The Elements of Logic, Book 5
¶ The fift Booke. OF THE MASTER-PEECE OF LOGICK called DEMONSRATION.
The firſt Chapter. What Science is.
THIS word Science is ſomtimes taken for the whole bodie of one kind of learning. Thus Ethicks, Phyſicks, Metaphyſicks, civill Law, are called Sciences. Sometimes the word Science ſignifieth onelyonly the knowledge of a concluſion prooved by Demonſtration. And this is it whereof we purpoſe to treat of in this place; which is thus defined.
Science is a certaine knowledge of a thing certaine, whoſe proofe is drawne from the cauſe.
To hauehave the Science of a thing, two certainties are required. The one is, that the thing be certaine of it ſelfe and vnchangeable. The ſecond is, that the perſwaſion which wee hauehave of it be firme and cleare. If either of theſe two certainties be wanting it is no Science, but opinion. For a man may hauehave a doubtfull opinion of a thing certaine. As he that doubteth whether there be a God.
And on the contrary, a man may hauehave a firme and ſtedfaſt perſwaſion of that which is vncertaine and falſe. As thoſe that ſuffer death for the defence of a falſe Religion.
And therefore it is not amiſſe to know the difference between Science, Faith, and Opinion. Science is a certaine knowledge of a certaine thing by the next cauſe. Opinion is a doubtfull or falſe knowledge. Faith is a firme perſwaſion grounded vponupon the Teſtimonie of ſome other.
If a man know certainly a thing becauſe he ſeeth it, or toucheth it, that is neither called Science, nor Faith, nor opinion; but ſenſe, which knoweth onelyonly things ſingular: but Science is of things vniverſall.
The ſecond Chapter. What a Demonſtration or Demonſtratiue Syllogiſme is.
A Demonſtratiue Syllogiſme is that which giveth or bringeth certaine knowledge of the concluſion. If we will define it more exactly, we muſt define it thus. A demonſtratiue Syllogiſme is that which prooveth that the attribute of the concluſion is truely attributed vntounto the ſubject, by a Meane that muſt be the next efficient or finall cauſe of the attribute of the ſaid concluſion. Theſe two ſorts of cauſes were called externall, in the Chapter of Cauſes aboue mentioned: becauſe they are no parts of the effect, nor of the thing compounded, though ſometimes the efficient cauſe be in the very ſame ſubject. As, the ſoule of man is the cauſe of the ſenſe in man: and the thickneſſe of gold is the cauſe of the weight of it. In theſe examples the efficient cauſe and the effect are in the ſame ſubject.
The third Chapter. What queſtions are demonſtrable.
SVch queſtions wherein the attribute is a ſubſtance, cannot bee prooved by demonſtration: becauſe ſubſtances hauehave no certaine efficient cauſe proper vntounto them. For the will of God is an vniverſall cauſe common to all things, and by conſequent it can be no Meane in a demonſtratiue Syllogiſme.
Againe, ſuch queſtions or concluſions wherein the attribute is a mutable or caſuall accident, cannot be proved by demonſtration: becauſe theſe accidents hauehave no certaine and aſſured cauſe. As, Philip is rich. Bucephalus halteth.
But thoſe queſtions are demonſtrable, whoſe attribute is a proper and immutable accident, whereof the next efficient or finall cauſe may be given. For example, theſe queſtions may be prooved by demonſtration.
A tranſparent bodie is without colour.
Eunuches are never bald.
Fixt Starres doe twinckle.
The Moone ſuffers obſcuritie.
Of all eſtates Oligarchie is the most ſubiect to civill warre.
Lines paralell never meet.
All bodies compounded of Elements are corruptible.
Ʋnder the ſcorching Zone it is very hot.
For the next efficient or finall cauſe of the attribute of theſe queſtiōs may be given.
The fourth Chapter. What the propoſitions of a demonſtratiue Syllogiſme ought to be.
THe Demonſtration muſt conſiſt of neceſſary propoſitions; among which thoſe are the moſt neceſſarie, which are called Immediate.
There be two ſorts of immediate propoſitions, that is to ſay, ſuch as are without any middle. For ſome are immediate in regard of the ſubject, and others are immediate in regard of the cauſe.
Immediate propoſitions in regard of the ſubject are when the attribute agreeth next of all and immediately to the ſubject, ſo as a neerer ſubject cannot be given. In ſuch propoſitions the attribute agreeth with the ſubject, becauſe it is ſuch a ſubject. For example, if I ſay that a horſe hath ſenſe, this attribute agrees not next and immediately to a horſe; for there is a neerer ſubject, namely, an Animal, vntounto the which ſenſe belongeth. But if I ſay that a horſe neigheth, this agreeth next and immediately to a horſe, as he is a horſe, and not by reaſon of any other neerer ſubject.
Immediate propoſitions in regard of the cauſe are, when an attribute is ſo neerely joyned to the ſubject, as that the cauſe or reaſon cannot bee yeelded why it ſhould be ſo. For example, here is a Demonſtration:
Whatſoever hath a ſenſitiue ſoule hath touching.
Every animal hath a ſenſitiue ſoule.
Therefore every animal hath touching.
In this Syllogiſme the concluſion is immediate in regard of the ſubject, but not in regard of the cauſe. For in this Syllogiſme the Meane is the cauſe of the concluſion. But the two propoſitions are immediate, both in regard of the cauſe, as alſo of the ſubject, for nothing can be alledged as a cauſe of their truths.
Sometimes the efficient and finall cauſes are linked together with a long chaine. As, VnderUnder the Aequator the aire is very hot, becauſe it is very ſubtill; The aire is very ſubtill, becauſe the Sunne doth rarefie it very much; The Sunne rarefies the aire, becauſe the beames fall in right angles; The beames fall in right angles, becauſe the Sunne is there in the Zenith. Thus it is in the finall cauſe.
The Lungs draw in the aire to refreſh the heat of the heart: The heat of the heart is refreſhed to keepe the Temperature: The Temperature is kept to preſerue life.
So many cauſes, ſo many demonſtrations. But the laſt where alſo the chiefeſt and laſt cauſe ſtands for the Meane, is the nobleſt of all: becauſe it can no further be demonſtrated: and the two propoſitions are immediate every manner of way.
The fifth Chapter. A ſpeciall note to know a perfect Demonſtration.
OF all the markes of a perfect Demonſtration, this is the moſt evident, when it may be conver…ed or reduced to a definition. For we hauehave ſaid heretofore that the definition of a proper accident is compounded of three parts; namely,L. 2. c. 8. of the Genus of that which is defined, and of the proper ſubject, and of the cauſe thereof. As the definition of Death is, the deſtruction of the life of the creature by the extinguiſhing of vitall heat. Out of this definition a demonſtration may be framed, making the Subject of this accident to be the ſubject of the concluſion, the Genus to be the attribute, and the cauſe the Meane. As thus,
Whenſoever the vitall heat is extinguiſhed, life is deſtroyed.
But in a living creature the vitall heat is extinguiſhed.
Therefore in a living creature life is deſtroyed.
The ſame may be ſaid of theſe definitions following. Sleepe is the heavineſſe of a living creature, by the ceſſation of the common ſenſe. Thunder is a noyſe in the clouds, by the breaking out of the fire.
The ſixth Chapter. Of an Imperfect Demonſtration.
WEE hauehave ſhewed that a perfect demonſtration is that, which proveth by the next efficient or finall cauſe of the attribute; that the attribute of the concluſion agrees with the ſubject.
If any of theſe perfections be wanting, the demonſtration is the weaker, and leſſe perfect.
If the Meane be not the next cauſe of the attribute, but onelyonly a remote cauſe, then is the demonſtration weaker, and more imperfect. And ſuch demonſtrations for the moſt part conclude negatiuely. For example.
Where there is no oppoſition of contrary qualities, there is no death.
But in the heavens there is no oppoſition of contrary qualities.
Therefore in heaven there is no death.
Or
He that is of a cold temperature will never be bald.
But Eunuches are of a cold temperature,
Therefore Eunuches will never be bald.
In theſe demonſtrations the propoſitions are not immediate: For the Meane is not the next cauſe of the attribute. To hauehave no contrary qualities is not the next cauſe of not dying, but a remote cauſe: for the next cauſe of not dying in mans body is the continual preſervation of the humors in an equall temperature; and the cauſe hereof is to hauehave no contrarietie or combate betweene the elementarie qualities in the bodie.
Thus the cauſe why Eunuches become not bald is, become the radicall humor of the haires is not ſpent: and the remote cauſe is, becauſe they hauehave but little heat.
In theſe demonſtrations the propoſitions are not immediate, for the Meane is not the next cauſe of the attribute.
And though the propoſitions be immediate, yet if the Meane be not the cauſe, but the effect of the attribute, then it ſhall be a leſſe perfect demonſtration; proving not the effect by the cauſe, but the cauſe by the effect. This kinde of demonſtration ſhewes not why the concluſion is, but onelyonly that it is. As,
All that louelove God are beloved of God.
But all that hauehave faith in Chriſt, louelove God.
Therefore all that hauehave faith in Chriſt are beloved of God.
The Meane is to louelove God, which is not the cauſe, but the effect of the louelove which God beareth vntounto vsus; which louelove is the attribute of the concluſion in this demonſtration, wherein the cauſe is proved by the effect: whereas in a perfect demonſtration we proue effects by their cauſes. Therefore this imperfect demonſtration proveth onelyonly that the thing is, but ſheweth not why it is. The effect may very well be the cauſe of knowing, but not of being. As the ſmoake which we ſee come out of a chimney may be a cauſe to make vsus know that there is fire in the houſe: but it is not the cauſe of the fire, but onelyonly the effect. And the vnequall beating of the pulſe is not the cauſe of the Ague, but it is a cauſe which makes vsus know that ſuch a one hath an Ague.