The Stanford Encyclopedia of Philosophy had a good section on Philodemus and Canonics:
Epicurus was perhaps the originator of the Hellenistic debates over the nature and existence of a ‘criterion of truth’, which allows us to separate true from doubtful or false beliefs. This debate, conducted by both philosophers and medical writers, also concerned methods of proof and sign-inference to extend knowledge beyond our immediate perceptions (overview in Allen 2001).
The final portion of On Signs III is all we have of the work, the full title of which was apparently On Phenomena and Sign-inferences (sêmeiôseôn). It comprises four sections (labeled here §§1–4, followed by column and line numbers from DeLacy and DeLacy 1978) and reports the ways in which three Epicureans responded to criticisms of their theory of sign-inference. First is Philodemus’ teacher, Zeno (§1, §2); then Demetrius Laco (§3, xxviii 13–xxix 19), whose interest in proof is known from Sextus (M 8.348); and finally another, unnamed, colleague (§4, xxix 20–xxxviii 22). The authors of the initial criticisms are unknown, but probably include the Dionysius who is named as author of replies to the Epicurean rebuttals of the first round of criticisms (§1, vii 5–viii 21; Zeno’s replies occupy viii 21–ix 26), and he may be a Stoic or Peripatetic. On the other hand, the method favored by the opponents, EM or the elimination mode (anaskeuê, which is not the same as contraposition, as scholars used to think), is not positively attested as Stoic.
Both the EM and the Epicurean similarity mode (SM) of sign-inference move to the non-evident from the evident. We do not know how the opponents defined what is evident, but the SM starts from empirical generalisations that have been, in their turn, built up from individual observations, and, ultimately, from perceptions and feelings, these being two of the standard Epicurean criteria. The experiences of others (if reliable), accessed through research (historia), as well as things proved earlier, may also furnish suitable starting-points for the construction (sunthesis) of inferential transitions (metabaseis) to the non-evident. All this empirical input is most often referred to as ‘things hereabouts’ (ta par’ hêmin), and it stands in opposition both to perceptible things outside our experience, e.g., from living things here to those in chilly ‘Britain, if any’ (§1, v 35–6), and also to those that are in principle imperceptible, as from moving things hereabouts to atoms moving in the void.
Epicurus himself had appealed to what is evident to provide positive ‘attestation’ (epimarturêsis) of true beliefs about perceptibles ‘hereabouts’, and ‘contestation’ (antimarturêsis) of false beliefs about theoretical items such as atoms, and about extremely distant perceptible objects; always provided it is explanatorily adequate, lack of evidence of any kind against a theoretical belief is sufficient grounds for taking it to be true, (Ep. Herodot. 80, Ep. Pythocles 86–88; each such belief will constitute a true explanation of this type of phenomenon in one or other of the infinite number of world-systems in the universe). In On Signs, in contrast, what phenomena ‘conflict’ (antipiptein, makhesthai) with, if they do, are empirical generalizations, which are thereby falsified (e.g., §1, xvii 28–xviii 16). Thus while Epicurus argues that the non-existence of void is contested by the phenomenon of movement, these Epicureans argue that nothing evident contests the local generalization that moving things hereabouts all move through empty spaces.
Such localized empirical generalizations are produced by the Epicureans’ method of ‘applied reasoning’ (epilogismos), i.e., reasoning applied to experience: similarities (homoiotêtes) and differences among things in our experience are collected and scrutinized so as to identify properties belonging to all, or all observed, local members of some kind or group without exception. These properties can then safely be projected, by sign-inference, to all or any other members of the kind, as, for example, it is inferred that mortality belongs to all human beings everywhere (e.g., §4, xxxiii 24–32)—a type of sign-inference that the Epicureans claim is simply not captured by the EM (e.g., §1, xvii 8–11). While local generalizations are all constructed by the detection of similarities, in the case of imperceptibles property-projection will rather be by analogy (§4, xxxvii 24–xxxviii 8, the DeLacys’ unfortunate translation of homoiotês as ‘analogy’ notwithstanding): atoms, e.g., are analogous, but not identical, to macroscopic bodies in their property of solidity.
Epilogismos must be conducted with due diligence and caution (e.g., §3, xxix 1–4), but this seems an inadequate defense against the possibility raised by their opponents that counter-examples to generalizations—unique individuals or rare species—may always exist undiscovered. More convincing is the response that, since freaks and rarities were discovered empirically, to project the existence of such things into unknown realms is simply to apply the SM (e.g., §3, xxviii 29–37). While this does not prove that the EM is superfluous, it does raise another unsettled question, whether all these Epicureans believe that there is only one mode of sign-inference, the SM, or two (as suggested by Zeno in §1, e.g., xii 2–31). It is probably helpful to see this problem in light of a basic disagreement that emerges in On Signs between the Epicureans and their opponents: that the Epicureans are mainly concerned, not with arriving, somehow or other, at true beliefs, but with how we can be certain that our beliefs are true, experience being the only secure foundation for any property-projection. Sign-inferences here and in other sources often take the form of a conditional (sunêmmenon), such as: ‘If there is smoke, there is fire’, or a para-conditional (parasunêmmenon), such as ‘Since there is smoke, there is fire’ (equivalent to a conditional plus its antecedent), and the EM is built around a criterion of truth for conditionals: the antecedent must be ‘eliminated’, or negated, simply by the ‘elimination’ of the consequent (§1, xii 1–14). In the void/movement case, then, if movement is a sign of void, elimination of void thereby eliminates movement, and the inference seems to be valid by the EM.
But the author of §4, at any rate, insists that it is only because we have observed that moving things hereabouts, despite other differences, all share the property of moving through empty spaces, that we affirm that the same thing holds without exception in non-evident places too (xxxv 36–xxxvi 7). The full form of this sign-inference would therefore run: “Since moving things hereabouts all move through empty space, all moving things move through empty spaces; and since all moving things move through empty space, and there are moving things, there is such a thing as empty space”. But if assurance (diabebaiôsis) that the conclusion is true is produced in all cases by experience of similar cases (xxxvii 31–35), whether a sign is similar to what it signifies—as with the revelation that all human beings are mortal by their being so hereabouts—or it is not, as with movement’s being a sign of void (xxxi 1–7), then there will indeed be only one mode of sign-inference, and the EM, which does not proceed in this way, will be excluded.
A second major disagreement is that the Epicureans apparently claimed that SM sign-inferences had a ‘necessitating’ (anankastikos) character, which their opponents denied (e.g., §1, iv 5–37; §2, xxvi 25–6). There has been modern debate over whether the Epicureans meant that the premisses of SM sign-inferences necessitate their conclusions, as in deductive arguments (Barnes 1988: 107–111), or that SM sign-inferences are ‘cogent’ and ‘demand assent’ and may be thought of as inductive arguments, which antiquity called epagôgê and in which the premisses do not necessitate the conclusions (Long 1988: 136–40).
Perhaps, however, the important point is rather that SM sign-inference is concerned with the relation between an individual object and its properties, a relation of metaphysical necessity (e.g., §1, viii 32–6; §4, xxxiii 35, xxxv 22–9). It is these necessary properties that epilogismos seeks to identify (e.g., §1, xvii 3–11; §4, xxxv 4–31) and that sign-inference should project: they help constitute the nature of a thing (cf. §1, xv 11–12; §3, xxiv 6–8). When he rebuts the opponents’ objection that SM sign-inferences are not necessitating, therefore, Zeno adduces the kind of property from which a sign-inference should proceed. Thus whatever necessity an SM sign-inference has comes from the metaphysical necessity of a property-property pairing, which is expressed in a qua truth: “For when we say that, since those hereabouts are such, those in the unknown realm are also such, insofar as those hereabouts are such, in this way we believe that something unknown is conjoined with them. For example: since humans hereabouts, qua humans, are mortal, then if there are humans anywhere, they too are mortal” (§4, xxxiii 24–32). Each of the four senses of ‘qua’ discussed in the next lines joins properties with the force of necessity and is used in sign-inferences (xxxiii 24–29).
The Epicureans are epistemological realists who postulate that we naturally form conceptions corresponding to types of object and property in our experience. The metaphysical necessity of property-property pairing explains why the best test of a conditional or of a particular sign is that it is inconceivable that the antecedent exists and the consequent does not (§4, xxxiii 1–7), why someone making a sign-inference on the basis of the evident “locks away in inconceivability” the proposition that things hereabouts are such, but things elsewhere are not such (§1, xv 37–39).
As with On Signs, what remains of a badly damaged treatise on the senses attributed to Philodemus (PHerc. 19/698, ed. Monet 1996) takes the Epicurean theory of perception, with its description of the atomic basis of the senses and their irrationality, as a background against which to discuss developments of the theory due to the confrontation with opponents, in this instance Stoics and Aristotelians. Of special concern are: the unity of sensation (I-VIII) and the ‘common sense’ (XX-XXVII) as opposed to the particular objects of each sense (XXVIII-XXIX); and the rejection of Stoic ‘grasping’ (katalêpsis) once one admits the Epicurean theory of ‘affection’ (pathos), which includes both perceiving and perceiving that one is perceiving (IX-XVII).