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Fallacy of division

 

 
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Fallacy of division
 
 
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A fallacy
Fallacy

A fallacy is an argument which may convince some people but is not logically sound. Note that the truth of the conclusions of an argument does not determine whether the argument is a fallacy - it is the argument which is incorrect....
 of division occurs when one reasons logic
Logic

Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical Trivium . The word derives from Greek language ?????? , fem....
ally that something true of a thing must also be true of all or some of its parts.

An example:

  1. A Boeing 747 can fly unaided across the ocean.
  2. A Boeing 747 has jet engines.
  3. One of its jet engines can fly unaided across the ocean.


The converse of this fallacy is called fallacy of composition
Fallacy of composition

A fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some part of the whole ....
, which arises when one fallaciously attributes a property of some part of a thing to the thing as a whole.

Another example:

  1. Functioning brains think.
  2. Functioning brains are nothing but the neurons that they comprise.
  3. If functioning brains think, then the individual neurons in them think.
  4. Individual neurons do not think.
  5. Functioning brains do not think.






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    A fallacy
    Fallacy

    A fallacy is an argument which may convince some people but is not logically sound. Note that the truth of the conclusions of an argument does not determine whether the argument is a fallacy - it is the argument which is incorrect....
     of division     occurs when one reasons logic
    Logic

    Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical Trivium . The word derives from Greek language ?????? , fem....
    ally that something true of a thing must also be true of all or some of its parts.

    An example:

    1. A Boeing 747 can fly unaided across the ocean.
    2. A Boeing 747 has jet engines.
    3. One of its jet engines can fly unaided across the ocean.


    The converse of this fallacy is called fallacy of composition
    Fallacy of composition

    A fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some part of the whole ....
    , which arises when one fallaciously attributes a property of some part of a thing to the thing as a whole.

    Another example:

    1. Functioning brains think.
    2. Functioning brains are nothing but the neurons that they comprise.
    3. If functioning brains think, then the individual neurons in them think.
    4. Individual neurons do not think.
    5. Functioning brains do not think. (From 3 & 4)
    6. Functioning brains think and functioning brains do not think. (From 1 & 5)


    Since the premises entail
    Entailment

    In logic and mathematics, entailment or logical implication is a logical relation that holds between a set T of propositions and a proposition B when every Model theory of T is also a model of B....
     a contradiction (6), at least one of the premises must be false. We may diagnose the problem as located in premise 3, which quite plausibly commits the fallacy of division.

    An application: Famously and controversially, in the philosophy of the Greek Anaxagoras
    Anaxagoras

    Anaxagoras was a Pre-Socratic philosophy Greek philosophy famous for introducing the cosmological concept of Nous , the ordering force....
     (at least as it is discussed by the Roman Atomist Lucretius
    Lucretius

    Titus Lucretius Carus was a Roman Republic poet and philosopher. His only known work is the epic philosophical poem on Epicureanism De rerum natura, translated into English as On the Nature of Things....
    ), it was assumed that the atoms constituting a substance must themselves have the salient observed properties of that substance: so atoms of water would be wet, atoms of iron would be hard, atoms of wool would be soft, etc. This doctrine is called homeomeria, and it plainly depends on the fallacy of division.

    If a system as a whole has some property that none of its constituents has (or perhaps, it has it but not as a result of some constituent having that property), this is sometimes called an emergent
    Emergence

    In philosophy, systems theory and science, emergence is the way complex systems and patterns arise out of a Multiplicity of relatively simple interactions....
     property of the system.

    External link

    • The Fallacy Files