peirce as one of the greatest philosophers ever.

Charles Sanders Peirce bibliography

This Charles Sanders Peirce bibliography consolidates numerous references to Charles Sanders Peirce's writings, including letters, manuscripts, publications, and Nachlass. For an extensive chronological list of Peirce's works (titled in English), see the Chronologische Übersicht (Chronological Overview) on the Schriften (Writings) page for Charles Sanders Peirce.

Codrin Țapu

Codrin Ștefan Țapu (born 17 December 1973) is a Romanian author and psychologist. His works are centered on describing and changing the "aspects" of personality, and propose a perspective of interconnected spiritual support systems.

Concept

Concepts are mental representations, abstract objects or abilities that make up the fundamental building blocks of thoughts and beliefs. They play an important role in all aspects of cognition.In contemporary philosophy, there are at least three prevailing ways to understand what a concept is:

Concepts as mental representations, where concepts are entities that exist in the mind (mental objects)

Concepts as abilities, where concepts are abilities peculiar to cognitive agents (mental states)

Concepts as Fregean senses (see sense and reference), where concepts are abstract objects, as opposed to mental objects and mental statesConcepts can be organized into a hierarchy, higher levels of which are termed "superordinate" and lower levels termed "subordinate". Additionally, there is the "basic" or "middle" level at which people will most readily categorize a concept. For example, a basic-level concept would be "chair", with its superordinate, "furniture", and its subordinate, "easy chair".

A concept is instantiated (reified) by all of its actual or potential instances, whether these are things in the real world or other ideas.

Concepts are studied as components of human cognition in the cognitive science disciplines of linguistics, psychology and philosophy, where an ongoing debate asks whether all cognition must occur through concepts. Concepts are used as formal tools or models in mathematics, computer science, databases and artificial intelligence where they are sometimes called classes, schema or categories. In informal use the word concept often just means any idea.

Continuous predicate

Continuous predicate is a term coined by Charles Sanders Peirce (1839–1914) to describe a special type of relational predicate that results as the limit of a recursive process of hypostatic abstraction.

Here is one of Peirce's definitive discussions of the concept:

When we have analyzed a proposition so as to throw into the subject everything that can be removed from the predicate, all that it remains for the predicate to represent is the form of connection between the different subjects as expressed in the propositional form. What I mean by "everything that can be removed from the predicate" is best explained by giving an example of something not so removable.

But first take something removable. "Cain kills Abel." Here the predicate appears as "— kills —." But we can remove killing from the predicate and make the latter "— stands in the relation — to —." Suppose we attempt to remove more from the predicate and put the last into the form "— exercises the function of relate of the relation — to —" and then putting "the function of relate to the relation" into another subject leave as predicate "— exercises — in respect to — to —." But this "exercises" expresses "exercises the function". Nay more, it expresses "exercises the function of relate", so that we find that though we may put this into a separate subject, it continues in the predicate just the same.

Stating this in another form, to say that "A is in the relation R to B" is to say that A is in a certain relation to R. Let us separate this out thus: "A is in the relation R¹ (where R¹ is the relation of a relate to the relation of which it is the relate) to R to B". But A is here said to be in a certain relation to the relation R¹. So that we can express the same fact by saying, "A is in the relation R¹ to the relation R¹ to the relation R to B", and so on ad infinitum.

A predicate which can thus be analyzed into parts all homogeneous with the whole I call a continuous predicate. It is very important in logical analysis, because a continuous predicate obviously cannot be a compound except of continuous predicates, and thus when we have carried analysis so far as to leave only a continuous predicate, we have carried it to its ultimate elements. (C.S. Peirce, "Letters to Lady Welby" (14 December 1908), Selected Writings, pp. 396–397).

Hypostasis

Hypostatic, Hypostasis, or Hypostatization (from the Ancient Greek ὑπόστᾰσις, "under state") may refer to:

Hypostasis (philosophy and religion), the essence, or underlying reality

Hypostatic abstraction (mathematics and logic)

Hypostasis (linguistics), personification of entities

Hypostasis (literature), awareness by a fictional character of the fictional world

Hypostatic gene, as a result of epistasis

Hypostasis or Livor mortis

Hypostatic model of personality, a psychological model, or theory, of personality masks

Hypostatic union, Christian concept

Holding current (electronics) known as the hypostatic

Reification (fallacy) where hypostasis is a technical term to identify a thing which is reified, and hypostatization refers to the thought process

Sediment in a liquid, including:

Sediment#Dregs

Hypostasis (philosophy and religion)

Hypostasis (Greek: ὑπόστασις) is the underlying state or underlying substance and is the fundamental reality that supports all else. In Neoplatonism the hypostasis of the soul, the intellect (nous) and "the one" was addressed by Plotinus.

In Christian theology, a hypostasis is one of the three hypostases (Father, Son, Holy Spirit) of the Trinity.

Hypostatic model of personality

The hypostatic model of personality is a view asserting that humans present themselves in many different aspects or hypostases, depending on the internal and external realities they relate to, including different approaches to the study of personality. It is both a dimensional model and an aspect theory, in the sense of the concept of multiplicity. The model falls into the category of complex, biopsychosocial approaches to personality.

The term hypostasis can cover a wide range of personality-related entities usually known as type, stage, trait, system, approach. The history of the concept can be traced back to Peirce's hypostatic abstraction, or personification of traits. Different authors have described various dimensions of the self (or selves), personality dimensions and subpersonalities. Contemporary studies link different aspects of personality to specific biological, social, and environmental factors.

The work on subpersonalities was integrated into a hypostatic model. The model describes personality aspects and dimensions, as well as intra- and interpersonal relations. Not the person whole and alone, nor the relationship, but the relation between parts of person(s) is held as a central element that promotes both personal and social organization and disorganization. Personality is viewed as both an agency and a construction, along with its development and psychopathology, as the model is accompanied by specific methods of assessment and therapy, addressing each of the personality dimensions. The hypostatic relations of the human mind also imply the existence of a hypostatic model of consciousness, representing the contents of consciousness as an identity of various aspects, different only with respect to each other, but tending to coincide in a certain aspect of their consideration.

Object (philosophy)

An object is a technical term in modern philosophy often used in contrast to the term subject. A subject is an observer and an object is a thing observed. For modern philosophers like Descartes, consciousness is a state of cognition that includes the subject—which can never be doubted as only it can be the one who doubts—and some object(S) that may be considered as not having real or full existence or value independent of the subject who observes it. Metaphysical frameworks also differ in whether they consider objects existing independently of their properties and, if so, in what way.The pragmatist Charles S. Peirce defines the broad notion of an object as anything that we can think or talk about. In a general sense it is any entity: the pyramids, Alpha Centauri, the number seven, a disbelief in predestination or the fear of cats. In a strict sense it refers to any definite being.

A related notion is objecthood. Objecthood is the state of being an object. One approach to defining it is in terms of objects' properties and relations. Descriptions of all bodies, minds, and persons must be in terms of their properties and relations. The philosophical question of the nature of objecthood concerns how objects are related to their properties and relations. For example, it seems that the only way to describe an apple is by describing its properties and how it is related to other things. Its properties may include its redness, its size, and its composition, while its relations may include "on the table", "in the room" and "being bigger than other apples".

The notion of an object must address two problems: the change problems and the problems of substances. Two leading theories about objecthood are substance theory, wherein substances (objects) are distinct from their properties, and bundle theory, wherein objects are no more than bundles of their properties.

Philosophical zombie

The philosophical zombie or p-zombie argument is a thought experiment in philosophy of mind and philosophy of perception that imagines a being that, if it could conceivably exist, logically disproves the idea that physical stuff is all that is required to explain consciousness. Such a zombie would be indistinguishable from a normal human being but lack conscious experience, qualia, or sentience. For example, if a philosophical zombie were poked with a sharp object it would not inwardly feel any pain, yet it would outwardly behave exactly as if it did feel pain. The argument sometimes takes the form of hypothesizing a zombie world, indistinguishable from our world, but lacking first person experiences in any of the beings of that world.

Philosophical zombie arguments are used in support of mind-body dualism against forms of physicalism such as materialism, behaviorism and functionalism. It's an argument against the idea that the "hard problem of consciousness" (accounting for subjective, intrinsic, first person, what-it's-like-ness) could be answered by purely physical means. Proponents of the argument, such as Australian philosopher David Chalmers, argue that since a zombie is defined as physiologically indistinguishable from human beings, even its logical possibility would be a sound refutation of physicalism, because it would establish the existence of conscious experience as a further fact. However, physicalists like Daniel Dennett counter that philosophical zombies are logically incoherent and thus impossible.

Pragmaticism

"Pragmaticism" is a term used by Charles Sanders Peirce for his pragmatic philosophy starting in 1905, in order to distance himself and it from pragmatism, the original name, which had been used in a manner he did not approve of in the "literary journals". Peirce in 1905 announced his coinage "pragmaticism", saying that it was "ugly enough to be safe from kidnappers" (Collected Papers (CP) 5.414). Today, outside of philosophy, "pragmatism" is often taken to refer to a compromise of aims or principles, even a ruthless search for mercenary advantage. Peirce gave other or more specific reasons for the distinction in a surviving draft letter that year and in later writings. Peirce's pragmatism, that is, pragmaticism, differed in Peirce's view from other pragmatisms by its commitments to the spirit of strict logic, the immutability of truth, the reality of infinity, and the difference between (1) actively willing to control thought, to doubt, to weigh reasons, and (2) willing not to exert the will, willing to believe. In his view his pragmatism is, strictly speaking, not itself a whole philosophy, but instead a general method for the clarification of ideas. He first publicly formulated his pragmatism as an aspect of scientific logic along with principles of statistics and modes of inference in his "Illustrations of the Logic of Science" series of articles in 1877-8.

Problem of why there is anything at all

The question "Why is there anything at all?", or, "Why is there something rather than nothing?" has been raised or commented on by philosophers including Gottfried Wilhelm Leibniz, Ludwig Wittgenstein, and Martin Heidegger − who called it the fundamental question of metaphysics.

The Master and His Emissary

The Master and His Emissary: The Divided Brain and the Making of the Western World is a 2009 book written by Iain McGilchrist that deals with the specialist hemispheric functioning of the brain. The differing world views of the right and left brain (the "Master" and "Emissary" in the title, respectively) have, according to the author, shaped Western culture since the time of the ancient Greek philosopher Plato, and the growing conflict between these views has implications for the way the modern world is changing. In part, McGilchrist's book, which is the product of twenty years of research, reviews the evidence of previous related research and theories, and based on this and cultural evidence, the author arrives at his own conclusions.

The Master and His Emissary received mostly favourable reviews upon its publication. Critics praised the book as being a landmark publication that could alter readers' perspective of how they viewed the world; A. C. Grayling, however, commented about the book that "the findings of brain science are nowhere near fine-grained enough yet to support the large psychological and cultural conclusions Iain McGilchrist draws".The Master and His Emissary was shortlisted for the 2010 Bristol Festival of Ideas Book Prize, and was longlisted for the Royal Society 2010 Prize for Science Books.

Universal (metaphysics)

In metaphysics, a universal is what particular things have in common, namely characteristics or qualities. In other words, universals are repeatable or recurrent entities that can be instantiated or exemplified by many particular things. For example, suppose there are two chairs in a room, each of which is green. These two chairs both share the quality of "chairness", as well as greenness or the quality of being green; in other words, they share a "universal". There are three major kinds of qualities or characteristics: types or kinds (e.g. mammal), properties (e.g. short, strong), and relations (e.g. father of, next to). These are all different types of universals.Paradigmatically, universals are abstract (e.g. humanity), whereas particulars are concrete (e.g. the personhood of Socrates). However, universals are not necessarily abstract and particulars are not necessarily concrete. For example, one might hold that numbers are particular yet abstract objects. Likewise, some philosophers, such as D. M. Armstrong, consider universals to be concrete.

Most do not consider classes to be universals, although some prominent philosophers do, such as John Bigelow.

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