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Object Of The Mind
An object of the mind is an object that exists in the imagination, but which, in the real world, can only be represented or modeled. Some such objects are abstractions, literary concepts, or fictional scenarios. Closely related are intentional objects, which are what thoughts and feelings are about, even if they are not about anything real (such as thoughts about unicorns, or feelings of apprehension about a dental appointment which is subsequently cancelled). However, intentional objects may coincide with real objects (as in thoughts about horses, or a feeling of regret about a missed appointment). Mathematical objects Mathematics and geometry describe abstract objects that sometimes correspond to familiar shapes, and sometimes do not. Circles, triangles, rectangles, and so forth describe two-dimensional shapes that are often found in the real world. However, mathematical formulas do not describe individual physical circles, triangles, or rectangles. They describe ideal shapes th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object (philosophy)
An object is a philosophical term 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, gods, Socrates, 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 approac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Strip
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE. The Möbius strip is a non-orientable surface, meaning that within it one cannot consistently distinguish clockwise from counterclockwise turns. Every non-orientable surface contains a Möbius strip. As an abstract topological space, the Möbius strip can be embedded into three-dimensional Euclidean space in many different ways: a clockwise half-twist is different from a counterclockwise half-twist, and it can also be embedded with odd numbers of twists greater than one, or with a knotted centerline. Any two embeddings with the same knot for the centerline and the same number and direction of twists are topologically equivalent. All of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a ''possible world''. A formula's truth value at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensional Logic
Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe (''extensions''), by additional quantifiers that range over terms that may have such individuals as their value (''intensions''). The distinction between intensional and extensional entities is parallel to the distinction between sense and reference. Overview Logic is the study of proof and deduction as manifested in language (abstracting from any underlying psychological or biological processes). Logic is not a closed, completed science, and presumably, it will never stop developing: the logical analysis can penetrate into varying depths of the language (sentences regarded as atomic, or splitting them to predicates applied to individual terms, or even revealing such fine logical structures like modal, temporal, dynamic, epistemic ones). In order to achieve its special goal, logic was forced to develop its own formal tools, mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probability
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A: P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone unwell (sick) is coughing might be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subjunctive Possibility
Subjunctive possibility (also called alethic possibility) is a form of modality studied in modal logic. Subjunctive possibilities are the sorts of possibilities considered when conceiving counterfactual situations; subjunctive modalities are modalities that bear on whether a statement ''might have been'' or ''could be'' true—such as ''might'', ''could'', ''must'', ''possibly'', ''necessarily'', ''contingently'', ''essentially'', ''accidentally'', and so on. Subjunctive possibilities include logical possibility, metaphysical possibility, nomological possibility, and temporal possibility. Subjunctive possibility and other modalities Subjunctive possibility is contrasted with (among other things) epistemic possibility (which deals with how the world ''may'' be, ''for all we know'') and deontic possibility (which deals with how the world ''ought'' to be). Epistemic possibility The contrast with epistemic possibility is especially important to draw, since in ordinary language ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subjunctive
The subjunctive (also known as conjunctive in some languages) is a grammatical mood, a feature of the utterance that indicates the speaker's attitude towards it. Subjunctive forms of verbs are typically used to express various states of unreality such as: wish, emotion, possibility, judgment, opinion, obligation, or action that has not yet occurred; the precise situations in which they are used vary from language to language. The subjunctive is one of the irrealis moods, which refer to what is not necessarily real. It is often contrasted with the indicative, a realis mood which is used principally to indicate that something is a statement of fact. Subjunctives occur most often, although not exclusively, in subordinate clauses, particularly ''that''-clauses. Examples of the subjunctive in English are found in the sentences "I suggest that you ''be'' careful" and "It is important that she ''stay'' by your side." Indo-European languages Proto-Indo-European The Proto-Indo-European ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypothetical
A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories. Even though the words "hypothesis" and "theory" are often used interchangeably, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a provisionally accepted hypothesis proposed for further research in a process beginning with an educated guess or thought. A different meaning of the term ''hypothesis'' is used in formal logic, to denote the antecedent of a proposition; thus in the proposition "If ''P'', then ''Q''", ''P'' denotes the hypothesis (or antecedent); ''Q'' can be called a consequent. ''P'' is the assumption in a (possibly counterfactual) ''What If'' question. The adjective ''hypothetical'', meaning "havin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counterfactual Conditional
Counterfactual conditionals (also ''subjunctive'' or ''X-marked'') are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with indicatives, which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of fake tense morphology, which some languages use in combination with other kinds of morphology including aspect and mood. Counterfactuals are one of the most studied phenomena in philosophical logic, formal semantics, and philosophy of language. They were first discussed as a problem for the material conditional analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic possible world approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequences
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be ''finite'', as in these examples, or ''infinit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deductive Reasoning
Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is ''sound'' if it is ''valid'' and all its premises are true. Some theorists define deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning. Psychology is interested in deductive reasoning as a psychological process, i.e. how people ''actually'' draw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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