Chap. IX. ANTIENT METAPHYSICS. 457 



every effeB muft have upon its caufe ; for the two lines would not be 

 equal if the axiom were not true : Whereas, on the other hand, the 

 axiom would have been true, if thefe particular lines had never ex- 

 ifted ; fo that there is no mutual or reciprocal dependence in the 

 cafe. 



And it is the fame with ideas that it Is with propofitions ; for the 

 more general idea is the caufe of the particular idea under it, becaufe 

 it comprehends it. Thus, the idea of animal comprehends man ; the 

 confequence of which is, that man could not have exifted without a- 

 nifnalf but animal might have been without man. Therefore animal 

 is the cai{/e of ?nany according to the definition that I have given of 

 caufe, but not man of animal: So that, in the whole procefs of the 

 human mind, the formation of our ideas, as well as our reafonings, 

 what is general is prior in excellence and dignity to what is particu- 

 lar, which is included in it, and produced out of it. 



And here we may very clearly fee the difference betwixt in- 

 dudive reafoning and demonftrative ; for, tho' the indudion were ne- 

 ver fo full, fuppofe the thing could be fliown to hold in ten thou- 

 fand different inftances, yet we never could from thence infer that it 

 was univerfally true. And why ? Becaufe particulars do not con- 

 tain the general, but the general the particulars ; therefore the ge- 

 neral is the cau/e of the particulars, but not the particulars of the^^- 

 7teral. And, if it were otherwife, all iiuclid's reafonings from defi- 

 nitions and axioms would be no better than indudlive reafoning. For 

 it is certainly true, what Ariftotle fays *, that there is no demonftra- 

 tive or fyllogiftlcal reafoning, of any kind, in geometry, or in any o- 

 ther fcience, without a general propofition, from which the particular 

 proportion made ufe of in the fyllogifm is deduced. Of this Ari- 



M m m ftotle 



* Firft Analyt. book i. cap. 24. 



