upon the Axiom Things that agree with one and the fame, agree between themselves;' by which they confined their reafoning to general Relations, and to the Agreement and Difagreement of Ideas, measured by a third, as a Carpenter measures a piece of timber by the application of his rule.*

i Nonnulli autem Logici (noftri feculi, aut fuperioris) posthabita veterum probatione per Dictum de Omni et de Nullo; aliud fubftituunt illius loco Poftulatum; nimirum, Que conveniunt in eodem tertio, conveniunt inter fe. Atque ad hanc regulam exigentes fingulos fyllogifmorum Modos, inde conclufum eunt juftam eorum confecutionem. Quique fic procedunt; negligere poffunt eam distinctionem modorum perfectorum et imperfectorum; ut quæ ortum ducit ab ea methodo qua ufi fi funt veteres, in probatione fua ab illo Dito. Wallis's Logic. B. iii. chap. 5.

* Mr. Locke is the great advocate for the Perception of the agreement and disagreement of ideas being the criterion of all truth, and in exemplifying this great logical maxim he uses the following words; When a Man has in his • Mind the Idea of two Lines, viz. the Side and Diagonal ' of a Square, whereof the Diognal is an Inch long, he

may have the Idea alfo of the Divifion of that Line into a ' certain Number of equal Parts; v. g, into Five, Ten, an Hundred, a Thoufand, or any other Number; and may ' have the Idea of that Inch Line being divifible or not divi'fible into such equal Parts, as a certain Number of them will be equal to the Side-line, Now, whenever he perceives, believes or fuppofes fuch a kind of Divifibility to agree or difagree to his Idea of that Line, he, as it were,

Of these two Logics, both of which are partial and imperfect, the former is entitled to the preference; because, when the general Principles are once established, it is the guide to truth in all parts of knowledge; whereas, out of Mathematics, pure or mixed, the latter can usefully apply to none.

W

SECT III.

Of Mathematical TRUTH.

HEN fuch abftract and general ideas as are appropriated to Mathematics in both its branches, which, befides

joins or feparates thofe two Ideas, viz. the Idea of that 'Line, and the Idea of that kind of Divifibility, and so makes ' a mental Propofition, which is true or false, according as 'fuch a kind of Divisibility, a Divifibility into fuch aliquot Parts, does really agree to that Line or no. When Ideas ' are fo put together or separated In the Mind, as they, or 'the Things they ftand for, do agree or not, that is, as I 'may call it, mental Truth. But Truth of Words is fomething more, and that is the affirming or denying of Words ' one of another, as the Ideas they stand for agree or disagree.' Ellay, B. IV, C. v. §. 6.

the

the exclufive privileges that have been enumerated are permanent and eternal, are thus Syllogiftically compared in their numerous relations, and ultimately brought to the test of a few fimple Axioms or Univerfal Propofitions which are palpably and felf-evidently certain, the TRUTHS that refult from fuch an operation of reason must be particularly clear and luminous, bearing down all poffibility of doubt, and carrying the most ABSOLUTE and IRRESISTIBLE CONVICTION.

This part of learning is, therefore, diftinguished by the name of SCIENCE, underftood in its special and appropriated fignification; and it is awarded by Aristotle to the province of the INTELLECT or THEORETIC MIND, as producing abstract, unchangeable1 and neceffary Truths," which exclude from

1

m

Περὶ τῶν μὴ ἐνδεχόμενων ἄλλῶς ἔχειν. Ariftot.

Αλλ' ἔτι καὶ ἡ ΜΑΘΗΜΑΤΙΚΗ ΘΕΩΡΗΤΙΚΗ.

Αλλ' εἰ ακινήτων καὶ χωριςῶν ἐσι, νῦν ἄδηλον. Οτι μὲν ἦν ἔνια μαθήματα ἢ ἀκίνητα καὶ ᾗ χωριςὰ θεωρεῖ, δῆλον. Ariftot. Metaph. lib. vi. cap. I.

the

the understanding all manner of uncertainty; and also as containing in themselves the End for which they were contemplated."

* Επισήμη μὲν ἔν τί ἐςιν, ἐντεῦθεν φανερὸν, εἰ δεῖ ἀκριξολογεῖσθαι, καὶ μὴ ακολεθεῖν ταῖς ὁμοιότησι πάντες γὰρ ὑπολαμβάνομεν, ὃ ἐπισάμεθα μὴ ἐνδέχεσθαι ἄλλως ἔχειν. Τὰ δὲ ἐνδεχόμενα ἄλλως, ὅταν ἔξω τα θεωρεῖν γίνηται, λανθάνει εἰ ἔσιν, ἢ μή. Εξ ἀνάγκης ἄρα ἐςὶ τὸ ἐπιζητόν. Αἴδιον ἄρα. Τὰ γὰρ ἐξ ἀνάγκης ὄντα ἁπλῶς, αΐδια πάντα· Τὰ δ' αΐδια, αγένητα καὶ ἄφθαρτα., Ariftot. Εth. Nicom. lib. vi. cap. 3.

Έξι διδάξη 1.

CHAP.

T

Of the Logic of PHYSICS.

HOUGH TRUTH does not appear in the other departments of learning with that bold and irrefiftible conviction with which it prefides in Mathematical Science, it shines through them all, if not interrupted by prejudice or perverted by error, with a clear and useful, though inferior, ftrength. And, as it is not neceffary for his general fafety or convenience, that the traveller should always enjoy the heat and fplendor of a mid-day fun, whilst he can pursue his journey with more pleasure and accommodation under the weaker influence of a morning or evening ray; fo it is not requifite