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  • nature 5 note 196
    Thomas because we ultimately are dealing with their and that of some recent followers of them as well substance accident metaphysics And it is their philosophy which holds and I think rightly so that logic to which a treatment of

    Original URL path: http://www.metafysica.nl/nature/nature_5_note_196.html (2016-02-01)
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  • nature 5 note 197
    of this metaphysics of being metaphysics of substance depends on the universal applicability of the Substance Accident S c h e m e The investigation concerning the universal applicability of

    Original URL path: http://www.metafysica.nl/nature/nature_5_note_197.html (2016-02-01)
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  • nature 5 note 200
    is a substance All individual material things are substances This individual dog is an individual material thing Therefore this individual dog is a substance Here individual material thing s is middle term At least the minor must be demonstrated All mammals are individual material things This individual dog is a mammal Therefore this individual dog is an individual material thing Here mammal s is middle term So between dog and

    Original URL path: http://www.metafysica.nl/nature/nature_5_note_200.html (2016-02-01)
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  • nature 5 note 201
    consecutive ones already existing in contrast to merely add one in the sense of attaching it to the end of the series it appears that the series of syllogisms insofar as it appears in its mentioned ordering from less general to more general is not denumerable because we do not know the immediately next middle term for having successfully inserted a middle term that was forgotten to be placed in the sequence between two consecutive existing ones one can always insert yet another middle term between the inserted term and the previous term and so on and so on resulting in the fact that we never reach the last term substance and thus can never present a complete definition However insertion of more and more middle terms might be done after the manner of rational numbers or even the algebraic numbers and then the set is denumerable NOTE 201 1 for although we can never in these rational numbers determine the qua magnitude immediately next number the set can nevertheless be indexed with the whole numbers 1 2 3 4 5 etc on the basis of some other method and thus rendered denumerable and indeed it it is shown that the rational numbers are denumerable in contrast to real numbers But because here the indexing does not correspond with the magnitude of the numbers the existence of a qua magnitude first and last number does not mean that the series is finite Those rational numbers as they generally have their positions on the number line that lie between say 1 8 and 1 3 form a set consisting of an infinite number of elements despite the fact that we have a qua magnitude first 1 8 and a qua magnitude last 1 3 number And thus there may exist infinitely many syllogisms which are denumerable between the first and the last one after all Summarizing all this we can departing from the existence of a qua degree of generality first and last syllogism say the following If the sequence or chain of syllogisms is denumerable and when the indexing of this denumeration corresponds to the degree of generality then the series is countable exhaustively denumerable and thus finite If on the other hand the indexing of the denumeration does not follow the degree of generality then the series is it is true denumerable but not per se countable and thus not per se finite Although we can generate an ascending or descending sequence of syllogisms ascending or descending with respect to the degree of generality the sequence is not therefore necessarily denumerable because it might be that we can insert middle terms indefinitely In the ascending sequence of natural numbers positive integers we can always insert a number between two chosen numbers of this sequence but this has its limit meaning that the above always must be qualified At some point we arrive at say the numbers 2 and 3 and between them nothing can be inserted anymore also not

    Original URL path: http://www.metafysica.nl/nature/nature_5_note_201.html (2016-02-01)
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  • nature 5 note 202
    202 The term is universal not the thing The one universal term stands for many individuals So the term dog stands for Fido or Bruno or Blacky or Back to

    Original URL path: http://www.metafysica.nl/nature/nature_5_note_202.html (2016-02-01)
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  • nature 5 note 203a
    not the complete definition of the term dog involves the more general term mammal and this term in turn needs to be defined thereby making more complete the definition of the term dog And the definition of the term mammal involves the more general term vertebrate which embodies a second middle term a vertebrate with hairs But now the term vertebrate must be defined in turn involving the yet more

    Original URL path: http://www.metafysica.nl/nature/nature_5_note_203a.html (2016-02-01)
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  • nature 5 note 203b
    thereby changing the differentia part of the former mammal with fangs So we then get for dog A carnivore that can bark is a dog definition of the term dog This thing is a carnivore that can bark Therefore this thing is a dog A mammal with fangs is a carnivore definition of the term carnivore This thing is a mammal with fangs Therefore this thing is a carnivore A

    Original URL path: http://www.metafysica.nl/nature/nature_5_note_203b.html (2016-02-01)
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  • nature 5 note 205
    Note 205 See for this VIA PRAEDICATIONIS c 1 Meaning and Extension Distinction among the several Predicables revisited 2nd half of subsection Back to main text

    Original URL path: http://www.metafysica.nl/nature/nature_5_note_205.html (2016-02-01)
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