Group:
philosophy
Group:
philosophy of science
Group:
science
Topic:
abstraction
Topic:
classification
Topic:
denoting phrases and definite descriptions
Topic:
law of nature
Topic:
limitations of formalism
Topic:
logic
Topic:
metaphysics and epistemology
Topic:
mathematics as a formal system
Topic:
Newtonian physics
Topic:
reality is a machine
Topic:
physics as computation
Topic:
reduction languages
Topic:
referential transparency
Topic:
scientific paradigms and research programs
Topic:
semantic truth; s iff p
Topic:
sentences, propositions, and truth
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Summary
Reductionism is the attempt to reduce knowledge to a small set of concepts. There are three different goals: scientific, mathematical, and universal.
The scientific goal is to reduce subjective experience to objective models. For example heat is reduced to physical motion and lightening is reduced to electricity. It has been immensely successful in improving our understanding and control of the world. Typically, a cause is hypothesed to explain the facts and new experiments are developed to confirm the hypothesis. Once firmly established, the hypothesized cause becomes the observed object itself.
The mathematical goal is to reduce thought and language to symbols and their manipulation. It has been largely successful in formalizing mathematics. It is an assumption of artificial intelligence and is commonly seen as the foundation for understanding intelligence and thought. In brief, everything is a machine, so mind must be a symbolic machine. Leibnitz was an originator of the idea.
Radical reductionism is to reduce everything to atoms of experience. It has not been successful. (cbb 4/94)
Subtopic: reduction to other concepts 
| Quote: it is rational to redefine notions like heat to their causes; better control of reality, and fits nature at its causal joints [»searJR_1992]
| | Quote: ontological reduction shows that objects of a certain type are nothing but objects of other types; target for science [»searJR_1992]
| | Quote: causal reduction shows that the existence and causal powers of objects of a certain type are due to the causal powers of objects of another type [»searJR_1992]
| | Quote: in the history of science, causal reductions lead to ontological reductions; e.g., reduction of heat to molecular motion redefines heat
| | Quote: when turn causal into ontological reduction, redefine notions to exclude subjective appearances; e.g., heat from feeling hot to molecular motions [»searJR_1992]
| | Quote: Galileo found a formal description of physical motion that ignored secondary qualities and teleological considerations
| | Quote: the success of 19c physics lead to the belief that all phenomena can be explained in a similar way; including life and thought
| | Note: Physicalism is that all facts are either physical or mathematical and that scientific claims and concepts are reducible [»tarsA_1944, OK]
| | Quote: some of the chief spokesman of reductionism were the popularizers of physical science [»jakiSL_1969]
| | Quote: large complex structures are built up step-by-step from simpler structures using discoverable natural laws; includes linguistic structures [»rossDT_1963]
| | Quote: if the natural laws of complex structures can be formulated mechanically, then the grand complexity will arise naturally and of itself
| | Quote: psychological theory can not rest on intentional terms; otherwise it presupposes the very thing it is explaining
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Subtopic: logical reduction
| Quote: can reduce any system of logical equations to a single, equivalent equation [»boolG_1854, OK]
| | Quote: a dominant theory is one with perfectly known terms and infallible inferences; incorporating other, non-Euclidean theories enriches their development [»lakaI_1976]
| | Quote: Aristotle defined categories for the primitive concepts (e.g., relation, time); build concepts from general type (genus) and differentia [»sowaJF_1984]
| | Quote: the intension of a complex concept may be defined by more primitive concepts
| | Quote: if terms are written as their indefinable, first terms, it is easy to resolve predicates and derive terms [»leibGW_1666]
| | Quote: if expand an equivalence to simple primitives both sides will be the same; A and B are coincidents [»leibGW_1686]
| | Quote: A is true, if when we put A's value in place of A, a contradiction never occurs; reduce to simple primitives [»leibGW_1686]
| | Quote: to be certain of truth, analyze to the fundamentally true or prove that a contradiction will never occur; the latter can eliminate a long continuation [»leibGW_1686]
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Subtopic: substitutivity
| Quote: indiscernibility of identicals--identicals may be substituted in any true statement [»quinWV_1947]
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Subtopic: formalized vs. natural language
| Quote: there is no difference in principle between a formalized language and a natural language; differing degrees of completeness [»churA_1951]
| | Quote: seek a normative, abstract theory of language; like applied geometry is the abstract theory for surveying [»churA_1951]
| | Quote: radical reductionism: every meaningful statement is translatable into a predicate about immediate experience [»quinWV1_1951]
| | Quote: Carnap in Aufau used mathematics and a parsimonious experiential language to define important additional sensory concepts
| | Quote: Carnap proposed a principle of least action in assigning qualities to point-instants so that they match our experiences [»quinWV1_1951]
| | Quote: Carnap was not able to connect 'quality at location x;y;z;t' with his language of sense data and logic
|
Subtopic: formalizing knowledge
| Quote: semantic conception of truth has a precise, rigorous meaning only if a language is exactly specified with axioms and rules of inference [»tarsA_1944]
| | Quote: the goal of formalizing knowledge with syntactic manipulations has dominated Western thought since Galileo's time [»dreyHL_1979]
| | Quote: the ontological assumption is that the world can be exhaustively analyzed into atomic facts; underlies AI and philosophy [»dreyHL_1979]
| | Quote: Leibniz developed a system for assigning a characteristic number to every object; so all concepts analyzed into a small number of undefined ideas [»dreyHL_1979]
| | Quote: reductionism started by Lull in 13c; defined by Leibniz in his Universal Characteristic [»sowaJF_1984]
| | Quote: Leibniz represented primitives as primes and other concepts by their products; universal dictionary for mapping concepts to numbers
| | Quote: Leibniz invented first calculating machine; for manipulating concepts
| | Quote: Speciosa Generalis reduces truth and reason to a calculus of characters and words; a universal language, easily learned [»leibGW3_1714]
| | Quote: a Speciosa Generalis would guide reasoning, avoid errors, and estimate probabilities
| | Quote: construct a Universal Character by assigning symbols for simple notions and compose these symbols for everything else; like logic and mathematics [»sparK7_1972]
| | Quote: Dalgarno developed a universal language based on a hierarchical classification with three letter codes; e.g., 'g' is 'Qualitas Sensibilis', 'ga' is tactus, and 'gan' is humiditas [»sparK7_1972]
|
Subtopic: reduction to number
| Quote: atomic numbers allow an understanding of nature as pure numbers
| | Quote: analyze categories as mutipart numbers; e.g. 'Interval' is 2.3.10 where 2 is space, 3 is between, and 10 is whole [»leibGW_1666]
| | Quote: for every true universal, affirmative, categorical proposition the predicate is contained numerically in the subject [»leibGW4_1679]
| | Quote: want to represent chess as numbers and operations on numbers, and to reduce strategy to a sequence of computer orders [»shanCE3_1950]
|
Subtopic: reduction to true/false
| Quote: AI's data structures are primitive examples of representations that understand themselves; can conceivably replace the homunculus with an army of mechanical homunculi
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Subtopic: arithmetical reduction
| Quote: all arithmetical operations resolve to increase and decrease, i.e., addition and subtraction [»dattB_1935]
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Subtopic: formalizing psychology
| Quote: all of psychology is based on the activity of neuron nets, i.e., on two-valued logic [»mccuWS_1943]
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Subtopic: limits of reduction
| Quote: unlike AI, perhaps nature is graceful all the way down
| | Quote: probabilitistic laws of radiation fundamentally different than statistical analysis of complex system; with radiation, there is no individuality or elementary process [»bohrN_1949]
| | Quote: Skinner's avoidance of intentional idioms in psychology is too extreme; use intentional terms provisionally and eventually design a mechanism to replace them [»dennDC_1978]
| | Quote: Skinnerian explanation in terms of stimuli and responses fails to explain novelty and generality [»dennDC_1978]
| | Quote: the dogmas of empiricism are ill-founded (i.e., analytic vs. synthetic and reductionism) [»quinWV1_1951]
| | Quote: analyze categories to their indefinable terms; Aristotle--we must not seek a definition of everything
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Related Topics
Group: philosophy (60 topics, 2323 quotes)
Group: philosophy of science (10 topics, 406 quotes)
Group: science (45 topics, 1960 quotes)
Topic: abstraction (62 items)
Topic: classification (65 items)
Topic: denoting phrases and definite descriptions (21 items)
Topic: law of nature (28 items)
Topic: limitations of formalism (93 items)
Topic: logic (84 items)
Topic: metaphysics and epistemology (99 items)
Topic: mathematics as a formal system (30 items)
Topic: Newtonian physics (79 items)
Topic: reality is a machine (48 items)
Topic: physics as computation (31 items)
Topic: reduction languages (17 items)
Topic: referential transparency (26 items)
Topic: scientific paradigms and research programs (30 items)
Topic: semantic truth; s iff p (34 items)
Topic: sentences, propositions, and truth
(23 items)
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