Editing Chrysippus (section)

===Syllogistic===
Chrysippus developed a syllogistic or system of deduction in which he made use of five types of basic arguments or [[argument form]]s called indemonstrable syllogisms,<ref>Diogenes Laërtius, vii. 79</ref> which played the role of axioms, and four [[Rule of inference|inference rules]], called ''themata'' by means of which complex syllogisms could be reduced to these axioms.<ref name="Kneale">{{Harvnb|Kneale|Kneale|1962|pages=158–174}}</ref><ref>[[Susanne Bobzien]], Stoic Syllogistic, ''Oxford Studies in Ancient Philosophy'' 14, 1996, pp. 133–192</ref> The forms of the five indemonstrables were:<ref>Diogenes Laertius, vii. 80-81; Sextus Empiricus, ''Hyp. Pyr.'' ii. 156–159; cf. ''Adv. Math.'' viii. 223ff.</ref><ref name="Mates">{{Harvnb|Mates|1953|pages=67–73 }}</ref>

{| class="wikitable" style="margin:1.0em auto;"
!colspan=2| Name{{efn|These [[Latin]] names, unknown to Chrysippus, date from the Middle Ages.<ref>{{harvnb|Sharples|2014|p=24}}</ref>}}
! Description
! Example
|-
|colspan=2| [[Modus ponens]]
|style="white-space:nowrap;"| If A, then B.&nbsp; A.&nbsp; Therefore, B.
| ''If it is day, it is light. It is day. Therefore, it is light.''
|-
|colspan=2| [[Modus tollens]]
|style="white-space:nowrap;"| If A, then B.&nbsp; Not B.&nbsp; Therefore, not A.
| ''If it is day, it is light. It is not light. Therefore, it is not day.''
|-
|rowspan=2| [[Modus ponendo tollens]]&nbsp;
|style="width:1.5em;text-align:center;"| i
|style="white-space:nowrap;"| Not both A and B.&nbsp; A.&nbsp; Therefore, not B.&nbsp;
| ''It is not both day and night. It is day. Therefore, it is not night.''&nbsp;
|-
|style="text-align:center;"| ii
|style="white-space:nowrap;"| Either A or B.&nbsp; A.&nbsp; Therefore, not B.
| ''It is either day or night. It is day. Therefore, it is not night.''
|-
|colspan=2| [[Modus tollendo ponens]]
|style="white-space:nowrap;"| Either A or B.&nbsp; Not A.&nbsp; Therefore, B.
| ''It is either day or night. It is not day. Therefore, it is night.''
|}

Of the four inference rules (themata, θέματα),<ref name="L&S">{{Harvnb|Long |Sedley|1987|}}, §36 HIJ</ref> only two survived. One, the so-called first ''thema'', was a rule of antilogism. The other, the third ''thema'', was a cut rule by which chain syllogisms could be reduced to simple syllogisms.<ref name="Kneale2">{{Harvnb|Kneale|Kneale|1962|p=169}}</ref><ref>{{cite SEP |url-id=logic-ancient/#StoSyl |title=Ancient Logic: Stoic Syllogistic |last=Bobzien |first=Susanne}}</ref> The purpose of Stoic syllogistic was not merely to create a formal system. It was also understood as the study of the operations of reason, the divine reason (''[[logos]]'') which governs the [[universe]], of which human beings are a part.<ref name="sharples26">{{harvnb|Sharples|2014|p=26}}</ref> The goal was to find valid rules of inference and forms of proof to help people find their way in life.<ref name="johansen466"/>
[[File:New Guinea Singing Dog sniffing the ground.jpg|thumb|130px|Chrysippus argued dogs reason.]]

According to Sextus Empiricus, Chrysippus held that dogs use disjunctive syllogism, such as when using scent to pick which path to run down. This was in contrast to a tradition since Aristotle, who saw reasoning (and reasoning deductively) as man's defining aspect.<ref>Sextus Empiricus, Outlines of Pyrrhonism, I.69</ref>