PART xn.

the Sign confequently requiring a demonftration. of it felf, it runs into the Alternate common place ^ the demonftration requiring a fign, the iigii a’deraonftration, which is abfard. Neither can the controverfii concerning fign be judged, bccaufc.dijudicatioQ wanteth a Criicrie, it being ■conti30t;Qrted, as vve ftiewed, whether there be a CrlneriBf;and the Criterie confequently requi¬ ring a Demonftration to prove that there is a Criterie, it runs again into the Alternate place. If therefore neither by Demonftration, nor by Sign,nor. by Criterie,it can be proved, that there is Demon ftration, and it be not manifeft of it felf, as we have fhewn,it will be incomprehen- fible whether there be Demonftration ; there¬ fore Demonftration is inexiftent: For it is un- derftood by denionftrating, but not being com¬ prehended it cannot demonftrate , therefore tliere will be no Demonftration. This, by way of Summary, may ferve againft Demonftration.
But the Dogmatifts, on the other fide, fay , The Reafons all edged againft Demonftration, ci¬ ther are demonftrative,-or not demonftrativc - If not demonftrative, they are not able to prove there is no Deraonftratina v If demonftrative , they themfelves, by Retortion, prove the fiib Cftence of Demonftration. Hereupon they ar¬ gue thus. If there is Demonftration there is Demonftration if there is not Demonftration there is Demonftration, therefore there is De¬ monftration. Upon the fame grounds they alfo propofe this Reafon That which followeth from contraries, is not only True, but NeceflV ry, but, there is Demonftration, and, there is not Demonftrat!on,are oppofite one to another, from both which it foUoweth, that there is Demonftration, therefore there is Demonftrar tion.
But this may be contradi0:ed,as for Epmple, if we fay thus ^ Forafmuch as we conceive that there is not any Reafon demonftrative, neither do we conceive that the Reafons alledged againft Demonftrations are adfolutely demonftrative , but that they feem probable to us-, but Pro¬ bables are not neceflarily demonftrative, there¬ fore if the Demonftratives are ( which we al¬ low not ) neceflarily true, bat true Reafons col- le(ft true from true, their Inference is not true, and if not, it is no Demonftration ^ therefore ( by way of Retortion ) there is no Denionftra- tion. Befides, as purgative Medicines expel themfelves, together with the Humors which they purge, it is poflible that thefe Reafons may exclude themfelves, together with thofe which are faid to be Demonftratives. For this is not abfurd, feeing that this Sentence, That there is nothing T rue , not only takes away all other things, but it felf amongft the reft. Moreover, this Argument (If there be’ Demonftration there isDemonftration, if there is not Demonftration there is Demonftration, but either there is, or there is not, therefore there is) may many ways be {hewn to be Inconciuilve ; but, for the pre- fent,we (hall be contented with this Epicherem. If this Connex (If there is Demonftration there is Demonftration,) be not faulty, the contrary of its Confequent (that is, there is not Demon¬ ftration) muft be repugnant to its Antecedent, there is Demonftration, for that is the Antece¬ dent of the Connex : ^ut, according to them, it
is impolfible that a Connex can be found, if it confifts of contrary Propolitions, for a Connejc promifeth, that if its Antecedent be, its Confe- quenc is alfo but in Oppofites quite contrary, which of them foever is, the other muft not be. Therefore if this be a true Connex, If there ia Demonftration, there is Demonferation, this other cannot be true'. If there is not Demon¬ ftration, there is Demonftration
Moreover, If we grant by Suppofition, that this is a found Connex, If there is not Demon¬ ftration, there is Demonftration, this part, if there is not Demonftration, may coexift with the other, there is Demonftration: But if it may coexift with it, it cannot be repugnant to it,ro that in this Connex, if there is Demonftration, there is Demonftration, the contrary of the Con- fequent is not repugnant to the Antecedent , therefore it is not found. Again, IfthisCon- nes which, by way of Conceflion, is laid down for ibundjandthis part, there is no Demonftra- tion, be repugnant to that part, there is not Demonftration, neither will this be agood-Dif- junft, either there is Demonftration, of there is not Demonftration for a good Disjunft pro¬ mifeth that one of its parts is true, and that the other is falfe and repugnant. Or if the Dif- juiiht be found, this, if there is not Demonftra¬ tion, there is Demonftration, will again be found to be faulty, a Connex confifting of Repugnants. Wherefore the Sumptions in theforefaid Reafoa are inconfiftent, and deitroy one another, therefore the Reafon is not found. But neitlrer can they ftiew that fomthing followeth updn Re- pngoants, not having a Criterie of theConfo- queats, as we arped before. But this is (aid over and above. Now if the Reafons for De¬ monftration be probable, and the Reafons again& Demonftration be probabU alfo, we muft fuf- pend, faying no more, that there is Demonftra¬ tion, than that there is not.
CHAP. XIV,
Of Synogifm.
Concerning thofe which they call Syllogifmt^ perhaps it were fuperfluous todifcourfe, as well for that they are fubverted by taking away Demonftration, ( for if there be no De¬ monftration, there is no Demonftrative Reafon) as alfo, forafmuch as what we have already (aid may ferve for Confutation of them, whereas we over and above delivered a Method, to fliew, that all the Demonftrative Reafonsof the Stoklvs and Peripateticks are inconclufive. But perhap® it would not be amifs to lay fomething in par¬ ticular concerning thefe, efpecially, feeing they have a high conceit of them. But whereas many things might be alledged, tenftiew, they can¬ not exift ’j yet we, perfuing'cur defign of at Summary, will ofe our firft Method.
Let us firft fpeak of Indemonftrables •, for if they be taken away, all other Reafons are over¬ thrown, as being by them demonferated to be Conclufive. Now this Propofition, Every Man. vs a living Creature^ is inductively proved by par¬ ticulars •, becaufe from Socrateses being a Man, and a living Creature, and fo P/4fo’sand Dion\
and
V