Category:Culture

Culture generally refers to ritual human activity, including such broad fields as art, entertainment, social structure, and religion. Different definitions of culture reflect different theories for understanding, or criteria for valuing, human activity. The word comes from the Latin root colere, (to inhabit, to cultivate, or to honor).

Main subcategories: Art, Arts Entertainment, Religion, Philosophy

Category:Art


Art is a broad term, which may be interpreted in many ways, often relating to creativity, aesthetics and generation of emotion. See the overview article about Art, Arts, Fine art

"Art" is often used only for visual art, but here refers to all art. There are 20 subcategories to this category.

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Category:Arts

The Arts constitute those areas of study, personal endeavour, and higher education (particularly at a post-secondary level) in fine art and humanities as opposed to the sciences which include science, mathematics, engineering and technology; or the professions or callings which include, architecture, medicine, law, and theology.

For more information, please see the main article about The Art


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Category:Entertainment


Entertainment is an amusement or diversion intended to hold the attention of an audience or its participants.

For more information, please see the main article about Entertainment.

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Category:Religion


Religion is commonly defined as belief concerning the supernatural, sacred, or divine, often resulting in worship, and possibly including related institutions and organizations.

For more information, please see the main article about Religion.

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Category:Philosophy

Philosophy is the critical study of the most fundamental questions that humankind has been able to ask. Philosophers ask questions such as

  • Metaphysics: What sorts of things exist? What is the nature of those things? Do some things exist independently of our perception? What is the nature of space and time? What is the nature of thought and thinking? What is it to be a person? What is it to be conscious? Is there a god?
  • Epistemology: Is knowledge possible? How do we come to know what we know? How can we know that there are other minds?
  • Ethics: Is there a difference between morally right and wrong actions (or values, or institutions)? If so, what is that difference? Which actions are right, and which wrong? Are values absolute, or relative? In general or particular terms, how should I live?
  • Logic: What makes for good thinking? When can I say for sure that something just doesn't make sense? How can I think critically about complicated arguments?

See list of philosophical topics for a more complete listing of topics beyond this category.

For more information, please see the main article about Philosophy.

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Culture

The word culture comes from the Latin root colere, (to inhabit, to cultivate, or to honor). In general it refers to human activity; different definitions of culture reflect different theories for understanding, or criteria for valuing, human activity. In 1952 Alfred Kroeber and Clyde Kluckhohn compiled a list of over 200 different definitions of culture in their book, Culture: A Critical Review of Concepts and Definitions.

Presently, the UNESCO defines culture as the "set of distinctive spiritual, material, intellectual and emotional features of society or a social group". Culture encompasses "in addition to art and literature, lifestyles, ways of living together, value systems, traditions and beliefs".

Popular use of the word culture in many Western societies can reflect the stratified character of those societies. Many use the word culture to refer to elite consumption goods and activities such as fine cuisine, art, and music. Some label this as "high" culture to distinguish it from "low" culture, meaning non-elite consumption goods and activities.

Related topics

Cultural studies developed in the late 20th century, in part through the reintroduction of Marxist thought into sociology, and in part through the articulation of sociology and other academic disciplines such as literary criticism, in order to focus on the analysis of subcultures in capitalist societies. Following the non-anthropological tradition, cultural studies generally focus on the study of consumption goods (such as fashion, art, and literature). Because the 18th and 19th century distinction between "high" and "low" culture seems inappropriate to apply to the mass-produced and mass-marketed consumption goods which cultural studies analyses, these scholars refer instead to popular culture.

Today some anthropologists have joined the project of cultural studies. Most, however, reject the identification of culture with consumption goods. Furthermore, many now reject the notion of culture as bounded, and consequently reject the notion of subculture. Instead, they see culture as a complex web of shifting patterns that link people in different locales, and link social formations of different scales. In such a view, any group can construct its own cultural identity.

A culture system (also known as a cultural system or just culture) can be considered a part of the social system and hierarchically equal to economic system, political system, legal system, etcetera

Architecture

This article is about the built environment. For other uses of the term "Architecture" see Architecture (disambiguation)

Architecture is the art and science of designing buildings. A wider definition would include within its scope the design of the total built environment, from the macrolevel of town planning, urban design, and landscape architecture to the microlevel of furniture or product design and Destination design/Architecture.

The Parthenon on top of the Acropolis, Athens, Greece
The Parthenon on top of the Acropolis, Athens, Greece
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Scope and intentions

According to the very earliest surviving work on the subject, Vitruvius' De Architectura, good building should have Beauty (Venustas), Firmness (Firmitas) and Utility (Utilitas); architecture can be said to be a balance and coordination among these three elements, with none overpowering the others. A modern day definition sees architecture as addressing aesthetic, structural and functional considerations. However, looked at another way, function itself is seen as encompassing all criteria, including aesthetic and psychological ones.

Architecture is a multi-disciplinary field, including within its fold mathematics, science, art, technology, social sciences, politics, history, philosophy, and so on. In Vitruvius' words, "Architecture is a science, arising out of many other sciences, and adorned with much and varied learning: by the help of which a judgement is formed of those works which are the result of other arts". He adds that an architect should be well versed in fields such as music, astronomy, etc. Philosophy is a particular favourite; in fact one frequently refers to the philosophy of each architect when one means the approach. Rationalism, empiricism, structuralism, poststructuralism, and phenomenology are some directions from philosophy influencing architecture.

Theory and practice

The importance of theory in informing practice cannot be overemphasised, though many architects shun theory. Vitruvius continues: "Practice and theory are its parents. Practice is the frequent and continued contemplation of the mode of executing any given work, or of the mere operation of the hands, for the conversion of the material in the best and readiest way. Theory is the result of that reasoning which demonstrates and explains that the material wrought has been so converted as to answer the end proposed. Wherefore the mere practical architect is not able to assign sufficient reasons for the forms he adopts; and the theoretic architect also fails, grasping the shadow instead of the substance. He who is theoretic as well as practical, is therefore doubly armed; able not only to prove the propriety of his design, but equally so to carry it into execution".

Architecture and buildings

The difference between architecture and building is a subject matter that has engaged the attention of many. According to Nikolaus Pevsner, European historian of the early 20th century, "A bicycle shed is a building, Lincoln Cathedral is a piece of architecture". In current thinking, the division is not too clear. Bernard Rudofsky's famous Architecture Without Architects consolidated a whole range of structures designed by ordinary people into the realm of architecture. The further back in history one goes, the greater is the consensus on what architecture is or is not, possibly because time is an efficient filter. If like Vitruvius we consider architecture as good building, then does it mean that bad architecture does not exist? To resolve this dilemma, especially with the increasing number of buildings in the world today, architecture can also be defined as what an architect does. This would then place the emphasis on the evolution of architecture and the architect.

Architectural history

Architecture first evolved out of the dynamics between needs (shelter, security, worship, etc.) and means (available building materials and attendant skills). Prehistoric and primitive architecture constitute this early stage. As humans progressed and knowledge began to be formalised through oral traditions and practices, architecture evolved into a craft. Here there is first a process of trial and error, and later improvisation or replication of a successful trial. The architect is not the sole important figure; he is merely part of a continuing tradition. What is termed as Vernacular architecture today falls under this mode and still continues to be produced in many parts of the world.

Early human settlements were essentially rural. As surplus of production began to occur, rural societies transformed into urban ones and cities began to evolve. In many ancient civilisations such as the Egyptians' and Mesopotamians' architecture and urbanism reflected the constant engagement with the divine and the supernatural. However, the architecture and urbanism of the Classical civilisations such as the Greek and the Roman evolved from more civic ideas and many new building types emerged. Architectural styles developed and texts on architecture began to be written. These became canons to be followed in important works, especially religious architecture. Some examples of canons are the works of Vitruvius, the Kaogongji of ancient China and Vaastu Shastra in ancient India. In Europe in the Classical and Medieval periods, buildings were not attributed to specific individual architects who remained anonymous. Guilds were formed by craftsmen to organise their trade. Over time the complexity of buildings and their types increased. General civil construction such as roads and bridges began to be built. Many new building types such as schools, hospitals, and recreational facilities emerged.

With the Renaissance and its emphasis on the individual and humanity rather than religion, and with all its attendant progress and achievements, a new chapter began. Buildings were ascribed to specific architects - Michaelangelo, Brunelleschi, Leonardo da Vinci - and the cult of the individual had begun. But there was no dividing line between artist, architect and engineer, or any of the related vocations. At this stage, it was still possible for an artist to design a bridge as the level of structural calculations involved were within the scope of the generalist.

With the consolidation of knowledge in scientific fields such as engineering and the rise of new materials and technology, the architect began to lose ground on the technical aspects of building. He therefore cornered for himself another playing field - that of aesthetics. There was the rise of the "gentleman architect" who usually dealt with wealthy clients and concentrated predominantly on visual qualities derived usually from historical prototypes. In the 19th century Ecole des Beaux Arts in France, the training was toward producing quick sketch schemes involving beautiful drawings without much emphasis on context.

Meanwhile, the Industrial Revolution laid open the door for mass consumption and aesthetics started becoming a criterion even for the middle class as ornamented products, once within the province of expensive craftmanship, became cheaper under machine production. Such products lacked the beauty and honesty associated with the expression of the process in the product.

The dissatisfaction with such a general situation at the turn of the twentieth century gave rise to many new lines of thought that in architecture served as precursors to Modern Architecture. Notable among these is the Deutscher Werkbund, formed in 1907 to produce better quality machine made objects. The rise of the profession of industrial design is usually placed here. Following this lead, the Bauhaus school, founded in Germany in 1919, consciously rejected history and looked at architecture as a synthesis of art, craft, and technology.

When Modern architecture first began to be practiced, it was an avant garde movement with moral, philosophical, and aesthetic underpinnings. Truth was sought by rejecting history and turning to function as the generator of form. Architects became prominent figures and were termed masters. Later modern architecture moved into the realm of mass production due to its simplicity and economy.

However, a reductive quality began to be perceived in modern architecture by the general public from the 1960s. Some reasons cited for this are its perceived lack of meaning, sterility, ugliness, uniformity, and psychological effects.

The architectural profession responded to this partly by attempting a more populist architecture at the visual level, even if at the expense of sacrificing depth for shallowness, a direction called Postmodernism. Robert Venturi's contention that a "decorated shed" (an ordinary building which is functionally designed inside and embellished on the outside) was better than a "duck" (a building in which the whole form and its function are considered together) gives an idea of this approach.

Another part of the profession, and also some non-architects, responded by going to what they considered the root of the problem. They felt that architecture was not a personal philosophical or aesthetic pursuit by individualists; rather it had to consider everyday needs of people and use technology to give a livable environment. The Design Methodology Movement involving people such as Chris Jones, Christopher Alexander started searching for a more inclusive process of design in order to lead to a better product. Extensive studies on areas such as behavioural, environmental, and social sciences were done and started informing the design process.

As many other concerns began to be recognised and complexity of buildings began to increase in terms of aspects such as services, architecture started becoming more multi-disciplinary than ever. Architecture now required a team of professionals in its making, an architect being one among the many, sometimes the leader, sometimes not. This is the state of the profession today. However, individuality is still cherished and sought for in the design of buildings seen as cultural symbols - the museum or fine arts centre has become a showcase for new experiments in style: today Deconstructivism, tomorrow maybe something else.

Conclusion

Buildings are the most visible productions of man. However, most of them are still designed by people themselves or masons as in developing countries, or through standardised production as in developed countries. The architect remains at the fringes of building production. The skills of the architect are sought only in complex building types or those seen as cultural and political symbols. And this is what the public perceives as architecture. The role of the architect, though changing, has not been central and never autonomous. There is always a dialogue between society and the architect. And what results from this dialogue can be termed architecture - as a product and as a discipline.

Four architectural styles in London, England, including the egg-shaped Swiss Re tower. In 2004 this building won the Stirling Prize for its architects Foster and Partners
Four architectural styles in London, England, including the egg-shaped Swiss Re tower. In 2004 this building won the Stirling Prize for its architects Foster and Partners

See also

External links

Theology

Theology is literally rational discourse concerning God (Greek θεος, theos, "God", + λογος, logos, "rational discourse"). By extension, it also refers to the study of other religious topics.

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History of the term

The term theologia is used in Classical Greek literature, with the meaning "discourse on the Gods or cosmology" (see Lidell and Scott's Greek-English Lexicon for references). Aristotle divided theoretical philosophy into mathematice, phusike and theologike, with the latter corresponding roughly to metaphysics, which for Aristotle included discussion of the nature of the divine.

Drawing on Greek sources, the Latin writer Varro influentially distinguished three forms of such discourse: mythical (concerning the myths of the Greek gods), rational (philosophical analysis of the gods and of cosmology) and civil (concerning the rites and duties of public religious observance).

The term was taken up by Christian writers. It appears once in some biblical manuscripts, in the heading to the book of Revelation: apokalupsis ioannou tou theologou, "the revelation of John the theologos". There, however, we are probably dealing with a slightly different sense of the root logos, to mean not "rational discourse" but "word" or "message": ho theologos here is probably meant to tell us that the author of Revelation has presented God's revealed messages – words of God, logoi tou theou – not that he was a "theologian" in the modern English sense of the word.

Other Christian writers used the term with several different ranges of meaning.

  1. Some Latin authors, such as Tertullian and Augustine followed Varro's threefold usage, described above.
  2. In patristic Greek sources, theologia could refer narrowly to the discussion of the nature and attributes of God.
  3. In other patristic Greek sources, theologia could also refer narrowly to the discussion of the attribution of divine nature to Jesus. (It is in this sense that Gregory Nazianzus was nicknamed "the theologian": he was a staunch defender of the divinity of Christ.)
  4. In medieval Greek and Latin sources, theologia (in the sense of "an account or record of the ways of God") could refer simply to the Bible.
  5. In scholastic Latin sources, the term came to denote the rational study of the doctrines of the Christian religion, or (more precisely) the academic discipline which investigated the coherence and implications of the language and claims of the Bible and of the theological tradition (the latter often as represented in Peter Lombard's Sentences, a book of extracts from the Church Fathers).

It is the last of these senses which lies behind most modern uses (though the second is also found in some academic and ecclesiastical contexts), and while the term "theology" can refer to any discussion of the nature of God or the gods, or indeed the discussion of any religious topic, it is also regularly used to denote the academic study (in Universities, seminaries and elsewhere) of the doctrines of Christianity, or of any other religion, or of the relationships and contrasts between various different religions, although the latter is a field more usually termed "comparative religion."

Theology and religions other than Christianity

In academic theological circles, there is some debate as to whether "theology" is an activity peculiar to the Christian religion. It is seen by some to be a term appropriate to a religion which is significantly organised around complexes of belief - a religion focused on certain doctrines which invite rational investigation and testing - particularly beliefs or doctrines concerning a deity (a theos) - and so to be less appropriate in religious contexts which are organized or perceived differently. So, for instance, some academic courses on Buddhism which are dedicated to the rational investigation of a Buddhist understanding of the world prefer the designation "Buddhist philosophy" to the term "Buddhist theology". Others have argued that, say, in Islam, theological discussion which parallels Christian theological discussion has, in the modern period, been a minor activity, and that the Islamic analogue of Christian theological discussion would more properly be the investigation and elaboration of Islamic law.

Theology and the philosophy of religion

Theology generally assumes the truth of at least some religious beliefs and is therefore often distinguished from the philosophy of religion, which does not presume the truth of any religious beliefs.

Drawing on the work of the American theologian Hans Frei, we may describe the relationship between theology and the philosophy of religion in the following way. At one end of the spectrum we find discussions of religious phenomena and religious claims which seek to explain those phenomena and claims entirely within the terms of some secular discipline (such as psychology or social anthropology), without regard to the view which the practitioners of the religion in question would have of those phenomena or claims (except insofar as those views are symptoms which the investigator is seeking to explain). At the other end of the spectrum we have discussions of these phenomena and claims which seek to work entirely within the religious practitioners' own terms, investigating the internal structures of a particular religious worldview. Between these two extremes are any number of forms of theological inquiry which look for some kind of correlation between these two forms of description - and this is as true of conservative theological approaches as it is of liberal approaches. (For instance, a conservative theologian will tend to correlate the claims they find in their religious scriptures about particular events in the past with the kind of description of the past allowed by historical criticism, arguing at least for compatibility between the two descriptions and possibly for some stronger relationship. A liberal theologian might be more interested in, say, exploring the correlation between the religion's ethical claims and the ideas of some secular philosophy like existentialism.) Forms of correlational discussion will differ, however, according to whether they give priority to the secular discourse or to the internal religious description: which is allowed to set the agenda, which is allowed to over-rule the other, and so on. The term "theology" can be used to denote any of these forms of correlational discourse, as well as the extreme which restricts itself to religious self-description; the term "philosophy of religion" will be used both for the opposite extreme and for many of the correlational forms of discourse; it is, however, more likely to be restricted to forms of correlation which give some form of priority to the secular discourse.

To the extent that theology relies upon the religious practitioners' own terms, it is likely to be explored by those who have some kind of commitment to those terms: i.e., by those who are either practitioners of the religion, or sympathisers. This is not, however, to say that one must have religious belief in order to be a theologian: some undertake it simply in order better to understand a religion's structure and implications, or as a form of thought experiment - though the further one moves from the "philosophy of religion" end of the spectrum to the "theology" end, the rarer non-practitioners become.

Theology and transformation

In Eastern Christianity, there is more emphasis on prayer than on intellectual thought and study as a means to learn about God, and so as the proper form of "theology". Many of the early church fathers described the theologian as a person who "truly prays."

Similarly, some other Christians, and some practitioners of other theistic religions, believe that to study God without any kind of relationship or desire for relationship with God is almost meaningless, as they believe that it is only in such a relationship that one finds an encounter with God sufficient to allow the testing and refining of claims about God. As the discussion above suggests, however, others would argue that one can engage with issues in terms of notions around "God" as an exercise in history, anthropology, and/or sociology, yet not have any desire for engagement in terms of the personal God offered in terms of certain forms of religion.

More generally, however, many theologians consider that, because the topics considered in theology touch on the theologians' deepest commitments and beliefs, it is impossible to study theology with complete detachment: the study of theology is "self-involving" in a way that makes some kinds of objectivity difficult. The study of theology, such theologians argue, is (if undertaken seriously and with an open mind) likely to lead to personal transformation of some sort - although that transformation might take many different forms.

Divisions of theology

Theology can be divided up in any number of ways. Many of these divisions have originated in the study of the Christian religion, although some have been adapted and extended to apply to other religions, or to the study of multiple religions.

Theology can be divided up into academic subdisciplines, often into some division like this:

  • biblical theology - focused on the investigation and interpretation of a religions' scriptures,
  • historical theology - focused on the intellectual history of the religion
  • systematic theology (or doctrinal theology, or dogmatic theology) - focused on the attempt to arrange and interpret the ideas current in the religion.
  • Comparative religion - focused on the comparison of common themes among different religious traditions

Theology can also be divided up by topic (or by 'loci'):

Theology can also be divided up into different modes, including

  • natural theology - the discussion of those aspects of theology that can be investigated without the help of revelation, scriptures or tradition (sometimes contrasted with "positive theology") - the discussion of those aspects of theology
  • apophatic theology (or negative theology; sometimes contrasted with "cataphatic theology") - the discussion of what God is not, or the investigation of how language about God breaks down

See also: dialectical theology

Theology can also be divided up into various movements, including

Quotes

  • "Theology is the effort to explain the unknowable in terms of the not worth knowing." - H.L. Mencken
  • "An authentic theology will not allow man to be obsessed with himself." - Thomas F. Torrance in Reality and Scientific Theology
  • "God is love." - John the Apostle

See also

Ascetical theology, biotheology, creationism, heresy, history of theology, liberal theology, liberation theology, metaphysics, natural theology, neurotheology, odium theologicum, philosophy of religion, process theology, propitiation, religion, scholasticism, systematic theology

List of Christian theologians

External links

Wikiversity, is developing courses on Theology.


Category:Skills

This is the category of Skills in general.

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Category:Abstraction

Abstraction is the thought process in which ideas are distanced from objects. Abstraction uses a strategy of simplification of detail, wherein formerly concrete details are left ambiguous, vague, or undefined; thus speaking of things in the abstract demands that the listener have an intuitive or common experience with the speaker, if the speaker expects to be understood.

For more information, please see the main article about Abstraction.

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Category:Fundamental

Ideally, a category illuminates a relationship between the subjects and objects of knowledge. A fundamental is basic; it is important because it is something that other things can be built upon. Thus the fundamental category includes those sub-categories which are highlighted on the Main Page of Wikipedia.

We start with Nature, the material world we inhabit. It is the object of study of the natural sciences. We, as humans, have survived as a species by applying our technology to survive and adapt to change. We propagate what we have learned to others by documentation and communication. In our communities, our social structures are the object of study of the social sciences; in society in general, and in the Wikipedia community in particular, we collaborate and cooperate to preserve what we have learned in references. One place to start in this encyclopedia is Wikipedia:Browse by category.

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Abstraction

This article is about the concept of abstraction in general. For other uses, please see abstract (disambiguation).


Abstraction is the thought process wherein ideas are distanced from objects.

Abstraction uses a strategy of simplification of detail, wherein formerly concrete details are left ambiguous, vague, or undefined; thus speaking of things in the abstract demands that the listener have an intuitive or common experience with the speaker, if the speaker expects to be understood.

For example, lots of different things have the property of redness: lots of things are red. And we find the relation sitting-on everywhere: many things sit on other things. The property of redness and the relation sitting-on are therefore abstract.

Problems begin to arise; however, when we try to define specific rules by which we can determine which things are abstract, and which concrete.

Contents [hide]

Conceptual schemes for abstraction

Instantiation

Something is often considered abstract if it does not exist at any particular place and time but instances, or members, of it can exist in many different places and/or times (we say that what is abstract can be multiply instantiated).

If however we just say that what is abstract is what can be instantiated, and that abstraction is simply the movement in the opposite direction to instantiation, we haven't explained everything. That makes 'dog' and 'telephone' abstract ideas, but even small children can recognise a dog or a telephone despite their varying appearances in particular cases. You could say that these concepts are abstractions but are not found to be very abstract in a conceptual sense. We can look at the progression from dog to mammal to animal, and see that animal is more abstract than mammal; but on the other hand mammal is a harder idea to express, certainly in relation to marsupial.

Physicality

Things are often said to be concrete, that is, not abstract, when they have physical existence or when they occupy space.

In general, a concept is considered concrete if it is not abstract: it must be both particular and an individual, and hence occupy both space and time. To say that a physical object is concrete is to say, approximately, that it is a particular individual that is located at a particular place and time.

Realness

Abstract things are sometimes defined as those things that do not exist in reality or exist only as sensory experience, like red. The problem begins to arise here when we try to decide which things are, in fact, real. Is God real, or abstract? Even if real, could God also be abstract? Is the number 2 real? Is goodness real, or only its effects, or is it just an abstract idea created by humans?

Abstraction used in philosophy

Abstraction in philosophy is the (oft-alleged) process, in concept-formation, of recognizing among a number of individuals some common feature, and on that basis forming the concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism and the problem of universals.

Ontological status of abstract concepts

If we say that properties and relations are, or have being, clearly we mean they have a different sort of being from that which physical objects, like rocks and trees, have. That accounts for the usefulness of the word abstract. We apply it to properties and relations to mark the fact that if they exist, they do not exist in space or time, but that instances of them can exist in many different places.

On the other hand the apple and an individual human being are said to be concrete, and particulars, and individuals.

Confusingly, philosophers sometimes refer to tropes, or property-instances (e.g., the particular redness of this particular apple), as abstract particulars.

Gottlob Frege abstracts abstraction

To be filled with a paragraph or two describing Frege's definition of abstraction.

Reification

Reification, also called hypostatization, is usually considered a logical fallacy wherein an abstract concept, such as "society" or "technology" is treated as if it were a concrete thing. It is important to note that reification necessarily occurs linguistically in the English language and many other languages wherein abstract objects are referred to using the same sorts of nouns that signify concrete objects. This can further confuse us about which things are abstract and which concrete, as our language tends to influence us toward reification.

The neurology of abstraction

Some research into the human brain suggests that the left and right hemispheres differ in their handling of abstraction. One side handles collections of examples (eg: examples of a tree) whereas the other handles the concept itself.

Abstraction in Art

Most typically abstraction is used in the arts as a synonym of Abstract art in general. It can, however, refer to any object or image which has been distilled from the real world, or indeed another work.

Related articles

External links


Abstraction


This article is about the concept of abstraction in general. For other uses, please see abstract (disambiguation).


Abstraction is the thought process wherein ideas are distanced from objects.

Abstraction uses a strategy of simplification of detail, wherein formerly concrete details are left ambiguous, vague, or undefined; thus speaking of things in the abstract demands that the listener have an intuitive or common experience with the speaker, if the speaker expects to be understood.

For example, lots of different things have the property of redness: lots of things are red. And we find the relation sitting-on everywhere: many things sit on other things. The property of redness and the relation sitting-on are therefore abstract.

Problems begin to arise; however, when we try to define specific rules by which we can determine which things are abstract, and which concrete.

Contents [hide]

Conceptual schemes for abstraction

Instantiation

Something is often considered abstract if it does not exist at any particular place and time but instances, or members, of it can exist in many different places and/or times (we say that what is abstract can be multiply instantiated).

If however we just say that what is abstract is what can be instantiated, and that abstraction is simply the movement in the opposite direction to instantiation, we haven't explained everything. That makes 'dog' and 'telephone' abstract ideas, but even small children can recognise a dog or a telephone despite their varying appearances in particular cases. You could say that these concepts are abstractions but are not found to be very abstract in a conceptual sense. We can look at the progression from dog to mammal to animal, and see that animal is more abstract than mammal; but on the other hand mammal is a harder idea to express, certainly in relation to marsupial.

Physicality

Things are often said to be concrete, that is, not abstract, when they have physical existence or when they occupy space.

In general, a concept is considered concrete if it is not abstract: it must be both particular and an individual, and hence occupy both space and time. To say that a physical object is concrete is to say, approximately, that it is a particular individual that is located at a particular place and time.

Realness

Abstract things are sometimes defined as those things that do not exist in reality or exist only as sensory experience, like red. The problem begins to arise here when we try to decide which things are, in fact, real. Is God real, or abstract? Even if real, could God also be abstract? Is the number 2 real? Is goodness real, or only its effects, or is it just an abstract idea created by humans?

Abstraction used in philosophy

Abstraction in philosophy is the (oft-alleged) process, in concept-formation, of recognizing among a number of individuals some common feature, and on that basis forming the concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism and the problem of universals.

Ontological status of abstract concepts

If we say that properties and relations are, or have being, clearly we mean they have a different sort of being from that which physical objects, like rocks and trees, have. That accounts for the usefulness of the word abstract. We apply it to properties and relations to mark the fact that if they exist, they do not exist in space or time, but that instances of them can exist in many different places.

On the other hand the apple and an individual human being are said to be concrete, and particulars, and individuals.

Confusingly, philosophers sometimes refer to tropes, or property-instances (e.g., the particular redness of this particular apple), as abstract particulars.

Gottlob Frege abstracts abstraction

To be filled with a paragraph or two describing Frege's definition of abstraction.

Reification

Reification, also called hypostatization, is usually considered a logical fallacy wherein an abstract concept, such as "society" or "technology" is treated as if it were a concrete thing. It is important to note that reification necessarily occurs linguistically in the English language and many other languages wherein abstract objects are referred to using the same sorts of nouns that signify concrete objects. This can further confuse us about which things are abstract and which concrete, as our language tends to influence us toward reification.

The neurology of abstraction

Some research into the human brain suggests that the left and right hemispheres differ in their handling of abstraction. One side handles collections of examples (eg: examples of a tree) whereas the other handles the concept itself.

Abstraction in Art

Most typically abstraction is used in the arts as a synonym of Abstract art in general. It can, however, refer to any object or image which has been distilled from the real world, or indeed another work.

Related articles

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Critical thinking

Within the framework of skepticism, critical thinking is the mental process of acquiring information, then evaluating it to reach a logical conclusion or answer. Critical thinking is synonymous with informal logic. Increasingly, educators believe that schools should focus more on critical thinking than on memorization of facts.

Although no hard and fixed sequence of steps is required, the following is a useful sequence to follow:

  • itemize opinions from all relevant sides of an issue
  • collect up arguments supporting the various opinions
  • break down the arguments into their constituent statements
  • draw out various additional implications from these statements
  • examine these statements and implications for internal contradictions
  • locate opposing claims between the various arguments
  • assign relative weights to opposing claims
    • increase the weighting when the claims have strong support especially distinct chains of reasoning or different sources
    • decrease the weighting when the claims have contradictions
    • adjust weighting depending on relevance of information to central issue
    • require sufficient support to justify that any incredible claims; otherwise, ignore these claims when forming a judgment
  • tally up the weights of the various claims
  • the opinion with the strongest supporting claims is more likely to be correct
  • mind maps are an effective tool for organizing and evaluating this information; in the final stages, numeric weights can be assigned to various branches of the mind map

Of course, critical thinking doesn't assure reaching correct conclusions. First, one may not have all the relevant information; indeed, important information may not be discovered (see progress) or the information may not even be knowable (see New Mysterianism). Second, one's biases may prevent effective gathering and evaluation of the available information.

To reduce one's bias, measures can be taken during the process of critical thinking:

  • instead of asking "How does this contradict my beliefs?", one should be asking "What does this mean?"
  • in the earlier stages of gathering and evaluating information, one should:
  • be aware of one's own fallibility by:
    • accepting that everyone has subconscious biases so question any reflexive judgments
    • adopting an egoless and, indeed, humble stance
    • recalling previous beliefs that one strongly held but, now, reject and even consider ridiculous; then, realize one likely has still numerous blind spots


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Lateral thinking

Lateral thinking is a term invented by Edward de Bono. He defines it as a technique of problem solving by approaching problems indirectly at diverse angles instead of concentrating on one approach at length. For example:

It took two hours for two men to dig a hole five feet deep. How deep would it have been if ten men had dug the hole for two hours?

Simplistically, the answer appears to be 25 feet deep. This is based on a few incorrect assumptions :

  • Holes usually need to be deep as possible, rather than long or wide, as with a ditch.
  • Ten men have just as much room to move around and shovel in (without getting in the way of other men) as two men do.
  • Each of the ten men will work just as hard as the two men will—generally, the more people you have working on a project, the more each person will assume he can slack off and there's more people to talk to.

The correct answer—whatever it is—goes against standard mathematical training. This does not make it incorrect; standard mathematical training does not teach how to apply math to the real world very well, except with finances. Lateral thinking gets answers that are correct (or closer to the truth) because it takes into account more factors and the meanings of the words.

Example problems

  • How long would it take to dig half a hole?
    • You can't dig half a hole.
  • If one egg takes three minutes to boil, how long do two eggs cook?
    • About three minutes (the energy needed to get the eggs to boil is small in comparison to the energy needed to get the surrounding water to boil)
  • If a knot in a 5-foot rope takes five minutes to undo, how long would a knot in a 10-foot rope take to undo?
    • Also five minutes (the length of rope usually has nothing to do with the complexity of the knot).

See also

Further reading


Picture thinking

In psychology, picture thinking is often confused with dyslexia, and it is true that people who 'think in pictures' often have difficulty with learning to read, but not all picture thinkers suffer from the normal symptoms associated with dyslexia. Some autistics think in pictures.

Symptoms that most picture thinkers do share are:

  • Problems remembering abstract chains of letters, like names.
  • Difficulty in explaining concepts they have invented.
  • Writing in a very convoluted style.
  • Natural ability to 'quick read' whole sentences instead of word for word, but when asked to read out loud what they have read they often use other words than what is actually written.
  • Ability to remember exactly the location and relative position of objects they have placed somewhere.
  • Ability to intuitively come to conclusions that are very hard to reach by using normal linear reasoning.

What a picture thinker is or does is still debated, but some research has been done in the Netherlands where they call picture thinking beelddenken. in particular, the Maria J. Krabbe Stichting is doing some research (see link below). Researchers there have developed a method of detecting picture thinking in young children by using the so called "the world game" ( het wereldspel ).

Picture thinkers, as the word says, think in pictures, not in the linear fashion using language that is normally associated with thinking. Of course this is a simplification as a complete picture thinker would not be able to use language.

Picture thinkers can come to conclusions in an intuitive way, without reasoning with language. Instead, they manipulate with logical/graphical symbols in a non linear fashion; they “see” the answers to problems.

Picture thinkers are often inventors, architects or electronic engineers.

You could say picture thinkers are persons with vision.

The book The Gift of Dyslexia by Ronald D. Davis and Eldon M.Braun describes the relationship of picture thinking to dyslexia. Another book, Thinking in Pictures, by Temple Grandin, focuses on the role of picture thinking in autism.

There are many famous people who were probably picture thinkers, here is a short list:



External links

Thought

Thought or thinking is a mental process which allows beings to model the world, and so to deal with it effectively according to their goals, plans, ends and desires. Concepts akin to thought are sentience, consciousness, idea and imagination.

Thinking involves manipulation of information, as when we form concepts, engage in problem solving, reason and make decisions. Thinking is a higher cognitive function and the analysis of thinking processes is part of cognitive psychology.

In the Myers-Briggs Type Indicator, thinking means you tend to put a higher priority on impersonal factors than personal factors.

Aids to thinking

  1. Use of models, symbols, diagrams and pictures
  2. Use of abstraction to simplify the effort of thinking
  3. Use of metasyntactic variables to simplify the effort of naming
  4. Use of iteration and recursion to converge on a concept
  5. Limitation of attention to aid concentration and focus on a concept. Use of peace and quiet to aid concentration.
  6. Goal setting and goal revision. Simply letting the concept percolate in the subconscious, and waiting for the concept to re-surface.
  7. Talking with like-minded people. Resorting to communication with others, if this is allowed.

See George Polya's books on Heuristics

See also

See: Eric Baum What is Thought MIT Press 2004 ISBN 0-262-02548-5 - Chapter Two: The Mind is a Computer Program


Category:Mind

The mind is the subject of theorizing, experimenting, and expostulating in philosophy (studied under the heading philosophy of mind), in psychology, and in religion, where it is considered alongside the spirit and soul. Some people think mind is synonymous with the brain in the body.

For more information, please see the main article about Mind.

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Cognitive psychology

Cognitive psychology is the psychological science which studies cognition, the mental processes that are hypothesised to underlie behaviour. This covers a broad range of research domains, examining questions about the workings of memory, attention, perception, knowledge representation, reasoning, creativity and problem solving.

Cognitive psychology is radically different from previous psychological approaches in two keys ways.

The school of thought arising from this approach is known as cognitivism.

Cognitive psychology is one of the more recent additions to psychological research, having only developed as a separate area within the discipline since the late 1950s and early 1960s (though there are examples of cognitive thinking from earlier researchers). The term came into use with the publication of the book Cognitive psychology by Ulrich Neisser in 1967. However the cognitive approach was brought to prominence by Donald Broadbent's book Perception and Communication in 1958. Since that time, the dominant paradigm in the area has been the information processing model of cognition that Broadbent put forward. This is a way of thinking and reasoning about mental processes, envisaging them like software running on the computer that is the brain. Theories commonly refer to forms of input, representation, computation or processing, and outputs.

This way of conceiving mental processes has pervaded psychology more generally over the past few decades, and it is not uncommon to find cognitive theories within social psychology, personality, abnormal psychology, developmental psychology; the application of cognitive theories in comparative psychology has led to many recent studies in animal cognition.

The information processing approach to cognitive functioning is currently being questioned by new approaches in psychology, such as dynamical systems, and the embodiment perspective.

Because of the use of computational metaphors and terminology, cognitive psychology was able to benefit greatly from the flourishing of research in artificial intelligence and other related areas in the 1960s and 1970s. In fact, it developed as one of the significant aspects of the inter-disciplinary subject of cognitive science, which attempts to integrate a range of approaches in research on the mind and mental processes.

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Major research areas in cognitive psychology

Perception

  • Attention and Filter theories (the ability to focus mental effort on specific stimuli while excluding other stimuli from consideration)
  • Pattern recognition (the ability to correctly interpret ambiguous sensory information)

Memory

Knowledge representation

Language

Thinking

Famous cognitive psychologists

See also

External link


Memory

For computer memory, see computer storage.
Some people use tricks to help improve their memory.
Some people use tricks to help improve their memory.

Memory is one of the activities of the human mind, much studied by cognitive psychology. It is the capacity to retain an impression of past experiences. There are multiple types of classifications for memory based on duration, nature and retrieval of perceived items.

The main stages in the formation and retrieval of memory, from an information processing perspective, are:

  • Encoding (processing and combination of received information)
  • Storage (creation of a permanent record of the encoded information)
  • Retrieval (calling back the stored information in response to some cue for use in some process or activity)
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Classification by duration

A basic and generally accepted classification of memory is based on the duration of memory retention, and identifies three distinct types of memory: sensory memory, short-term memory, and long-term memory.

The sensory memory corresponds approximately to the initial moment that an item is perceived. Some of this information in the sensory area proceeds to the sensory store, which is referred to as short-term memory. Sensory memory is characterized by the duration of memory retention from milliseconds to seconds and short-term memory from seconds to minutes. These stores are generally characterised as of strictly limited capacity and duration, whereas in general stored information can be retrieved in a period of time which ranges from days to years; this type of memory is called long-term memory.

It may be that short-term memory is supported by transient changes in neuronal communication, whereas long-term memories are maintained by more stable and permanent changes in neural structure that are dependent on protein synthesis. Some psychologists, however, argue that the distinction between long- and short-term memories is arbitrary, and is merely a reflection of differing levels of activation within a single store.

If we are given a random seven-digit number, we may remember it only for a few seconds and then forget (short-term memory). On the other hand, we can remember telephone numbers for many years, since we have stored them in our brain after long periods of consolidation and rehearsal (long-term memory).

Additionally, the term working memory is used to refer to the short-term store needed for certain mental tasks - it is not a synonym for short-term memory, since it is defined not in terms of duration, but rather in terms of purpose. Some theories consider working memory to be the combination of short-term memory and some attentional control. For instance, when we are asked to mentally multiply 45 by 4, we have to perform a series of simple calculations (additions and multiplications) to arrive at the final answer. The ability to store the information regarding the instructions and intermediate results is what is referred to as working memory.

Classification by information type

Long-term memory, the largest part of any model, can be divided into declarative (explicit) and procedural (implicit) memories.

Declarative memory requires conscious recall, in that some conscious process must call back the information. It is sometimes called explicit memory, since it consists of information that is explicitly stored and retrieved.

Declarative memory can be further sub-divided into semantic memory, which concerns facts taken independent of context; and episodic memory, which concerns information specific to a particular context, such as a time and place. Semantic memory allows the encoding of abstract knowledge about the world, such as "Paris is the capital of France". Episodic memory, on the other hand, is used for more personal memories, such as the sensations, emotions, and personal associations of a particular place or time. Autobiographical memory - memory for particular events within one's own life - is generally viewed as either equivalent to, or a subset of, episodic memory.

In contrast, procedural memory (or implicit memory) is not based on the conscious recall of information, but on an implicit learning of certain patterns about the world. It is revealed when we do better in a given task due only to repetition - no new explicit memories have been formed, but we are unconsciously accessing aspects of those previous experiences. Classical conditioning can be seen as a form of implicit memory, as can memory resulting from motor learning, which depends upon the cerebellum and basal ganglia.

Memory disorders

Much of the current knowledge of memory has come from studying memory disorders, which are known collectively as amnesia. There are many sorts of amnesia, and by studying their different forms, it has become possible to observe apparent defects in individual sub-systems of the brain's memory systems, and thus hypothesize their function in the normally working brain.

The physiology of memory

Brain areas such as the mammillary bodies and hippocampus are thought to be involved in memory. It has been demonstrated that damage to these structures can result in impaired performance on certain memory tasks.

Related topics

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Category:Psychology

Psychology is a collection of academic, clinical and industrial disciplines concerned with the explanation and prediction of behavior, thinking, emotions, motivations, relationships, potentials and pathologies.

For more information, please see the main article about Psychology

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Language and thought

A variety of different authors, theories and fields purport influences between language and thought.

Many point out the seemingly common-sense realization that upon introspection we seem to think thoughts in the language we speak. A number of writers and theorists have extrapolated upon this idea.

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Scientific theories

  • The Sapir-Whorf hypothesis in linguistics states that the structure of one's mother language influences the way one's mind perceives the world. It has found at best very limited experimental support, at least in its strong form. For instance, a study showing that speakers of languages lacking a subjunctive mood such as Chinese experience difficulty with hypothetical problems has been discredited. However, another study has shown that subjects in memory tests are more likely to remember a given color if their mother language includes a word for that color.
  • In behavioral economics, according to experiments said to support to the theoretical availability heuristic, people believe more probable events that are more vividly described than those which were not. Simple experiments asking people to imagine something led them to believe it to be more likely. The mere exposure effect may also be relevant to propagandistic repetition like the Big Lie. According to prospect theory, people make different economic choices based on how the matter is framed.

Other schools of thought

  • General Semantics is a school of thought founded by engineer Alfred Korzybski and later popularized by S. I. Hayakawa and others, which attempted to make language more precise and objective. It makes many basic observations of the English language, particularly pointing out problems of abstraction and definition.
  • Neuro-linguistic programming, founded by Richard Bandler, claims that language "patterns" and other things can affect thought and behavior. It takes ideas from General Semantics and hypnosis, especially that of the famous therapist Milton Erickson. Many do not consider it a credible study, and it has no empirical scientific support.
  • Advocates of non-sexist language including some feminists say that the English language perpetuates biases against women, such as using male-gendered terms such as "he" and "man" as generic. Many authors including those who write textbooks now conspicuously avoid that practice, in the case of the previous examples using words like "he or she" or "they" and "human race". Political correctness is similar, but it is a loose cultural meme and has never been formally codified. Both are considered widely controversial.

Literature

  • George Orwell, the famous political writer, certainly believed in the interplay between language and thought. One of the most fundamental and enduring ideas of his dystopian novel Nineteen Eighty-Four was the control of "thoughtcrime" through omnipresent spying and propaganda, and the created language Newspeak. The purpose of this fictional language was to make thoughts unapproved by the state "literally unthinkable" by making language unable to express them. In a 1946 essay in which Orwell explores this topic further, Politics and the English Language, he wrote "if thought corrupts language, language can also corrupt thought."

Other


Logic

In ordinary language, logic is the reasoning used to reach a conclusion from a set of assumptions. More formally, logic is the study of inference—the process whereby new assertions are produced from already established ones. As such, of particular concern in logic is the structure of inference—the formal relations between the newly produced assertions and the previously established ones, where "formal" means that the relations are independent of the assertions themselves. Just as important is the investigation of validity of inference, including various possible definitions of validity and practical conditions for its determination. It is thus seen that logic plays an important role in epistemology in that it provides a mechanism for extension of knowledge.

As a byproduct, logic provides prescriptions for reasoning, that is, how people—as well as other intelligent beings, machines, and systems—ought to reason. However, such prescriptions are not essential to logic itself; rather, they are an application. How people actually reason is usually studied in other fields, including cognitive psychology.

Traditionally, logic is studied as a branch of philosophy. Since the mid-1800s logic has been commonly studied in mathematics, and, even more recently, in Computer Science. As a science, logic investigates and classifies the structure of statements and arguments and devises schemata by which these are codified. The scope of logic can therefore be very large, including reasoning about probability and causality. Also studied in logic are the structure of fallacious arguments and paradoxes. The ancient Greeks divided dialectic into logic and rhetoric. Rhetoric, concerned with persuasive arguments, would currently be seen as contrasted with logic, in some sense; as is dialectic in most of its acquired meanings.

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Scope of logic

As it has developed, many distinctions have been introduced into logic. These distinctions serve to help formalize different forms of logic as a science. Here are some of the more important distinctions.

Deductive and inductive reasoning

Originally, logic consisted only of deductive reasoning which concerns what follows universally from given premises. However it is important to note that inductive reasoning—the study of deriving a reliable generalization from observations—has sometimes been included in the study of logic. Correspondingly, we must distinguish between deductive validity and inductive validity. An inference is deductively valid if and only if there is no possible situation in which all the premises are true and the conclusion false. The notion of deductive validity can be rigorously stated for systems of formal logic in terms well-understood notions of semantics. Inductive validity on the other hand requires us to define reliable generalization of some set of observations. The task of providing this definition may be approached in various ways, some less formal than others; some of these definitions may use mathematical models of probability. For the most part our discussion of logic deals only with deductive logic.

Formal and informal logic

The study of logic is divided into formal and informal logic.

Formal logic (sometimes called "symbolic logic") attempts to capture the nature of logical truth and inference in formal systems, which consist of a formal language, a set of rules of derivation (often called "rules of inference"), and sometimes a set of axioms. The formal language consists of a (often small) set of discrete symbols, a syntax, and (often) a semantics, and expressions in this language are often called "formulas". The rules of derivation and potential axioms then operate with the language to specify a set of theorems, which are formulas that are either axioms or are derivable using the rules of derivation. In the case of formal logical systems, the theorems are often interpretable as expressing logical truths (tautologies), and in this way can such systems be said to capture at least a part of logical truth and inference. Formal logic encompasses a wide variety of logical systems. For instance, propositional logic and predicate logic are a kind of formal logic, as well as temporal logic, modal logic, Hoare logic, the calculus of constructions, etc. Higher order logics are logical systems based on a hierarchy of types.

Informal logic is the study of logic as used in natural language arguments. Informal logic is complicated by the fact that it may be very hard to tease out the formal logical structure embedded in an argument. Informal logic is also more difficult because the semantics of natural language assertions is much more complicated than the semantics of formal logical systems, due to the presence of such phenomena as defeasibility.

Following are more specific discussions of some systems of logic. See also: list of topics in logic.

Paradigms of logic

Throughout history, there has been interest in distinguishing good from bad arguments, and so logic has been studied in some more or less familiar form. Aristotelian logic has principally been concerned with teaching good argument, and is still taught with that end today, while in mathematical logic and analytical philosophy much greater emphasis is placed on logic as an object of study in its own right, and so logic is studied at a more abstract level.

Consideration of the different types of logic explains that logic is not studied in a vacuum. While logic often seems to provide its own motivations, the subject develops most healthily when the reason for our interest is made clear.

Aristotelian logic

Main article:Aristotelian logic

The Organon was Aristotle's body of work on logic, with the Prior Analytics constituting the first explicit work in formal logic, introducing the Syllogistic. The parts of syllogistic, also known by the name term logic, were the analysis of the judgements into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consisted of two propositions sharing a common term as premise, and a conclusion which was a proposition involving the two unrelated terms from the premises.

Aristotle's work was regarded in classical times and from medieval times in Europe and the Middle East as the very picture of a fully worked out system. It was not alone: the Stoics proposed a system of propositional logic that was studied by medieval logicians; nor was the perfection of Aristotle's system undisputed; for example the problem of multiple generality was recognised in medieval times. Nonetheless, problems with syllogistic were not seen as being in need of revolutionary solutions.

Today, Aristotle's system is mostly seen as of historical value (though there is some current interest in extending term logics), regarded as made obsolete by the advent of the predicate calculus.

Predicate logic

Main article:Predicate logic

Modal logic

Main article:Modal logic

Dialectical logic

Main article:Dialectical logic

The motivation for the study of logic in ancient times was clear, as we have described: it is so that we may learn to distinguish good from bad arguments, and so become more effective in argument and oratory, and perhaps also, to become a better person.

This motivation is still alive, although it no longer takes centre stage in the picture of logic; typically dialectical logic will form the heart of a course in critical thinking, a compulsory course at many universities, especially those that follow the American model.

Mathematical logic

Main article: Mathematical logic

Mathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic.

The boldest attempt to apply logic to mathematics was undoubtedly the logicism pioneered by philosopher-logicians such as Gottlob Frege and Bertrand Russell: the idea was that mathematical theories were logical tautologies, and the programme was to show this by means to a reduction of mathematics to logic. The various attempts to carry this out met with a series of failures, from the crippling of Frege's project in his Grundgesetze by Russell's Paradox, to the defeat of Hilbert's Program by Gödel's incompleteness theorems.

Both the statement of Hilbert's Program and its refutation by Gödel depended upon their work establishing the second area of mathematical logic, the application of mathematics to logic in the form of proof theory. Despite the negative nature of the incompleteness theorems, Gödel's completeness theorem, a result in model theory and another application of mathematics to logic, can be understood as showing how close logicism came to being true: every rigorously defined mathematical theory can be exactly captured by a first-order logical theory; Frege's proof calculus is enough to describe the whole of mathematics, though not equivalent to it. Thus we see how complementary the two areas of mathematical logic have been.

If proof theory and model theory have been the foundation of mathematical logic, they have been but two of the four pillars of the subject. Set theory originated in the study of the infinite by Georg Cantor, and it has been the source of many of the most challenging and important issues in mathematical logic, from Cantor's theorem, through the status of the Axiom of Choice and the question of the independence of the continuum hypothesis, to the modern debate on large cardinal axioms.

Recursion theory captures the idea of computation in logical and arithmetic terms; its most classical achievements are the undecidability of the Entscheidungsproblem by Alan Turing, and his presentation of the Church-Turing thesis. Today recursion theory is mostly concerned with the more refined problem of complexity classes -- when is a problem efficiently solvable? -- and the classification of degrees of unsolvability.

Philosophical logic

Main article philosophical logic

Philosophical logic deals with formal descriptions of natural language. Most philosophers assume that the bulk of "normal" proper reasoning can be captured by logic, if one can find the right method for translating ordinary language into that logic. Philosophical logic is essentially a continuation of the traditional discipline that was called "Logic" before it was supplanted by the invention of Mathematical logic. Philosophical logic has a much greater concern with the connection between natural language and logic. As a result, philosophical logicians have contributed a great deal to the development of non-standard logics (e.g., free logics, tense logics) as well as various extensions of classical logic (e.g., modal logics), and non-standard semantics for such logics (e.g., supervaluation semantics).

Logic and computation

Logic is extensively applied in the fields of artificial intelligence, and computer science, and these fields provide a rich source of problems in formal logic.

In the 1950s and 1960s, researchers predicted that when human knowledge could be expressed using logic with mathematical notation, it would be possible to create a machine that reasons, or artificial intelligence. This turned out to be more difficult than expected because of the complexity of human reasoning. In logic programming, a program consists of a set of axioms and rules. Logic programming systems such as Prolog compute the consequences of the axioms and rules in order to answer a query.

In symbolic logic and mathematical logic, proofs by humans can be computer-assisted. Using automated theorem proving the machines can find and check proofs, as well as work with proofs too lengthy to be written out by hand.

In computer science, Boolean algebra is the basis of hardware design, as well as much software design.

There are also various systems for reasoning about computer programs. Hoare logic is one of the earliest of such systems. Other systems are CSP, CCS, pi-calculus for reasoning about concurrent processes or mobile processes. There is interest in the idea of finding a logical calculus that naturally captures computability; the computability logic of Japaridze is an example of a recently embarked research programme in this direction.

Controversies in Logic

It is by no means the case that logicians agree on what the principles of logic are

Bivalence and the law of the excluded middle

The logics discussed above are all "bivalent" or "two-valued"; that is, the semantics for each of these languages will assign to every sentence either the value "True" or the value "False." Systems which do not always make this distinction are known as non-classical logics or non-Aristotelian logics.

In the early 20th century Jan Łukasiewicz investigated the extension of the traditional true/false values to include a third value, "possible", so inventing ternary logic, the first multi-valued logic.

Intuitionistic logic was proposed by L. E. J. Brouwer as the correct logic for reasoning about mathematics, based upon his rejection of the law of the excluded middle as part of his intuitionism. Brouwer rejected formalisation in mathematics, but his student Arend Heyting studied intuitionistic logic formally, as did Gerhard Gentzen. Intuitionistic logic has come to be of great interest to computer scientists, as it is a constructive logic, and is hence a logic of what computers can do.

Modal logic is not truth conditional, and so it has often been proposed as a non-classical logic. However modal logic is normally formalised with the principle of the excluded middle, and its relational semantics is bivalent, so this inclusion is disputable. However, modal logic can be used to encode non-classical logics, such as intuitionistic logic.

Logics such as fuzzy logic have since been devised with an infinite number of "degrees of truth", represented by a real number between 0 and 1. Bayesian probability can be interpreted as a system of logic where probability is the subjective truth value.

Implication: strict or material?

Main article paradox of material implication

It is easy to observe that the notion of implication formalised in classical logic does not comfortably translate into natural language by means of "if... then...", due to a number of problems called the paradoxes of material implication.

The first class of paradoxes are those that involve counterfactuals, such as "If the moon is made of green cheese, then 2+2=4", puzzling because natural language does not support the principle of explosion. Eliminating these classes of paradox led to David Lewis's formulation of strict implication, and to a more radically revisionist logics such as relevance logic and dialetheism.

The second class of paradox are those that involve redundant premises, falsely suggesting that we know the succedent because of the antecedent: thus "if that man gets elected, granny will die" is materially true if granny is in the throws of a terminal illness, reagrdless of the man's election prospects. The violate the Gricean maxim of relevance, and can be modelled by logics that reject the principle of monotonicity (logical), such as relevance logic.

Is logic empirical?

What is the epistemological status of the laws of propositional logic? In a paper entitled Is logic empirical, Hilary Putnam proposed the idea that the facts of propositional logic have the same epistemological status as facts about the physical universe, for example as the laws of mechanics or of general relativity. Note that the formal laws of a physical theory are justified by a process of repeated controlled observations; this from a physicist's point of view is the meaning of the empirical nature of these laws.

The idea of a propositional logic with rules radically different from Boolean logic in itself was not new. Indeed a sort of analogy had been established in the mid-nineteen thirties by Garrett Birkhoff and John von Neumann between a non-classical propositional logic and some aspects of the measurement process in quantum mechanics. Putnam and the physicist David Finkelstein proposed that there was more to this correspondence than a loose analogy; that in fact there was a logical system whose semantics was given by a lattice of projection operators on a Hilbert space which actually was the correct logic to reason about the microscopic world. In this view, classical logic was merely a limiting case of this new logic. If this were the case, then our "preconceived" Boolean logic would have to be rejected by empirical evidence in the same way Euclidean geometry (as being the correct geometry of physical space) was rejected by the facts of general relativity. This would support the view that the rules of logic are empirical.

This logic came to be known as quantum logic, although there are few philosophers today (probably including Putnam himself) who regard this logic as a replacement for classical logic. Quantum logic is still used as a foundational formalism for quantum mechanics, however, in a way in which primitive events are not interpreted as atomic propositions but rather in operational terms as possible outcomes of observations. As such quantum logic provides a unified and consistent mathematical theory of physical observables and quantum measurement.

See also

Concepts of logic

Techniques and rules

Related Topics

References

  • G. Birkhoff and J. von Neumann, The Logic of Quantum Mechanics, vol 37, 1936.
  • D. Finkelstein, Matter, Space and Logic, Boston Studies in the Philosophy of Science vol V, 1969
  • W. Hodges: Logic. An introduction to elementary logic, Penguin Books, 2001
  • W. Kneale and M. Kneale, The Development of Logic, Oxford University Press, 1988 (originally 1962)
  • H. Putnam, Is Logic Empirical, Boston Studies in the Philosophy of Science vol V, 1969