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Philosophical and Mathematical Commentaries of Proclus - Coggle Diagram

- - - - Science can never be obtained by experimental enquiries; as these must be liable to all the inaccuracy and imperfection of their material subjects
        
        The philosophy of Pythagoras and Plato will be found, when impartially considered, to contain every thing which can enlighten the mind, improve the morals, and exalt the character of man.
- - - - Unless the existence of these lucid beings (ideas) is admitted, there can be no such thing as science; nor, indeed, any genuine knowledge at all.
        
        Hence this will be an enquiry concerning their nature and reality, for in the Commentaries, ideas are considered as the stable pillars of all truth, and the prolific principles of the universe
    - - Pythagoras, after his mysterious manner, signified ideas by numbers
        
        Before Pythagoras, Orpheus was an asserter of ideas, and he called Jupiter, or the demiurgus of the word, "the idea of all things."
        
        The doctrine of ideas is an ancient as that of wisdom itself.
      - Without universals there can be no science; for the flowing and perishing nature of particulars is perfectly foreign from that stability and duration which is requisite to objects of invariable truth. Neither is it possible, that infinite individuals can exist without the subsistence of one cause endowed with infinite power; for all multitude must necessarily originate from one, and must resemble its cause in as great a degree of perfection as its nature can admit; by a diffused infinity, shadowing forth that infinite power which subsists in indivisible union. Hence, if this be the case, and if infinite men, horses, and a multitude of other univocals, are produced in an infinite time, an unity of infinite power must be the source of each, according to which they are generated in a terminaetd manner to infinity in the universe.
        
        Besides, the participation of universals, is evident in every sensible object. Thus, the rational nature is united with every individual men. Thus, animal subsists in a lion and a horse, in a man and a dog. And thus the pentad, or number five, is participated in the five fingers, and the duad in the nostrils, eyes, hands, and feet.
        
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    - - The perfect must necessarily antecede and presie over the imperfect; unity over multitude; the impartible over the partible; and that which is perpetaully the same, over that which admits of variation and change. From whence it may be inferred, that things do not originate from baser natures, but that their gradual processions end in these; and that they begin from the most perfect, best, and most beautiful natures.
    - - There are no ideas of things evil and base, becuse these subsist in nature rather by a privation and absence of ideas.And, on this account, they are said to exist contrary to nature.
        
        Nor, secondly, are there ideas of negations, for these are destructive of the bound and limitation which is attributed to every thing from the unifying and comprehending nature of ideas
        
        Nor, again, are there ideas of things which at different times receive a variety of conditions. For these participate of transmutation from a moveable cause, but not from the immoveable and stable illustration of ideas.
        
        There are also no ideas of parts, such as the hand, head, fingers, and the like. For the causes of things existing entire, produce whole species and forms, not divided about the parts of these, like the reasons of nature.
        
        Since ideas are simple, they preside over the simple essence of every thing and cannot be composite on account of superlative simplicity
        
        Ideas must be confined to universal and perfect essences, and to whatever confers to their natural position; as for instance, to man, and every thing perfective of man, such as wisdom and ivrute.
        
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    - - It is not consonant to reason to suppose that the conception of one arises from the sensation of one particular subject.
        
        It is not possible to understand any thing without one or two or some other number, and thus it is by no means proper to deny existence to that, without which we cannot comprehend the existence or properties of any being.
        
        If unity has no real subsistence, and is nothing more than a name or conception of the mind, it may be destroyed without the destructino of its subject.
        
        Unity is participated by every being, and so the Pythagoreasn placed a super-essential one at the top of the unvierse, intelligibly abstracted from all beings in simplicity and excellence of nature. For they onsidered, that unless there was a self-subsistgng one in all things, there could neither be universals nor particulars.