horn'd sorites / an enthymematical progression

A tip of the hat to the OED, and we're off ... Best of good luck! It's something of a slalom. Or is that just me?

1. Logic. ‘A series of propositions, in which the predicate of each is the subject of the next, the conclusion being formed of the first subject and the last predicate’ (Mansel).
In the GOCLENIAN form, ‘the subject of each proposition is the predicate of the next, the conclusion being formed of the last subject and the first predicate’.
1551 T. WILSON Logike Hiij, We ioyne many causes, and many effectes together, wherof is made an argument, called Sorites. 1588 FRAUNCE Lawiers Log. II. ix. 99 As of many graynes is made a heape of corne, so of many degrees an argument called Sorites by this enthymematicall progression. 1654 Z. COKE Logick 148 Sorites is an imperfect Syllogism [etc.]. 1693 DRYDEN Persius VI. (1697) 296 note, Chrysippus the Stoick invented a kind of Argument, consisting of more than three Propositions; which is call'd Sorites, or a Heap. 1838 SIR W. HAMILTON Logic xix. (1866) I. 369 The Sorites can be resolved into as many simple syllogisms as there are middle terms between the subject and predicate of the conclusion. 1870 JEVONS Elem. Logic xviii. 156 The chain of syllogisms commonly called the Sorites.

b. An instance of this type of syllogism. Also as pl. (quot. 1798).
1581 J. BELL Haddon's Answ. Osor. 223b, The Logicians that have described the fourme of a Sorites. 1588 FRAUNCE Lawiers Log. II. ix. 99 A sorites [is] but enthymematicall progression by certain degrees. 1620 T. GRANGER Div. Logike 285 A Syllogisme many wayes cryptike, is a Dilemma, and a Sorites. 1643 SIR T. BROWNE Relig. Med. I. §18 An easie Logick may..with lesse than a Sorites resolve all things into God. 1725 WATTS Logic III. ii. §6 A Sorites is when several middle terms are chosen to connect one another successively [etc.]. 1798 EDGEWORTH Pract. Educ. (1811) II. 361 We have seen syllogisms, crocodiles, enthimemas, sorites, &c. explained and tried upon a boy of nine. 1860 H. ROGERS Ess. III. 277 An ingenious sorites, by which we may at any time dispense with the positive testimony of an historian. 1870 K. H. DIGBY Halcyon Hours 261 No horn'd soritès here would I employ, No captious argument that would annoy.

c. In allusive use.
1711 ADDISON Spect. No. 239 {page}10 These Disputants convince their Adversaries with a Sorites, commonly called a Pile of Faggots.

2. transf. A series, chain, or accumulation of some thing or things.
1664 POWER Exp. Philos. III. 191 Though Democritus his pit be never so deep, yet by a long Sorites of Observations, and chain of Deductions, we may at last fathom it. a1670 HACKET Abp. Williams I. xiii. (1693) 11 Such a long Sorites of Sciences and Tongues. 1875 M. COLLINS in F. Collins Lett. & Friendsh. (1877) II. 24 Note this significant fact or sorites of facts.

b. Math. (See quots.)
1880 J. J. SYLVESTER in Coll. Math. Papers (1909) III. 440 Any such determinate representation of a fractional quantity I shall term a sorites. Ibid., The elements of a sorites are analogous to the partial quotients of a regular continued fraction.

3. A sophistical argument turning on the definition of a ‘heap’.
1768-74 TUCKER Lt. Nat. (1834) II. 140 The like attack as was made of old by the Academics and Sceptics against the judgment of the senses, with their sophism of the sorites, or argument of the ‘heap’.

4. A heap, pile.
1871 M. COLLINS Marq. & Merch. III. ix. 230 Such sorites of flaming anthracite may possibly cause cephalalgia.

Hence soritic a., soritical.
1656 BLOUNT Glossogr., Soritical, pertaining to such an Argument [sc. Sorites]. a1693 Urquhart's Rabelais III. xxxviii. 320 Soritick fool. 1877 BLACKMORE Cripps II. v. 73 Nebules of logic, dialectic fogs, and..the pelting of soritic hail.