deduction

n.

1. The act of deducting; subtraction.
2. An amount that is or may be deducted: tax deductions.
3. The drawing of a conclusion by reasoning; the act of deducing.
4. Logic.
   1. The process of reasoning in which a conclusion follows necessarily from the stated premises; inference by reasoning from the general to the specific.
   2. A conclusion reached by this process.

Any item or expenditure subtracted from gross income to reduce the amount of income subject to tax.

Also referred to as "allowable deduction".

Investopedia Says:
For example, if you make $40,000 and you have a deduction for $1,000, then your taxable income is reduced to $39,000.

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1. expense allowed by the Internal Revenue Service as a subtraction from adjusted gross income in arriving at a person's taxable income. Such deductions include some interest paid, state and local taxes, charitable contributions.

2. adjustment to an invoice allowed by a seller for a discrepancy, shortage, and so on.

noun

1. An amount deducted: abatement, discount, rebate, reduction. See increase/decrease.
2. A position arrived at by reasoning from premises or general principles: conclusion, illation, illative, inference, judgment. See reason/unreason.

n

Definition: conclusion, understanding
Antonyms: confusion

n

Definition: something subtracted
Antonyms: addition, increase, rise

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Deducing or inferring the general from the particular; using particular statements as premisses from which future developments are shown to proceed logically. Put more simply, deduction begins with a theory from which a hypothesis is derived and then tested. An outstanding example is Burgess's concentric zone theory, based, as it was, on an observation of the Chicago of the late 1920s and early 1930s. Deduction provides laws from which outcomes may be predicted but such prediction plays little part in human geography because of the extreme complexity of the systems involved. Compare with induction.

For more information on deduction, visit Britannica.com.

The amount deducted from the contract sum by a change order.

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A process of reasoning in which a conclusion is drawn from a set of premises. Usually confined to cases in which the conclusion is supposed to follow from the premises, i.e. the inference is logically valid. See also logical calculus, model theory, proof theory. In spite of his own claims, Sherlock Holmes's methods were not typically deductive, but rather exercises of abduction.

A logical method of reasoning from generalizations to specific relations or facts. Compare induction.

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This entry contains information applicable to United States law only.

That which is deducted; the part taken away; abatement; as in deductions from gross income in arriving at net income for tax purposes.

In civil law, a portion or thing that an heir has a right to take from the mass of the succession before any partition takes place.

A contribution to a charity can be used as a deduction to reduce income for income tax purposes if the taxpayer meets the requirements imposed by law.

A cost or expense subtracted from revenue, usually for tax purposes.

In the more general sense any process of reasoning by means of which one draws conclusions from principles or information already known. Thus Isaac Newton talks of making deductions from his experiments with prisms, and G. K. Chesterton's Father Brown, after visiting the scene of the crime, deduces that Flambeau was responsible. But within logic and philosophy deduction is contrasted with induction. Frequently the contrast is made by use of a directional metaphor: by induction one moves from particular to general and from the less general to the more general, ascending the theoretical ladder which terminates in first principles; by deduction one moves from more general to less general and from general to particular, descending the theoretical ladder which terminates in facts about particular individuals or events. This image of the ascent and descent of reason is to be found in Plato, Aristotle, in many medieval treatises on logic, and also in the works of Francis Bacon.

In the logic of scholastic tradition, deduction is equated with syllogistic inference, for it was by means of the definition and study of syllogisms and their possible forms that Aristotle introduced a framework for both a codification and a theoretical discussion of the principles of valid deductive inference, the kind of inference that can be accepted as providing proofs or demonstrations. The central idea here is that in a valid deductive argument the truth of the premisses guarantees the truth of the conclusion; in some sense the conclusion is already contained in the premisses. Thus Aristotle defined a syllogism as 'a discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so. I mean by the last phrase that it follows because of them, and by this that no further term is required from without in order to make the consequence necessary' (Prior Analytics, 24b 18–23). But the further idea underlying the study of deductive inference, and indeed behind the notion of logic generally, is that this is a study of the principles of correct reasoning and that as such it must be independent of any particular subject matter about which we might want to reason. The laws of logic, if they are to be universally applicable, must thus concern the forms or structures of arguments only, omitting all reference to content. On Aristotle's account, which was dominant for 2,000 years, all deduction is a matter of establishing connections between general terms. He defines a proposition as 'a statement affirming or denying something of something' (24a 16). In other words, a (categorical) proposition is thought of as a statement that a certain relation holds between its subject S and its predicate P. Propositions are then classified according to the relation asserted to hold: Universal Affirmative — 'All S are P' (SaP), Universal Negative — 'No S are P' (SoP), Particular Affirmative — 'Some S are P' (SiP), Particular Negative — 'Some S are not P' (SoP). A syllogism is the making of a new connection between terms which goes via a third, or middle term. Syllogisms were traditionally classified into four figures according to the arrangement of their terms (although only the first three of these were recognized by Aristotle, who did not regard the fourth as a distinct figure). The figures are:Thus an example of a valid first-figure syllogism would be:

SaM	(All) whales are mammals.
MaP	(All) mammals are warm-blooded.
∴ SaP	∴ (All) whales are warm-blooded.

An example of a plausible but invalid first-figure syllogism would be:

SaM	(All) larches are conifers.
MiP	Some conifers are deciduous.
∴ SiP	∴ Some larches are deciduous.

The invalidity of this form becomes obvious if 'Scots pine' is substituted for 'larch'. Any valid deduction will then be required to be reducible either to a syllogism or to a sequence of syllogisms which traces a chain of connections between the subject and predicate terms of its conclusion.

In the 17th and 18th centuries, partly as a result of the increased hold of nominalism, partly as a result of the dominance of a (Cartesian) thinking-subject-centred approach to philosophy, the Aristotelian view of deductive reasoning was internalized. Instead of referring to classes or to universals, general terms were taken as standing for ideas (mental representations). (Categorical) propositions are thus interpreted as assertions about the relations between ideas, and deductive reasoning becomes a matter of perceiving the relations between ideas. From this perspective the laws of logic become the laws of thought, laws basic to the structure of the human intellect and constitutive of its rationality.

This conception finds perhaps its clearest expression in Immanuel Kant's Critique of Pure Reason. But it is here also that the seeds are sown of the fundamental revisions both in logic and in conceptions of the nature and structure of thought which were brought about as a result of the work of Gottlob Frege and others working in the late 19th and early 20th centuries. For Kant, in spite of his use of a very traditional Aristotelian framework for the construction of his table of judgements, (i) places primary emphasis on judgements as cognitive acts, rather than on ideas as the referents of general terms, and (ii) sees judgement as a matter of the application of a concept to an object according to a rule.

Frege strenuously rejected the idea that laws of logic are laws of thought. It was his view that, if a valid deductive argument is to be one where the truth of its premisses guarantees the truth of its conclusion, the laws of logic must be laws of truth, founded on the way in which language represents reality, not on the nature of the psychological processes by means of which human beings represent reality to themselves and then manipulate these representations. But Frege did retain and build on the Kantian emphasis on judgement which gives logical priority to propositions rather than to terms. Deductive argument is now seen to depend on establishing relations between the possible truth values of propositions (thoughts) expressed by (indicative) sentences; the proposition becomes the basic logical unit and truth the fundamental semantic notion. The simplest (atomic) propositions are regarded as expressing the application of a concept to an object (symbolized as 'Fa'), where there is a fundamental asymmetry at both logical and ontological levels between concepts and objects. Concepts are treated by analogy with mathematical functions. This allowed Frege to develop a logical framework of much greater power and flexibility than Aristotle's. In particular it enabled him to incorporate arguments where the propositions involve relations and where the validity of the argument depends on the characteristics of the relation concerned, as, for example: 'A is heavier than B. B is heavier than C. Therefore A is heavier than C.' In addition, by the device of introducing quantifiers and bound variables, Frege was able to treat such statements as 'Every natural number has a successor' and 'There is no largest natural number'. Present logical systems all exploit the basic Fregean innovations.

(Published 1987)

— Mary Elizabeth Tiles

Bibliography
• Aristotle (1949). Prior and Posterior Analytics. Rev. text with introd. and commentary by W. D. Ross.
• Frege, G. (1960). Philosophical Writings. Sel. and trans. P. Geach and M. Black.
• Kant, I. (1929). The Critique of Pure Reason. Trans. N. Kemp-Smith.
• Kneale, W. and M. (1962). The Development of Logic.

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The process of reaching a conclusion through reasoning from general premises to a specific premise. An example of deduction is present in the following syllogism: Premise: All mammals are animals. Premise: All whales are mammals. Conclusion: Therefore, all whales are animals.

IN BRIEF: The act of subtracting (removing a part from the whole); The act of reducing the selling price of merchandise; Something that is inferred.

We do not learn by inference and deduction and the application of mathematics to philosophy. — Henry David Thoreau

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Dansk (Danish)
n. - fradrag, fradragsbeløb, deduktion

Nederlands (Dutch)
aftrek, inhouding, gevolgtrekking, deductie

Français (French)
n. - déduction, retenue, prélèvement sur, défalcation de, raisonnement déductif

Deutsch (German)
n. - Abzug, Schlußfolgerung

Ελληνική (Greek)
n. - αφαίρεση, έκπτωση, συμπέρασμα, (παρα)κράτηση, (φιλοσ.) απαγωγή

Italiano (Italian)
defalco, deduzione, sconto

Português (Portuguese)
n. - dedução (f)

Русский (Russian)
вычитание, вывод, вычитаемая сумма

Español (Spanish)
n. - rebaja, retención, deducción, descuento, reducción

Svenska (Swedish)
n. - avdrag, slutledning

中文（简体）(Chinese (Simplified))
减除, 减除额, 扣除

中文（繁體）(Chinese (Traditional))
n. - 減除, 減除額, 扣除

한국어 (Korean)
n. - 연역법, 삭감

日本語 (Japanese)
n. - 差引き, 控除, 推理, 演繹, 推論

العربيه (Arabic)
‏(الاسم) عمليه استنتاج من مبادئ عامه لحاله معينه, استنتاج, الجز او المقدار المقتطع‏

עברית (Hebrew)
n. - ‮מסקנה, ניכוי, הפחתה‬

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