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Reductionism is the idea that knowledge at a higher level can be deduced from the entities and their interaction at a lower level. E.g. the claim that the properties of molecules can be deduced from the properties of atoms, the properties of cells can be deduced from the properties of molecules, . Do theories also have reductionist approach Theory T reduces to theory B when all of the truths of T (including the laws) have been translated into the language of B. Theory T reduces to theory B when all of the laws of T have been derived from those of B. Theory T reduces to theory B when all of the observations explained by T are also explained by B ?

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  • I think you want to say "property of molecules deduced from properties of atoms"
    – Rushi
    Jan 4 at 16:40
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    @Rushi thanks...
    – quanity
    Jan 4 at 17:20
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    What is the question? Jan 4 at 18:48
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    Reductionism is the idea that knowledge at a higher level can be deduced from the entities and their interaction at a lower level - there are multiple meanings to reductionism, and this is one of the stronger ones. There are weaker forms of reductionism. The way I like to phrase it is usually "ontological reductionism" vs "explanatory reductionism". An ontological reductionist need not commit to the idea that all higher level patterns are understandable in terms of lower level stuff, even if it's ontologically true that each instance of them is caused by lower level stuff happening.
    – TKoL
    Jan 5 at 12:24
  • @TKoL write answer
    – quanity
    Jan 6 at 8:11

2 Answers 2

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Reductionism is the idea that knowledge at a higher level can be deduced from the entities and their interaction at a lower level

there are multiple meanings to reductionism, and this is one of the stronger ones. There are weaker forms of reductionism. The way I like to phrase it is usually "ontological reductionism" vs "explanatory reductionism". An ontological reductionist need not commit to the idea that all higher level patterns are understandable in terms of lower level stuff, even if it's ontologically true that each instance of them is caused by lower level stuff happening.

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Agreeing with your scetch of reductionism in science I want to illustrate the principle of reductionism by the some examples from physics and chemistry:

  1. Theory T denotes thermodynamics. Typical physical quantities from T are pressure (P), temperature(t) and volume (V) of a certain quantity of an ideal gas. The main law is the state equation of the ideas gas

    P x V = n x R x t

    with n a measure of the quantity of gas contained in V and R a universal constant.

    Theory B is statistical mechanics applied to the corresponding set of gas molecules. The physical quantities of a single molecule within the given volume V are its kinetic energy (E) and its momentum (p; small letter). Taking the average for all molecules gives for the average energy of a molecule

    E_av ~ t

    and for the average squared momentum of a molecule

    (p^2)_av ~ P

    Statistical mechanics derives an equation between E_av and (p^2)_av, which reproduces the universal state equation from thermodynamics.

    For an introduction explaining the basic results from physics see the ideal-gas law.

    On the lower level of statistical mechanics the concepts of temperature and pressure of a molecule do not make any sense. On the higher level of thermodynamics the concept of the energy and momentum of a molecule make no sense. Hence both levels have their characteristic physical quantities which do not make sense on the other level.

  2. More advanced is the reduction of the termodynamic concept of entropy to certain probability distributions on the level of statistical mechanics.

  3. There are other examples of reductions, e.g., taking T the biological theory of information coding in genes, and B the chemistry of the composition of nucleid acids.

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