Nor does this precise Mathematical Method sute , in all regards , with the other parts of Philosophy . For the Notions that Science is employ'd in are , for the most part , Extension and Figure ; which being perceptible to our Sight , they show the thing , in some sort , to our Eye , as well as demonstrate it by Reason to our Understanding ; whereas , scarce any Other Science affords us this advantage ; which forces us to have recourse only to our Notions , and to strive to make them Clear by Definitions . In which , having no assistance from our Fancy or Material Representations , they are hence less easily Imprinted and Reflected on ; which makes our Attainment of Science more Laborious . Yet , notwithstanding this Accidental Disadvantage , their Productions are not at all less Evident or less Certain to the Judgment . For , it is not the Noting them with A , B , C , that either makes them True , or shows them to be so ; but the Connexion of the Notions we have of those Lines , Angles , or other Quantities , and of their Proportions to one another , which we voluntarily agree to signifie by such Letters . Whence results this Evident and Comfortable Corollary that Clear Demonstrations may be had , and , consequently , Science attain'd , in other parts of Philosophy , and in all Other Subjects , as well ( tho' not so easily ) as in those of the Mathematicks ; so the Notions belonging to those Subjects be but Clear'd and rightly Connected ; sinee 't is the Connexion of Notions , or ( as Logicians phrase it ) the Connexion of Terms , which does beget Science , and not the Formality of Lines and Letters us'd by Mathematicians .

By this time we may seem to have discover'd the true reason of the General Miscarriages of most Philosophers in the pursuit of Truth . For , since 't is Impossible that he who intends to Travel to London , tho' he have both Clear Eyes , and Strong Legs , and employs both of them to his utmost , should ever arrive at his Iourney 's End if he does not take the Right Way to it ; so it is equally Impossible any Man should arrive at Science , if he takes not the right Method or Way to attain it , tho' he have never so Clear a Natural Wit , and a Strong Brain , and labours never so industriously to make use of both to his best advantage . Providence therefore is justify'd , and the Ability of our Natural Faculty asserted ; and the Blame lies wholly at the doors of the Persons who do not first apply their Thoughts to know the Way to Truth , e'er they set forwards in quest of it : but chiefly in those who pretend to be Guides to others , and yet are Themselves Ignorant of the Method that can bring men to it . Mathematicians take the Way , and so arrive at it . Others ( a very few exeepted ) do not take it , and therefore miss of it . Whence we may establish this Fundamental and most Useful Maxim , that The First and Chief Study of those who pursue true Knowledge in Philosophy , is to apply their Industry to comprehend the METHOD or WAY to it : that , If they find not that , their most earnest Study is lost Labour ; but that , having once found it , they cannot doubt of compassing their End by using such Proper Means .

But is not the Knowledge of this Method insuperably hard to be attain'd ? For , if it be , we are never the nearer , but still at the same Loss . To give a Stop to such an apprehension , I must avow that no part of Mathematicks is more Demonstrable than is the Way to Demonstrate , or the METHOD TO SCIENCE . Nature ( as we experience ) gives us our Notions ; on which , as on its Elements , all Science is grounded . To make these Clear and Distinct , we can distribute them under Common Heads , and Divide those Heads by Intrinsecal Differences , or such as are Proper to each of them , till we come to the Notion we are to discourse of . While we thus Divide them , we at the same time , and with the same labour , frame Denitions of each Notion comprehended under those respective Heads ; by doing which we gain a Distinct and Clear Conception of them ; which does , to a fair degree , facilitate our Judging whether such or such of them may be with Truth connected in Propositions , ( or in such Speeches as Affirm or Deny , ) in which Truth does Formally consist . To do this more exactly , we consider that those Propositions must either be such as show of themselves that the Two Notions ( call'd it Terms ) must be Connected ; and then they are Self-connected or Self-evident : Or else they need to be shown Connected by means of some other Notion which is Connected with them both ; to show which we call Proving . Those of the Former sort , if perfectly such , are fit to be First Principles ; whose Nature , as Common Sense tells us , is not to need or admit of Proof . The Connexion of the later sort is made known by Proof , or by their joint Connexion with a Third , which we call the Middle Term , Medium or Argument ; to do which is the Proper work of Discourse or Ratiocination : These Three Terms rightly placed or put together , compound that most Close and Exact Discourse call'd a Syllogism . Certain and most Evident Rules may be assign'd how to place those Three Terms in the two first Propositions , so as that Discourse may be most Clear and Perspicuous ; as also , how to find out such a Middle Term as is Proper to Connect the other Two , whose Connexion or Truth is under Dispute ; and to show the Force of the Consequence , and why a New Proposition call'd the Conclusion , must most necessarily follow out of the Former ones . All which being Demonstrated , ( as I have reason to presume is done in this following Treatise ) and the Equivocation of the Words that express our Notions being avoided , I see not what more can be substantially necessary to the METHOD TO SCIENCE . For , our Notions being Clear'd , First Principles establish'd , the true Form of a Syllogism manifested , Proper Middle Terms found , and the Necessity of the Consequence evidenced ; all those Conclusions may be Deduced with Demonstrative Evidence , which ly within our Ken , or which we can have occasion to enquire after ; that is , all that we have Notions of : provided those Notions be not meerly Accidental , or very Remote from one another , and therefore Incapable of being Connected .

Yet still there is one Difficulty that sticks , and lies in our way ; and which is more , seems hard to be remov'd . For LOGICK , or the Art of Reasoning rightly , being the Skill which is to teach us this Method to Science ; and so many Logicks being written by Learned Men , and studied by such Multitudes ; how comes it that , notwithstanding such Helps , men do still differ in their Tenets , that is , many or most of them do still err , as much as if they had never had such Proper Assistances . For , if Logick shows them the way to Science , and they take that way , and have a Natural Ability to follow it or walk in it , they must all arrive at Science ; and their Thoughts center in the same Truths without any Disagreement ; the contrary to which we do notwithstanding Experience . To give an Answer to this , I shall be hard put to it how to bear my self between the two Extremes of Modesty , Dissimulation and Boasting . For , if I grant those Logicks are as they ought to be , that is , Full and Evident , and follow'd by Men of divers Sentiments , I must confess I know not how to reply , or solve the Objection . On the other side , to condemn all the Logicks since Aristotle's time , or all Logicks which are not according to his Grounds , is to set up our selves , and savours of Arrogancy . In this porplexity I have no way to secure my self but to speak the plain Truth , and to hope it will bear me out . I must then , in behalf of Truth , declare , that the Pretended Logicks themselves are in the greatest Fault . For , 't is easie to observe , that they do indeed give many dry and unprov'd Rules and Maxims ; they afford many Definitions , some right , some wrong , being oftentimes Illogical and fram'd out of Fancy ; they pester their Books with many unnecessary Divisions and Subdivisions ; they treat very largely of the Predicaments , of Single , Opposit and Aequipollent Propositions ; they are prolix and superfluous in their Doctrine about Syllogisms , their Moods , Figures , several sorts of idle Fallacies , &c. All which look very Learned to New Beginners ; who do , therefore , take much pains to lay them up in their Memory ; I say in their Memory , for none of those passages being Demonstrated , they never sunk into or settled in their Reason . And therefore , notwithstanding all this , when they have as it were got without Book all these particulars , the Readers are no wiser how to demonstrate any point practically , or how to set himself about it , than he was before he read those Treatises .

I have studied many of those Logicks my self when I was young , and all of any note I had seen then , and consider'd them very attentively , till I had almost lost my Natural Reason by dwelling upon them ; yet notwithstanding ( and I believe the same passes with other young Students ) I knew no more how to go to work to demonstrate any thing , than if I had never seen them . They started now and then some curious , amusing ( but jejune and useless ) Questions about Ens rationis , Unions , &c. and set many confused Ideas of the several parts of Logick in my Memory ; but still my Reason was not Enlighten'd , nor enabled to perform those fine things they had told me of . Nor was it any wonder ; for they spoke not to my Reason , nor endeavour'd to ground their Discourse on the Nature of the Things in hand ; nor to show demonstratively why every Step they led me , or Lesson they taught me , must be True ; nor how it did influence True Knowledge , or advance directly towards the Acquisition of Science ; so that it look'd more like a kind of History of what those Authours had said or writ , than like a Method to find out Truth ; insomuch that I came at length to suspect that the Intention of those kind of Logicians , was not to pursue the Knowledge of Truth , which is only to be had by Clear Demonstration ; but that they meant to furnish young Wits with certain Modes of Talking with a show of Learning , and of signalizing themselves for being able to argue pro or con indifferently in Scholastick Dissertations . It resembled the Tiring of a Hawk , serving only to exercise its Nibbling Faculty , and whet the Appetite , but had nothing of Nutritive in it to satisfie it . For , Reflexion will teach us very Evidently , that only that which is made Clear to our Reason , can Settle in it , Nourish and Dilate it , as being Proper and Connatural Food to a Rational Soul ; and that whatever we take in or carelesly swallow , that is not such , but meerly Wordish only fills us full of Wind and Ayr , which breaks out in Insipid Talk .

The Fault then lies evidently in the Logicks which have been us'd in the Schools hitherto , none of which have attempted to show Demonstratively the Way how to Demonstrate , or given us a Connected Discourse of the METHOD TO SCIENCE . 'T is noted that the Practice of the Preacher going along with his Doctrine , makes the Doctrine it self more Edifying : and , by parity , had the Teachers of Logick Practised Demonstration all the while they had taught how to Demonstrate , those Rules , so Rationally imprinted , sinking deep into their Soul , and thence becoming as it were a Limb or Faculty of their Judgment , would have truly Enabled them how to act accordingly ; whereas , while they swim only in their Memory , they serve for nothing but to pour out indigestedly what they had rawly taken in .

But now , where is that Authour who has hitherto made such an Useful and Necessary Attempt ? None that I know of . The Treatise call'd Ars cogitandi has divers Excellent things in it , and in some places has made many good steps towards True Logick ; and the Examples it brings are very Illustrating . But yet , in the main , it amounts to no more but The Schools Reform'd into Method and Elegancy . It abounds with many useless particulars : It does not bottom it self upon Nature , only which can give Solidity to our Reasons : It has many Unprov'd Suppositions , and bare Sayings without offering any Proof . And , yet I do verily believe that , had not the Authours calculated it for that particular sort of Philosophy they had espous'd , which could bear no Evidence , but had follow'd the guidance of their own Natural Genius ( which , doubtless , was very Extraordinary ) it would have much excell'd its present self . * Mr. Le Grand's Method says much , but proves little ; and I believe , both Cartesius , and himself , did first consider and survey the whole Scheme of their Doctrine , and then fitted their Logick to it . Which is Preposterous and Praeter-natural ; for the certain Way to the End of our Iourney should be foreknown , ere we set the First step towards it . Mr. Lushington has with much pains gone about to demonstrate some particulars of the Summulist part of Logick , and chiefly that about Predication . But , there is nothing at all of Nature in his Grounds . He regards not the Common Notions of Mankind , nor in what they consist ; and therefore his Discourses are so perfectly Artificial , that they have nothing to say to Nature , nor Nature to them . He imposes imprudently new Language and new Terms upon his Readers , which he might have assur'd himself they would never take pains to learn . He affects the way of A , B , C , which makes a show of Science ; but the Product of his Discourse is , oftentimes , no more but the bare Proposition he is to prove , onely drest up in a Mathematical Garb. His whole Book , in my judgment , might have been more clearly compriz'd in one Sheet of Paper : And , lastly , as for want of Nature to ground his Conceptions , his several Proofs can never enter into the Reason , so 't is almost Impossible they should ever stay long in the Memory . Yet his Attempt to demonstrate in such a Sceptical Age , and his Industry , deserve a fair Commendation , and may provoke others to make the same Attempt with better Success . Burgersdicius is clearly contriv'd for the Memory onely , and not for the Reason ; and he confounds and over-burthens it too , with the Multitude of his Canons , Rules , and Divisions ; for which he seldome or never gives any reason , but puts them to be Believ'd by his Reader if he pleases ; and , so leaves him still in the dark . Yet he might be made Useful to New Beginners ; were something of every thing , that is to purpose , pick'd out ; Unnecessary things ( in which he super-abounds ) cut off ; his Errours , which are not a few , Corrected by some Learned hand ; and his shatter'd thrums-ends woven into some kind of Connexion , and Dependence on one another ; to do which , little Transitions from one passage to another are Insufficient . But , as he is , he informs not the Understanding of any one thing groundedly or solidly . He falls exceedingly short of Ars cogitandi in many regards : How , he may please Climates of a duller Genius I know not ; but I should much wonder if any Learned Englishman should consider or esteem him . Mr. Clark , far exceeds him in good Sense , and in giving some Reasons for what he says in many particular passages . But , by his framing the Contexture of his Book out of Authours of different Principles , his Discourses do sometimes appear Desultory , and like a kind of Elaborate Rhapsody , laid well together by his own good Wit. He mistakes Aristotle now and then , by taking his Sentiments as represented by his Adversaries ; whose Interest and Principles conspire to make them misconceive him . He abounds with many Reflexions not all conducing to Science . A Fault , from which Aristotle himself was not altogether free ; which makes it more pardonable . For instance ; To what purpose are his many Distinctions of his Propositions , especially those he calls Exponibiles ? Let but the Learner know certainly and liquidly , what are the Subject and Predicate in any Proposition , which is easie to be discover'd by the Copula that is to come between them , and unite them ; and have a care that the words that express them are Univocal ; he will be furnish'd with means to see the Form of Connexion , which is Essential to a Proposition , and is onely Conducive to Science , which wholly consists in the Connexion of Terms . His chief Misfortune is , that he does not seem either at the beginning , or in the Process of his Book , to know , at least to build upon this Truth and stand to it , that our Notions , or ( as the Moderns have taken a Toy to call them ) Ideas , are the very Natures of the Things in our Understanding imprinted by Outward Objects ; without which no Stability of those Notions or Ideas can be , with Evidence , asserted ; nor any Solid knowledge possibly be had of our Predications ; nor the true Ground of Truth or Falshood be understood ; nor , consequently , ean there be any Firmness in our Judgments or Discourses . Whence , I could wish that every Beginner were at first well instructed and settled in this point ; for , without this , all will be but Loose , and Ungrounded Talk in the Air. And , tho' I lose Credit with our late Wits , I must avow that Aristotle's dry Assertion , that [ Anima intelligendo fit omnia , ] tho' it may seem to some a wild Paradox , has more Solid Sense in it , were it rightly understood , and is more Useful to true Philosophy , than all the other Maxims that do not proceed upon it , and suppose it ; which yet I see the Goodness of Nature intimates to many , and forces them to ground their Discourses on it Practically ; even tho' , while they speculate , they deny it , or , at least , seem to doubt of it , or disregard it .

Observing therefore this great want under which Philosophy ( which is the Study of Truth ) labours , I have , out of my true Zeal of improving Science , and beating down Scepticism , ( the profest Patron of Ignorance , and covert Parent of all Irreligion ) hazarded the Opinion of Singularity in endeavouring to write and publish a Demonstrative Logick ; at least I have given such Reasons , quite thorough it , as I judg'd to be Clear and Conclusive , in every piece of it that has any Influence upon Scientifical Knowledge . What my Reader may expect from me is this . I begin with our Natural Notions , the Bottom-Ground of all our Knowledge . I show them to be the very Natures of the Things ; whose Metaphysical Verity being Establish'd by Creative Wisdom , does , consequently , give Stability , and Solidity to all our Discourses that are built on them . I distribute those Natural Notions under those several Common Heads , and manifest why there must be so many and no 〈◊〉 show how their Definitions are to be fram'd , which make our Conceptions of the● 〈◊〉 and Distinct. I lay Rules to escape 〈◊〉 Snares , which Equivocal Words lay 〈…〉 way while we are Discoursing . I show ●he Reason of all Truth and Falshood in Connected Notions , or Propositions : Which , if Self-evident and Identical , have Title to be First Principles , as from many Heads I demonstrate . I trace Nature in all those nice and Immediate steps she takes to generate Knowledge in us at First . Coming to those Propositions that need Proof , and the Way of Proving them , I lay open the Fundamental Ground of the Force of Consequence , which gives the Nerves to every Act of True Reasoning , and of the Certainty and Evidence of every Conclusion which we rightly inferr . To perform which , I manifest that there can be but One Necessary or Natural Figure of a Syllogism , and but Four Moods of that Figure . I lay down and fix the Fundamental Laws of Concluding . I evidence the Nature of that Third Notion or Middle Term ; by the Connexion of which with the Two Terms of the Thesis to be Proved , they must inevitably be joyn'd with one another , and so the Thesis it self must be rightly Concluded ; and , therefore , Infallibly True . I show how to find out a Middle Term fit for our purpose , and thence prepare the way for Demonstration . I lay open how every Truth must have at the Bottom an Identical Proposition , and every Errour a Contradiction as their First Principles , and how they may be reduced to those Principles of theirs : To do which ( tho' more laborious ) is the best Way of Demonstrating . I manifest thence how one Truth is in another , and what strange Consequences follow thence . Also , how Middle Terms , Proper for Demonstration , may be taken from all the Four Causes . To clear better the Notion of Science , I treat of the Natures of Opinion , and ( Human ) Faith ; their Grounds , and how the Former of these two last Deviates from Right Reason ; and when the Later does , or does not . Then I consider the Effects issuing from all sorts of Proof ; viz. Assent , Suspense , Certainty , and Uncertainty . And , to put in Practise my self what I do persuade , and recommend to others , I add Seven Demonstrations of the most Considerable Theses in divers Sciences . And , lastly , I lay open the Ways and Methods of Disputation ; and detect the weak Stratagems , and inefficacious Attacques of Fallacies , or Paralogisms .

This is the Summ of my Endeavours in common . But , besides these , many particular Knowledges light in on the by , ( and , as I hope , very Useful ones ) which it would be tedious to enumerate . The Manner I use to carry on the Scheme of my Doctrin , is , not to propose my Conceptions Magisterially , or to expect any one should assent to the least Tittle of what I say upon my Word : But , I offer my Reasons for every Paragraph I advance , if it can be conceiv'd to need any ; by doing which I speak to the Reason of my Readers , and withall I expose my self to the Severe Examination of the most Acute and Iudicious Wits ; of which , I doubt not , there are Multitudes in those Seminaries of Learning , our two Famous Universities ; to whom I humbly dedicate this small Present . I neither strive to ingratiate my self by my Style , nor to surprize any by Plausible Discourses ; much less to Impose upon their Understandings by Voluntary Suppositions . I draw now and then divers Useful Corollaries , and some that will seem , I doubt not , Paradoxical ; that so I may carry on my Doctrine to farther Consequences , and show withall to what Unthought-of Conclusions Reason will lead us if we follow her close and home . Nor am I asham'd to declare openly , that I hold , that the Chief End of Science is to beget Virtue ; and not onely to raise us to Higher Contemplation , but also to comfort , and strengthen Divine Faith in us , and to make it more Lively and Operative . Whence I have taken occasion to excite my Reader 's Devotion out of the Reflexions on divers Points , that seem'd of themselves to be but Dry Speculations : making account that Good Thoughts arising , upon the Spot , but of Truths newly Clear'd to our Reason , do affect the Will most connaturally , raise Devotion , heighten Contemplation , and make it Solid ; and , consequently , keep the Soul Clear from Idle Fancies , and set her above Light Bigotteries .

I have not enumerated these Particulars to boast my Performances , ( for these are yet to be Decided , by examining whether the Reasons I have all along produced will bear the Test ) but to bespeak my Reader 's Pardon , if , travelling in an unbeaten Road , I happen now and then to stumble . Which as I am not conscious to my self to have done at all , so I shall hope I no where do in any passage that substantially concerns the METHOD TO SCIENCE : Rather , I must positively avow that it is impossible for any Wit of Man to invent any other Way , than what I have propos'd , that is Solid and Evident . For , 't is granted by all Mankind hitherto ( unless , perhaps , the Cartesians ) that Truth is fundamentally the Conformity of our Judgment to the Nature of the Thing , and that it consists Formally in the Connexion of the Terms ; both which I have follow'd most exactly ; and , as some Readers ( I doubt not ) will think , too superstitiously .

Now , since Rectum est mensura sui & obliqui , my Design engages me to show ( as far as the Brevity of a Preface will allow ) that the different Methods taken by Others do not lead us to true Science . And , indeed , there is a kind of Necessity laid upon me to make this Charge good : For , since we take Different Methods , if theirs be a Right one , mine must be a Wrong ; and my Publishing it no Advantage , but an Injury to Truth , and to my Greatest Neighbour , the World . The METHODS which I pitch upon to examine , shall be of two sorts , viz. that of Speculative , and that of Experimental Philosophers ; The Former of which pretend to proceed by Reason and Principles ; the Later by Induction ; and both of them aim at advancing Science . Looking about for an Instance if the Former sort , I did not think Epicurus , and his School worth my taking notice of ; for he who supposes all his Principles , bids Defiance to all Methods of Concluding any thing . And , as for our Modern School-Philosophers , they have so disputed themselves quite out of breath for want of any Certain Method , that they have brought all Science to an Indifferency of Opinions , or maintaining any thing with Equal Evidence ( or rather No-Evidence ) a thing absolutely impossible for those who lay any right Method to Science . And this Deficiency of theirs , losing their Credit with our late Wits , have given them occasion to east about how to model Philosophy a-new , and frame it wholly in another Mould : for the Schoolmen on the one side represented Aristotle wrong , and on the other side his ( perhaps affected ) Obscurity , won them rather to believe the Schools concerning his Doctrine , than to be at the Expence of Pains and Patience to understand him right , speaking by himself , or by his First Interpreters .