Philodemus - On Methods of Inference - Outline and Analysis

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This document has been edited by Cassius Amicus. It was initially prepared by asking ClaudeAI to synthesize the material and opinions found in the following two works, with emphasis on explaining the position of Philodemus as to the Epicurean view of knowledge and probability. Revisions are ongoing based on input received from EpicureanFriends.com.
P. and E. De Lacy, Philodemus: On Methods of Inference (Naples: Bibliopolis, 1978²). Includes Greek text, facing English translation, critical notes, and five Supplementary Essays.
David Sedley, “On Signs,” in Barnes, Brunschwig, Burnyeat, and Schofield (eds.), Science and Speculation: Studies in Hellenistic Theory and Practice (Cambridge, 1982), pp. 239–272.

I. BACKGROUND AND CONTEXT

The Work and Its Transmission

The treatise survives as PHerc. 1065, one of the Herculaneum papyri. Thirty-eight columns of continuous text have been restored, constituting only the final portion of the original roll; how much preceded the surviving text is unknown. The title is damaged; likely candidates include Peri phainomenon kai semeioseōn (“On Appearances and Sign-Inferences”) or Peri phantasion kai semeioseōn (“On Impressions and Sign-Inferences”). De Lacy uses the shorthand De Signis.

The text was first edited by T. Gomperz (1865); the De Lacy edition of 1978 is the first based on autopsy of the papyrus itself, with further collation by M. Gigante and associates in 1977. Many passages remain conjectural.

Authorship, Date, and Historical Setting

Philodemus of Gadara (c. 110–40/35 B.C.) was a student of Zeno of Sidon and Demetrius Lacon at Athens, subsequently founder and leader of an Epicurean school at Naples under the patronage of L. Calpurnius Piso. He was a contemporary of Cicero, Vergil’s teacher Siro, and the Roman literary circle that included Varius Rufus and Quintilius Varus (De Lacy, Essay I, pp. 145–154).

The treatise can be dated approximately: a reference to pygmies brought from Syria/Hyria by “Antony” (col. ii.18) places it either around 54 B.C. or around 40 B.C., with both dates defended in the scholarship (De Lacy, Essay II, pp. 163–164).

The Debate: Epicureans vs. Stoics on Inference from Signs

The De Signis records a live controversy between the Epicurean school and their Stoic opponents (identified by Sedley, pp. 240–241, and De Lacy, Essay V, pp. 206–207 as Stoics of the mid-to-late second century B.C., probably including the Stoic Dionysius of Cyrene). The central issue is the epistemological validity of empirical inference: can we know facts about the unperceived world with genuine certainty on the basis of observed experience, or is such inference inherently merely probable?

II. STRUCTURE OF THE SURVIVING TEXT

The extant columns fall into four major sections (De Lacy, Essay II, pp. 156–162):

Section 1 (Cols. ia–xi.28): From Zeno of Sidon’s writings

Stoic arguments against Epicurean empirical inference (cols. ia–xi.26)
Epicurean replies (cols. xi.29–xix.4)

Section 2 (Cols. xix.9–xxvii.28): From Bromius’ account of Zeno

Eight Stoic arguments and Epicurean replies

Section 3 (Cols. xxvii.28–xxix.16): From Demetrius Lacon

Five “pervasive errors” of those who oppose analogy

Section 4 (Cols. xxix–xxxviii.22): Anonymous Epicurean (possibly Demetrius continued)

Fifteen further points of analysis

Conclusion (Col. xxxviii.22–32): Brief half-hearted proposal to discuss medical empiricism.

Fragments (1–8): Loosely related material on broader epistemological topics (criteria of truth, knowledge of gods, distinction of temporally vs. naturally imperceptible things).

III. MAJOR ARGUMENTS: STOIC SIDE

The Foundational Stoic Distinction: Particular vs. Common Signs (Cols. i.1–19)

The Stoics argue that only particular signs (idion sēmeion) provide valid inference. A particular sign is one that cannot exist unless the thing it signifies also exists — its negation entails co-negation of the sign. A common sign (koinon sēmeion), by contrast, can exist whether or not what it signifies exists; therefore it provides no reliable basis for inference (col. i.1–19; De Lacy, pp. 91–92 n. 2).

The test of a particular sign is elimination/contraposition (anaskeuē, kat’ anaskeuen tropos): hypothetically “eliminate” the thing signified, and if the sign is thereby co-eliminated, the connection is sound.

Sedley’s analysis (pp. 242–248): The Stoic use of “common” here is unusual — normally “common” means a sign of multiple things; here it means common to truth and falsity. Sedley argues this terminology derives from the Stoic need to defend the infallible criterion of truth (katalēptikē phantasia) against the New Academy. The elimination method is connected to Chrysippus’ test of sunartēsis (cohesion): a sound conditional holds when the contradictory of the consequent conflicts with the antecedent. The method has Aristotelian roots (from Categories 7b15–8a12) but is applied innovatively to propositions rather than concepts.

Stoic Argument 1: The Non-Necessity of Generalization (Col. ia; cf. Ch. 1 of translation)

Things existing in our experience need not exist in places we cannot perceive, and vice versa. An inference from the presence of something in our experience to its presence everywhere is simply not “binding” (anankē). (The Epicurean reply is at chs. 18 and onward.)

Stoic Argument 2: Unique Cases Undermine Analogy (Cols. i.19–ii.25; Ch. 3)

There are unique objects within our experience: the magnet draws iron, amber attracts chaff, the square of four is the only square whose perimeter equals its area. If there are unique cases in our experience, there may be unique cases outside it that defeat analogical inference. How can we infer that all men die when their heart is cut, if exceptions might exist beyond our experience? (De Lacy, pp. 92–93; cf. Sedley pp. 248–249 on Dionysius’ use of “freaks”—terata.)

Stoic Argument 3: Rare Cases (Cols. ii–iii; Ch. 4)

Some things within our experience are rare rather than merely unique: the Alexandrian dwarf with the hammer-proof head, the man of Epidaurus who changed sex, the giant inferred from bones in Crete, the pygmies from Syria (col. ii.18). Such rare cases suggest the universe may contain rare analogues that invalidate induction (De Lacy, p. 93).

Stoic Argument 4: Contraposition Is the Only Formally Valid Method (Cols. ii.25–iv.37)

The Stoics argue that only inferences which pass the contraposition test are genuinely valid. Empirical inferences from similarity do not meet this standard. (Sedley, pp. 244–248: the elimination method establishes connections that hold necessarily and are knowable a priori, whether by formal entailment or by analytic dependence of meaning.)

Stoic Argument 5: Atomism Is Inconsistent with Empiricism (Cols. iv.37–v.7)

Since all bodies in experience are destructible and have color, the Epicureans should, on their own analogical method, ascribe destructibility and color to atoms. Their failure to do so betrays inconsistency in their own method (De Lacy, Essay V, pp. 215, 221).

Stoic Argument 6: Grounds for Preferring One Inference Over Another (Cols. v.8–36)

On what basis do the Epicureans select which similarities to use for inference? Any selection implies a criterion that goes beyond the mere observation of similarities (De Lacy, Essay II, p. 158).

Stoic Dilemma: Identity vs. Similarity (Cols. v.37–vi.36; Chs. 5–6)

The Stoics pose a dilemma: if inference requires identical objects, sign and signified collapse into one thing (no inference is possible); if inference requires merely similar objects, the difference present might be sufficient to destroy the inference. This dilemma appears to show that empirical inference is inherently unstable (De Lacy, Essay II, pp. 159; De Lacy p. 215 in Essay V).

Dionysius’ Specific Arguments (Cols. vii.5–xi.26; Chs. 7–11)

The Stoic Dionysius adds three further arguments:

Ambiguity of “similarity” (cols. vii.5–38; ch. 7): The word homoiotēs is equivocal; it covers both essential and accidental similarity. Unless the Epicureans can specify which similarity grounds inference, the method is indeterminate.
The qualifier “when nothing conflicts” is worthless (cols. vii.38–ix.8; chs. 8–9): The Epicureans say analogy holds “when nothing in appearances conflicts.” But it can never be empirically determined that nothing conflicts, since one can never examine all possible appearances. This makes the qualifier a blank check that can never be cashed (De Lacy, Essay II, p. 159; De Lacy p. 216).
Partial similarity (cols. ix.8–xi.26; chs. 10–11): Inference from partial similarity cannot establish facts about unperceived objects, since the dimension of similarity and the dimension of difference may coincide (De Lacy, Essay II, p. 159).

Bromius’ Eight Arguments Against Analogy (Cols. xix.9–xxvii.28; Section 2)

Bromius presents another version of the Stoic case (originally from Zeno). The eight arguments ask, respectively:

It is impossible to examine all appearances; examining only some is insufficient (cols. xix.12–19).
Wide variations within experience suggest uncontrollable variations outside it (cols. xix.19–25).
Neither identical nor non-identical objects can ground inference (cols. xix.25–36).
Inductive inference presupposes its conclusion (cols. xix.36–xx.4).
Peculiarities outside experience may defeat any inference (cols. xx.4–10).
Unique cases within experience cannot be extended beyond it (cols. xx.10–11).
Unusual things within experience defeat generalization (cols. xx.11–21).
Epicurean physics (gods, atoms) contradicts their own analogical method (cols. xx.21–30).

IV. MAJOR ARGUMENTS: EPICUREAN SIDE (PHILODEMUS’ POSITION)

The Two Methods of Sign-Inference (Cols. 8.7–10; cf. Sedley p. 242)

Philodemus accepts, as common ground with the Stoics, that there are exactly two methods of sign-inference:

The similarity method (ho kath’ homoiotēta tropos): inference from observed resemblance, covering both simple induction and analogy. This is the primary Epicurean method.
The elimination method (ho kat’ anaskeuen tropos): inference by which the negation of the consequent entails the negation of the antecedent. This is the Stoics’ preferred method, which the Epicureans do not wholly reject but regard as derivative.

The crucial Epicurean claim — against the Stoics — is that the similarity method is not merely probable but achieves genuine epistemic certainty when properly conducted.

Analogy Satisfies Formal Requirements (Cols. xi.29–xii.36; Chs. 11–12)

The first two Stoic arguments (lost but inferable from the replies) apparently challenged whether analogy meets any formal standard of valid inference. Philodemus replies that the similarity method does satisfy formal validity requirements: properly constructed analogical inferences are not logically defective (De Lacy, Essay II, p. 157).

The Criterion of Inconceivability (adianoeiston) (Cols. xiv.2–27; Ch. 14)

This is one of Philodemus’ most important epistemological contributions. Against the Stoic claim that only contraposition establishes particular signs, Philodemus argues that inconceivability provides an independent and equally valid criterion.

When the similarity between sign and thing signified is so strong that it becomes literally inconceivable that the one should exist without the other, we have established a particular sign — and thereby a necessary inference — through the empirical method. The example: “Since Epicurus is a man, Metrodorus is a man” (col. xiv.2–27). It is inconceivable that Epicurus should be a man while Metrodorus is not. This inconceivability is not a priori or analytic; it is grounded in extensive empirical observation of human nature. But it is genuinely necessary, not merely probable.

De Lacy’s comment (Essay V, p. 218): “Inconceivability, however, is an empirical test. A thing is inconceivable only in terms of our experience, and inferences based on inconceivability are examples of the method of analogy.”

Sedley’s comment (p. 257): This kind of inconceivability “may lack strict logical force, but it is regarded as an entirely cogent criterion of inference, and the best available.”

The Circularity of the Stoic Method (Cols. viii.26–ix.8; xvi.4–17)

Philodemus makes a fundamental counter-argument: Stoic contraposition is only valid insofar as it is grounded in empirical analogy. Unless we have first established by observation that motion cannot occur without void, the conditional “If there is motion, there is void” cannot be asserted at all. The formal Stoic test is epistemically parasitic on the empirical method it purports to supersede. If analogy lacks necessity and certainty, then so does contraposition (De Lacy, Essay V, p. 217–218; Sedley, pp. 258–262).

This is stated at cols. viii.32–ix.3 (De Lacy translation, p. 217):

“We first determine empirically all the conditions attendant on motion in our experience, apart from which we see nothing moved; then, in view of the similarity, we judge that all moving objects in every case are subject to these conditions; and this is the method by which we infer that it is not possible for motion to occur without void.”

Unique and Rare Cases Support Rather Than Undermine Analogy (Chs. 20–21; Cols. xiv.28–xvi.4)

The Epicurean reply to the argument from magnets and unique cases is elegant: uniqueness strengthens rather than undermines analogy. If some magnets drew iron and others did not, an analogical inference about magnets would be unreliable. But since all magnets within our experience draw iron without exception, we can legitimately infer that this is characteristic of all magnets everywhere. Perfect consistency within experience is the strongest possible basis for analogical inference (De Lacy, Essay V, p. 218–219).

Similarly, the range of variation within our experience is always bounded. We cannot conceive of men made of iron who walk through walls; variations outside our experience must be analogous in kind and degree to those within it (cols. xxi.30–xxii.2; cf. De Lacy, Essay V, p. 219):

“The degree of certainty of an inference is often relative to the amount of variation observable.”

Not All Appearances Need to Be Examined (Cols. xx.35–xxi.3)

Against the Stoic claim that empirical inquiry is interminable, Philodemus states (translation at De Lacy, Essay V, p. 219):

“We must encounter many homogeneous and varied appearances, so that from our experience of them and from the accounts of history concerning them we may establish the inseparable property of each particular thing, and from these pass to all the others.”

The number of cases required varies with circumstances: sometimes one instance suffices; sometimes only a few; sometimes many fail to remove all uncertainty (col. xxvi.32–39). The task is not infinite, and completion is achievable for most inferences.

The Defense of Epicurean Atomism (Cols. xvii.37–xviii.16)

Against the charge that atoms should be assigned color and destructibility by analogy with perceptible bodies, Philodemus draws on the Epicurean doctrine of primary and secondary qualities:

“Bodies in our experience are destructible not insofar as they are bodies, but insofar as they partake of a nature opposed to the corporeal and non-resistant. Similarly, bodies in our experience have color, but not insofar as they are bodies; for tangible objects insofar as they resist the touch are bodies, but insofar as they are tangible they reveal no color.” (Cols. xvii.37–xviii.8; De Lacy, Essay V, p. 221)

Inference requires identifying the relevant similarity — the quality as it belongs to a thing qua member of a class. Tangibility is a generic property of bodies as bodies; color is not. This is an empirically derived distinction, not an a priori one.

Resolution of the Identity/Similarity Dilemma (Cols. xxii.2–28)

The Stoic dilemma (infer from identical objects — no inference possible; infer from similar objects — difference may destroy the inference) is dissolved by specifying degrees of similarity and the level of inference. Inferences can be made:

From particular men to others especially like them
From one class of men to another
From classes of animals to those most closely related
Between identical objects if one is perceptible and the other not (e.g., the inferred void resembles motion-permitting space)
Between non-identical objects (men and gods) insofar as they share common attributes (De Lacy, Essay V, p. 220)

The Fourfold Meaning of “Insofar As” (Cols. xxxiii.21–xxxvi.7; Ch. 10 of pervasive errors list)

This is one of the most technically sophisticated sections. The anonymous Epicurean identifies four uses of the qualification hēi / kathō (“insofar as,” “qua,” “according as”):

Necessary concomitant: “Men, insofar as they are men, are prone to disease and aging” — a necessary empirical connection.
Definition/preconception (prolēpsis): “Man, insofar as he is man, is a rational animal” — a definitional connection.
Accident: “Man, insofar as he is man, [walks when he wishes]” — a contingent but regular property.
Necessary concomitant of a property: “[A man, insofar as he] is foolish, is utterly unhappy” — a necessary connection grounded in one specific property.

The Stoics assume that all “insofar as” premises are established by their elimination method. The Epicurean response: all four meanings involve some kind of necessary connection, but all are established empirically. Even apparently definitional truths like “men are mortal” must be confirmed by inductive research (cols. xxxv.4–29). To assume a priori that “men qua men are mortal” is to presuppose what only observation can establish (De Lacy, Essay II, pp. 161–162; Sedley, pp. 258–259).

Sedley characterizes this as “a head-on confrontation between empiricism and rationalism” (p. 259).

The Relation Between Elimination and Similarity Methods (Cols. xxxv.22–xxxvii; Sedley §3)

This section resolves an apparent inconsistency: in some passages Philodemus seems to grant the validity of the elimination method for inferences like “Since there is motion, there is void” (cols. 12.1–14, 35.29–36.7), yet in others he insists the similarity method is primary. Sedley’s interpretation (pp. 260–263), which De Lacy’s analysis supports, resolves this:

The two methods work at different stages of a single inquiry:

Stage 1 (Similarity method / sign-inference proper): Through extensive observation of moving objects within experience, we establish the empirical generalization that motion is impossible without empty space. This inductive stage is the genuine sēmeiōsis (sign-inference).
Stage 2 (Elimination method): Once Stage 1 has been completed, the formal step “Since there is motion, there is void” follows by the elimination method — trivially, because the nature of motion (as established by Stage 1) includes its inseparability from void.

The elimination method alone “is not in itself a further sign-inference, since on its own it is powerless to reveal anything” (Sedley, p. 263; cf. col. 30.33–31.36). It adds no epistemic content; it merely formalizes what Stage 1 discovered. The Epicureans call Stage 1 the “sign-inference” and explicitly withhold the term sēmeiōsis from Stage 2 precisely to prevent the Stoics from claiming that the formal step does the epistemic work.

De Lacy’s formulation (Essay V, p. 218): “The abstract principle of the Stoics can be formulated only after experience justifies it through an argument based on analogy. Therefore, the Epicurean concludes, inference by contraposition can claim no certainty if analogy has none, as the latter is the source and ultimate criterion of the former.”

The Non-Contestation Requirement (Cols. xxxvi.7–17; Ch. 11 of pervasive errors)

A sound analogical inference requires that no known appearance conflicts with its conclusion. This is the Epicurean principle of ouk antimarturēsis (“non-contestation”), carried into the De Signis:

“They are also mistaken not to see that we ascertain that there is no obstacle resulting from appearances. For it is not enough to accept the minimal swerves of atoms on the grounds of chance and free will, but it is necessary to show in addition that no other self-evident fact whatever conflicts with this.” (Cols. xxxvi.7–17)

Sedley (§4, pp. 263–272) provides an extended analysis of non-contestation in Epicurus, arguing that Antiochus of Ascalon’s summary in Sextus (M VII.211–16) misrepresents Philodemus’ own Epicurean contemporaries by conflating non-contestation (a method of confirmation) with sign-inference (a method of discovery).

V. THE CENTRAL EPISTEMOLOGICAL QUESTION: GENUINE KNOWLEDGE OR MERE PROBABILITY?

This is the deepest issue in the De Signis, and the texts give a remarkably clear answer.

The Stoic Position: Empirical Inference Yields Only the “Convincing” (Pithanon)

Sedley (pp. 250–255) demonstrates through a careful reading of de Signis col. vii.26–38 that the Stoic Dionysius, while using the elimination method for strict logical inferences, explicitly assigns similarity-based and experience-based inferences to the class of the pithanon — the “convincing but fallible.” He quotes Dionysius:

“…it is sufficient, concerning these things and concerning those which derive from experience, for us to be convinced in accordance with probability (eulogia), just as when we sail in summer we are convinced that we will arrive safely.” (Col. vii.33–4)

Sedley identifies this with the Stoic technical use of pithanon (convincing): not falsehood, and not worthless, but genuinely only probable — it “could be” wrong. Chrysippus used material implication rather than strict conditionals for astrological laws and sorites-type arguments precisely because they are convincing but fallible, not logically necessary (Sedley, pp. 252–255). The Stoic position therefore is:

A priori, contraposition-tested inferences: yield genuine knowledge (kathalēpton), necessity, certainty.
Empirical, similarity-based inferences: yield only pithanon — convincing probability, not knowledge.

The Epicurean Rebuttal: Properly Conducted Empirical Inference Is Knowledge

Philodemus explicitly and emphatically rejects the idea that analogical inference yields only probability. Fragment 2 of the De Signis states (De Lacy translation, cited Essay V, p. 222):

“One ought not stop with evident things but from them make inferences about the non-apparent, nor mistrust the things proved through them by analogy but trust them just as one trusts the things from which the inference was made.”

This is a strong epistemological claim: sound analogical inference carries the same epistemic weight as direct perception. The Epicurean position rests on several interlocking commitments:

1. Perceptions are unconditionally true. All sensations, as such, are true — they faithfully present the appearances that really occur. Error arises only when opinion (doxa) is added by the mind to the raw perceptual data (De Lacy, Essay IV, pp. 183–184; Sext. M VII.203–4 = fr. 247 Usener).

2. The inference, properly made, inherits this truth. If perceptions are the infallible foundation, and the analogical inference is correctly built from them (with wide and varied observation, no conflicting appearances, correct identification of the relevant qua-clause), then the conclusion is not merely probable but certain. The De Signis insists on this throughout: the method of analogy “must be the one naturally fine method” (col. xxxvii; cf. De Lacy, Essay V, p. 217).

3. Inconceivability is a criterion of necessity, not mere plausibility. When it is genuinely inconceivable that Epicurus could be a man while Metrodorus is not, this is not a matter of probability — it is a matter of necessity grounded in the nature of humanity as empirically understood. The inconceivability criterion converts what might look like an inductive inference into a claim about necessity (col. xiv.17–27; De Lacy, Essay V, p. 218).

4. Non-contestation (ouk antimarturēsis) is a sufficient condition for truth — not merely plausibility. Sextus Empiricus (M VII.211–16) reports the Epicurean principle: “Verification (epimarturēsis) and lack of evidence to the contrary (ouk antimarturēsis) are the criteria of the true; lack of verification and evidence to the contrary are the criteria of the false.” Philodemus’ contemporaries in the De Signis confirm this: they are “mistaken not to see that we ascertain that there is no obstacle resulting from appearances” (col. xxxvi.7–17). Non-contestation, combined with theoretical explanatory power, is sufficient for truth — not mere belief.

Sedley (pp. 269–271) argues that Epicurus’ own usage shows non-contestation as a confirmatory check applied to theories that already have explanatory merit, sufficient to establish their truth (not just possibility). The “multiple explanations” principle for celestial phenomena (where several non-contested explanations are all held true, perhaps in different worlds) is the exception, not the rule; for basic physics — the existence of atoms and void — only one explanation is consistent with the full range of phenomena, and that explanation is known, not merely believed.

5. The Stoics’ own a priori claims are secretly grounded in empirical inference. This is Philodemus’ master argument: if analogical inference lacks necessity and certainty, then so does the Stoic elimination method, because the latter has no epistemic content that is not derived from the former. The Stoics cannot claim a privileged access to necessity without implicitly relying on the same empirical basis the Epicureans make explicit. “Since the Stoic position rests ultimately on induction from experience, if the method of analogy has no necessity or compulsion, the Stoic inference has none” (De Lacy, Essay V, p. 217).

Qualification: Not All Inferences Are Equally Certain

While rejecting the Stoic demotion of all empirical inference to the merely probable, Philodemus does not claim that all analogical inferences are equally secure. The degree of certainty is proportionate to the quality of the evidence (col. xxvi.32–39):

Inferences backed by uniform, widespread, varied observation, with no conflicting appearances and no alternative explanation = certain (e.g., the void argument; the mortality of men).
Inferences backed by good but limited evidence, or where some variability exists = probable in the sense of strongly warranted, but subject to revision.
For celestial phenomena, where multiple explanations each pass the non-contestation test, Epicurus accepts all as possibly true (“multiple explanations” principle) — here the honest answer is acknowledged uncertainty about which holds in our world.

The key distinction is between (a) the epistemic status of properly-made inferences (which can be genuinely certain) and (b) the practical situation where a given inquiry has not yet reached the conditions for certainty.

Philodemus vs. the Stoic Pithanon: A Precise Summary

	Stoics	Philodemus/Epicureans
A priori/analytic inferences	Knowledge, certainty	Not independently valid; require empirical grounding
Similarity-based inferences	Pithanon (convincing, probable, fallible)	Genuine knowledge, if properly conducted
Experience-based generalizations	Pithanon only	Genuine knowledge (same test as for direct perception)
The elimination method	Primary; yields necessity	Derivative; borrows necessity from analogy
The similarity method	Invalid or at best pithanon	Primary; yields necessity via inconceivability
Knowledge of atoms, void	May use strict inference only	Established by analogy + non-contestation; genuinely true

VI. DE LACY’S SUPPLEMENTARY ESSAYS: KEY ANALYSES

Essay II: The Argument and Date of De Signis (pp. 156–164)

Provides the most complete structural overview of the treatise. Key finding: the text shows a “symmetrical sequence of objections and answers” (objections at ia–v.36, answers at xi.29–xix.4), then an interruption, then a second set of objections with answers (xix.9–xxvii.28), then the analysis of “pervasive errors” (Demetrius and the anonymous Epicurean, xxvii.28–xxxviii.22). This structure mirrors the pedagogical practice of Epicurean schools: first present the opponents’ case in full, then give the comprehensive Epicurean reply.

Essay III: The Sources of Epicurean Empiricism (pp. 165–182)

Traces Epicurean empiricism to its roots in Hippocratic medicine, Aristotelian natural science, and early Greek empirical crafts. Argues that Epicurean method, rather than being a novelty, generalizes a well-established empirical tradition in the sciences. The Stoics, by contrast, generalized the rationalistic method of mathematics. This explains the depth and bitterness of the controversy: both schools were claiming to capture the legitimate foundations of science.

Essay IV: Development of Epicurean Logic and Methodology (pp. 183–205)

Traces the development of Epicurean methodology from Epicurus through Metrodorus, Colotes, Polystratus, the Epicurean mathematicians, and Philodemus himself. Key contributions:

Epicurus’ core epistemology: All perceptions true; error from opining (doxazein). The criteria of truth are perception (aisthēsis), preconception (prolēpsis), mental attention (epibōlē), and feeling (pathos). The extension to non-evident objects uses epilogismos (inferential reasoning from data) checked by epimarturēsis (attestation) and ouk antimarturēsis (non-contestation).
Classification of unperceivable things (pp. 186): (a) altogether unperceivable (odd/even number of stars); (b) naturally unperceivable but knowable by inference (atoms, void); (c) temporarily unperceivable but potentially perceivable (distant objects, future events).
Philodemus’ applications: Uses empirical method in ethics (weighing pleasures and pains; epilogizesthai in moral guidance), rhetoric (conjectural art), religion (knowledge of gods by analogy with men). In all cases the method is the same: observation, analogy, inconceivability, non-contestation.

Essay V: The Logical Controversies of Stoics, Epicureans, and Sceptics (pp. 206–227)

The most philosophically rich essay. Key sections:

Stoic Semiotic (pp. 206–214): The Stoic sign is formally defined as “the proposition in a sound conditional which is antecedent and reveals the conclusion” (Pyrrh. Hyp. ii.104). The sign-relation is a relation between lekta (meanings/propositions), not physical things. Validity requires sunartēsis (conjoining) or anaskeuē (contraposition). Stoic semiotic “requires that necessary truth must be a priori and analytic” (p. 211, citing De Lacy op. cit. p. 211; cf. Sedley, p. 247).

The Epicurean Response (pp. 217–222): Philodemus’ fundamental claim is that “the necessary truths which the Stoics considered analytic and a priori are really established by induction from experience. The definitive or prescriptive level of analysis is secondary to the descriptive level, since the latter furnishes the material and the order from which the former is derived. Deductive logic is subsequent to inductive logic in order of development because it depends on the latter” (p. 221).

The Sceptic Position (pp. 223–227): Sextus Empiricus occupies a distinct position: he accepts admonitive signs (hypomnēstika sēmeia, which remind us of co-observed regularities) but rejects indicative signs (endeitika sēmeia, which are supposed to reveal things by nature unperceivable). His criticism of the Epicureans is not that their method is wrong, but that they overreach by using it to establish a dogmatic metaphysics of atoms and void. Sextus aims at phenomenalism, not at positive knowledge of unperceivables. Philodemus’ position is thus between Stoic rationalism and Sceptic phenomenalism: genuine empirical knowledge of the unperceived is possible, but only through properly conducted inductive inference, not through a priori deduction.

VII. SEDLEY’S ANALYSIS: DISTINCTIVE CONTRIBUTIONS

Sedley’s “On Signs” (1982) brings several important contributions beyond the De Lacy apparatus:

1. Identification of the Stoic opponents (pp. 240–241): Sedley argues that the opponents are Stoics of the mid-to-late second century B.C. (not the earlier Stoics described by Sextus). He identifies the principal Stoic opponent “Dionysius” with Dionysius of Cyrene, a pupil of Diogenes of Babylon and Antipater of Tarsus. This means the debate in the De Signis reflects the state of Stoic epistemology after Chrysippus, with modifications (e.g., use of the paraconditional “Since p, q” rather than the simple conditional “If p, q”) that post-date Chrysippus (pp. 243).

2. The Elimination Method and Sunartēsis (pp. 244–248): Sedley argues, against the received view (Bahnsch and others), that anaskeuē is not merely contraposition but something stricter: the test of Chrysippan sunartēsis, which obtains when the contradictory of the consequent conflicts with the antecedent — a much more demanding criterion than simple material implication. The elimination method establishes connections that are necessarily knowable a priori, whether formally or analytically.

3. The Stoic Pithanon and Its Scope (pp. 250–255): Through careful reading of col. vii.26–38, Sedley identifies Dionysius’ explicit concession that similarity-based and experience-based inferences belong to the pithanon — a class Chrysippus himself had designated for “convincing but fallible” propositions. This is a technically precise Stoic concession with profound implications: the Stoics themselves admitted that empirical science cannot achieve logical necessity. Sedley traces this to Chrysippus’ use of material implication (rather than strict conditionals) for astrological and sorites-type arguments.

4. The Smoke/Void Two-Stage Analysis (pp. 260–263): Sedley provides the clearest available explanation of why Philodemus sometimes treats “Since there is motion, there is void” as an elimination inference and sometimes as a similarity inference. The two-stage analysis (similarity to establish the necessity; elimination to formalize it) dissolves the apparent inconsistency and shows that for the Epicureans the elimination method adds no independent epistemic force.

5. Non-Contestation vs. Discovery (pp. 263–272): Sedley argues that Antiochus of Ascalon (the likely source of the section on Epicurus in Sextus, M VII.203–16) misrepresented non-contestation by conflating it with sign-inference (sēmeiōsis). Non-contestation is a method of confirmation for theories that already have explanatory merit; sign-inference is a method of discovery. Philodemus’ contemporaries were “perfectly well aware of the purely confirmatory role of non-contestation” (p. 271, citing de Signis 36.7–17).

VIII. KEY TECHNICAL TERMS

Greek Term	De Lacy Translation	Significance
sēmeiōsis	Sign-inference	The process of inferring from observed signs to unobserved facts
homoiotēs	Similarity, analogy	The ground of Epicurean inductive inference
anaskeuē / anaskeue	Elimination, contraposition	The Stoic method of testing conditionals
idion sēmeion	Particular sign	Sign that cannot exist without its signified
koinon sēmeion	Common sign	Sign that may or may not accompany its signified
adianoeiston	Inconceivability	The Epicurean criterion of necessity
sunartēsis	Conjoining / cohesion	Chrysippan criterion of conditional validity
epilogismos	Inductive reasoning / inferential reasoning	Mental process of drawing conclusions from empirical data
epimarturēsis	Attestation / verification	Positive confirmation of a belief by perception
ouk antimarturēsis	Non-contestation	Absence of conflicting evidence; Epicurean test for truth of non-evident beliefs
pithanon	Convincing / probable	Stoic category for fallible, non-necessary inference
eulogon	Reasonable, probable	That which has more chances of being true than false
adēla	Non-evident things	Things not accessible to direct perception
prolēpsis	Preconception	Innate or naturally acquired general concept serving as a criterion
hēi / kathō	Insofar as / qua	Used to specify the relevant property in an inference; four meanings analyzed in cols. xxxiii–xxxvi
kat’ anaskeuen tropos	Elimination method	Stoic-preferred mode of sign-inference
kath’ homoiotēta tropos	Similarity method	Epicurean-preferred mode of sign-inference

IX. SUMMARY OF PHILODEMUS’ POSITION

Philodemus defends the following set of claims, which together constitute the Epicurean philosophy of knowledge:

All perceptions are true in the sense of faithfully presenting the appearance that occurs. Error arises only from additional opinion.
Inference from perception, properly conducted, is genuine knowledge — not merely probable. The properly-made analogical inference carries the same epistemic status as perception itself (Frag. 2).
The criterion of inconceivability converts inductive inference into claims of necessity. When it is genuinely inconceivable (on the basis of broad empirical observation) that the sign could exist without what it signifies, we have established a necessary connection.
Non-contestation (ouk antimarturēsis) is a sufficient condition for truth when combined with explanatory power. A theory that conflicts with no phenomenon and explains what needs explaining is genuinely true (for basic physics), not merely probably true.
The elimination method is not independently valid but derives whatever force it has from the prior work of the similarity method. Stoic deduction is epistemically downstream from Epicurean induction.
The Stoic pithanon classification is rejected for properly-conducted empirical inference. It may apply to careless or premature inferences; it does not apply to inference conducted with wide and varied observation, correct identification of relevant qualities, and confirmed by non-contestation.
Degrees of certainty exist within the class of warranted inferences: some inferences are more secure than others, depending on the uniformity and breadth of the evidence. But the existence of more and less secure inferences does not mean that the more secure ones are merely probable.
The limits of knowledge are real: some things (the parity of the stars) are genuinely unknowable; for celestial phenomena, multiple explanations may all be equally acceptable; for basic physics, uniquely determined truth is achievable.

In short, Philodemus’ position is a robust empirical foundationalism: the senses give us infallible access to appearances; properly-made inferences from appearances give us genuine, necessary knowledge of the unperceived world. This is neither scepticism (knowledge is impossible) nor rationalism (knowledge requires a priori foundations). It is a demanding empiricism that claims genuine knowledge of atoms, void, and unperceived objects throughout the universe.

X. EXPANDED ANALYSIS: THE FOURFOLD MEANING OF HĒI / KATHŌ (“INSOFAR AS” / “QUA”)

Background and Stakes

The analysis of “insofar as” (hēi, kathō, or kath’ ho) in cols. xxxiii.21–xxxvi.7 is one of the most technically demanding passages in the De Signis. It is presented as part of the anonymous Epicurean’s response to the “pervasive errors” of those who attack analogy (De Lacy, Essay II, p. 161–162, pervasive error no. 10). The issue arises from a specific Stoic strategy. The Stoics had offered to “help” the Epicureans by reformulating their mortality argument:

Epicurean version: “Since men within our experience are mortal, men outside our experience are mortal.” — a straightforward similarity inference.
Stoic reformulation: “Since men within our experience are mortal insofar as they are men, men everywhere are mortal.” — now treated as passing the elimination test, because “mortal” is analytically contained in “man qua man.”

Zeno of Sidon rejected this Stoic offer without much argument (col. xvi.29–xvii.11); Demetrius was cautiously ambivalent (col. xxix.4–16); but the anonymous Epicurean in the final section of the De Signis meets the Stoic challenge head-on. His strategy is to show that the phrase “insofar as” (hēi) is not univocal — it covers at least four distinct types of relationship — and that in every one of those four meanings, the necessary connection expressed must be established empirically, not a priori (Sedley, pp. 258–259).

The Four Meanings (Cols. xxxiii.33–xxxiv.29)

The anonymous Epicurean distinguishes:

Meaning 1: Necessary Concomitant (symptōma) Example: “Men, insofar as they are men, are prone to disease and aging.”

This expresses a property that accompanies membership in a class necessarily but is not part of the definition of the class. It is an empirical regularity, confirmed by broad and consistent observation across all known instances of the class. It cannot be known a priori that mortality and susceptibility to disease belong to humanity; this must be discovered by examining men and finding no exceptions. That the connection holds necessarily is established by the breadth and consistency of the observations, not by inspecting the concept of “man.”

The Epicurean point: even if Dionysius is right that the “insofar as” formulation creates a necessary connection, the source of that necessity is empirical, not analytic.

Meaning 2: Definition and Preconception (prolēpsis) Example: “Man, insofar as he is man, is a rational animal.”

This appears to be the Stoic’s best case — a definitional truth where the predicate is analytically contained in the subject. The anonymous Epicurean concedes that this looks like an a priori connection. But he insists that even definitional connections are empirically derived: preconceptions (prolēpseis) are formed through repeated experience, and what we include in our concept of “man” reflects what we have learned about men empirically. The definition is not self-certifying; it is accountable to experience.

This move is consistent with the broader Epicurean philosophy of language: words refer primarily to perceivable objects; their meaning is fixed by empirical practice within a community, not by rational stipulation. An “empty” definition — one not grounded in observable properties — is simply meaningless (De Lacy, Essay IV, pp. 184–185; Epicurus, Ep. Hdt. 37, Rat. Sent. 37).

Meaning 3: Accident (symbebēkos) Example: “Man, insofar as he is man, [walks when he wishes].”

This is a regular property of men that is nonetheless contingent: men sometimes walk, sometimes not. The “insofar as” here signals a genuine but non-necessary concomitant — something that holds for men as such but does not hold invariably. The Epicurean analysis: this too is established entirely by observation. There is no a priori reason why men should walk; this is simply what we find them doing. The “insofar as” does not generate necessity here; it merely specifies the class within which the observation is made.

This meaning is included to show that “insofar as” does not always carry necessity — a point the Stoics had assumed without examination. By acknowledging this meaning, Philodemus prevents any blanket claim that all “insofar as” premises are necessarily true.

Meaning 4: Necessary Concomitant of a Property Example: “[A man, insofar as he] is foolish, is utterly unhappy.”

This picks out not a property of men as men, but a necessary consequence of one specific property. The connection between foolishness and unhappiness is necessary — it is inconceivable that a genuinely foolish person should be happy in the relevant sense. But this necessity is itself an empirical finding: we learn from extensive observation that foolishness invariably produces unhappiness. The “insofar as” here specifies the property that grounds the inference, not the species membership.

This meaning is particularly important for Epicurean ethics, where claims like “the pleasurable life is the good life” or “the wise man is always happy” function as necessary connections discovered empirically through the nature of pleasure, pain, and human psychology.

The Epicurean Conclusion from All Four Meanings

The anonymous Epicurean’s argument runs as follows (cols. xxxiv.29–xxxvi.7; Sedley, pp. 258–259; De Lacy, Essay II, p. 161):

All four uses of “insofar as” involve some kind of necessary connection (not just meanings 1 and 4; even the definitional meaning 2 and the apparently contingent meaning 3 have their own kinds of necessity).
None of these necessary connections is knowable a priori. Each must be established through painstaking empirical inquiry.
The Stoics assume that an “insofar as” premise automatically confers the elimination method on the inference that uses it. But this ignores the source of the “insofar as” connection — which is always, on examination, empirical.
Therefore: “In fact, establishing the necessary connection which ‘insofar as’ in all its senses marks can only be a painstaking empirical matter — even for apparently definitional properties like man’s mortality” (col. xxxv.4–29, paraphrased by Sedley, p. 259).

Significance: Empiricism vs. Rationalism

Sedley characterizes this as a “head-on confrontation between empiricism and rationalism” (p. 259), and the characterization is apt. The anonymous Epicurean is not merely saying that the Stoics have used “insofar as” too quickly in one case; he is making a general epistemological claim: there is no class of necessary truths accessible to reason independently of experience. The “insofar as” qualification can specify the basis of a necessary inference, but it cannot create that necessity or certify it from the armchair. Every instance of genuine necessity — whether definitional, property-based, or concomitant — is a discovery made through empirical inquiry and confirmed by the non-contestation of the resulting claim.

The implication for the mortality argument is clear: whether we say “men are mortal” (the Epicurean version) or “men are mortal insofar as they are men” (the Stoic reformulation), we are saying the same thing, and we know it by the same means — extensive observation showing that no man has ever been found immortal, no appearance conflicts with the claim, and the claim holds across all the varied circumstances in which men appear. The Stoic formulation adds no epistemic gain; it merely disguises the empirical origin of the claim in formal-looking language.

Connection to the Primary/Secondary Quality Distinction

The four meanings of “insofar as” connect directly to Philodemus’ defense of Epicurean atomism (cols. xvii.37–xviii.16). He uses hēi and kathō to distinguish properties that belong to bodies as bodies (tangibility, resistance) from properties that belong to bodies under a specific further description (color, destructibility — which belong to perceptible bodies insofar as they have a nature “opposed to the corporeal and non-resistant,” not insofar as they are bodies). The detailed analysis of “insofar as” in cols. xxxiii–xxxvi provides the conceptual toolkit for that earlier move: to make the right analogical inference you must identify the right “insofar as,” and the right one is always identified empirically (De Lacy, Essay V, pp. 220–221).

XI. EXPANDED ANALYSIS: SEDLEY ON ANTIOCHUS AS THE SOURCE OF SEXTUS M VII.211–16

The Problem

The passage at Sextus Empiricus, Adversus Mathematicos VII.203–16 contains what looks like a detailed account of Epicurean methodology — specifically, Epicurus’ use of epimarturēsis (attestation) and ouk antimarturēsis (non-contestation) as criteria of truth. This passage has long been regarded as a reliable guide to Epicurus’ own epistemological practice, used by scholars to reconstruct what Epicurus meant by these terms. The standard attribution of the passage’s source is to Demetrius Lacon, one of the Epicurean participants in the debate reported by Philodemus (Sedley, p. 264, following Natorp).

Sedley argues that this attribution is mistaken, and that the real source is more likely Antiochus of Ascalon — and that this matters greatly for understanding what the passage does and does not tell us about Epicurus.

Sedley’s Case for Antiochus as Source (Pp. 264–271)

Step 1: The contextual argument. The passage on Epicurus (M VII.203–16) is flanked on both sides by material securely identified as deriving from Antiochus’ Canonica (a history of theories of knowledge). The preceding section (M VII.141–89) is Antiochus’ history of the Academy; Antiochus is cited by name at 162. At 201–2, his words on Asclepiades are quoted verbatim from the Canonica. Following the Epicurus section (at 217–60) comes an account of Peripatetics and Stoics that Hirzel has identified as Antiochean on independent grounds (Sedley, pp. 265–266). The Epicurus section is thus sandwiched between Antiochean material on both sides, making it very likely that it too is Antiochean.

Step 2: Antiochus’ characteristics as a reporter. Antiochus was notoriously “unscrupulous” (Sedley, p. 266) in his doxographical work, particularly when he had his own agenda (establishing the unity of the Platonic tradition from Plato through the Stoics). He habitually attributed contemporary philosophical terminology to earlier thinkers, as Sedley notes from the passage at M VII.141–4, where the account of Plato “seizes on the word perilēptikos in the Timaeus and scandalously equates it with the Stoic term katalēptikos” (p. 265). When treating philosophers with whose views he was not closely familiar — and Antiochus was not an Epicurean — he was capable of significant misunderstanding.

Step 3: The specific misrepresentation Antiochus makes. Sedley’s key argument (pp. 269–271) is that the Sextus passage misrepresents non-contestation by confusing it with sign-inference (sēmeiōsis). In the passage, non-contestation is defined as “the following (akolouthia) from that which is apparent of the non-apparent thing posited and believed” — and the void inference is given as the example: if void does not exist, motion should not occur either, but motion is apparent, therefore void is confirmed.

The problem is that this makes non-contestation look like a method of discovery: the apparent thing (motion) leads us to the non-apparent thing (void). But Philodemus’ Epicurean contemporaries, as Sedley demonstrates from the De Signis itself, are clear that non-contestation is a method of confirmation, not discovery. The void’s existence is established by the similarity method (Stage 1: empirical observation that motion requires empty space); non-contestation then confirms this result by showing that the positing of void does not conflict with any phenomenon, while the denial of void does conflict with the evident fact of motion (col. xxxvi.7–17).

Any Epicurean who actually participated in the De Signis debate — Zeno, Demetrius, Bromius, or the anonymous Epicurean — would, Sedley argues, “be horrified by the false emphasis with which this is done, particularly by the assumption that it is the inference from motion to void that in itself ‘confirms’ the existence of void” (p. 265). The Sextus passage gets the formal structure right (void is established via the non-contestation of the denial of motion) but misrepresents which stage of inquiry does the real epistemic work.

Step 4: Why Demetrius is not a good candidate. The standard argument for Demetrius is that the void inference attributed to Epicurus in M VII.214 was also used by Demetrius (cited at M VIII.348). But Sedley notes this is weak evidence: all three Epicureans in the De Signis use the void inference (Sedley, p. 264 n. 60). Moreover, the Sextus passage’s misrepresentation is precisely the kind of error a non-combatant observer (Antiochus) would make when reading Epicurean material — “a passage like de Signis 12.1–14 into supposing the void inference to rely purely on the elimination method, provided that he did not scrutinise the broader context too carefully” (p. 265). Demetrius, as an actual participant in the debate, would never have made this error.

Step 5: Antiochus’ specific confusion. Antiochus, Sedley argues (p. 271), “clearly started with some general information about Epicurus’ terminology and usage, and, in characteristically unhistorical fashion, delved into contemporary Epicurean tracts for further elucidation.” Finding there the term sēmeiōsis prominently discussed, and not finding the crucial term “non-contestation” in that context, he “mistakenly identified it with the current Epicurean preoccupation sēmeiōsis, of which he had achieved a rather superficial understanding. He thus confused a method of confirmation with a method of discovery.”

What This Means for Reading the Sextus Passage

If Sedley’s argument is correct, the passage at M VII.211–16 cannot be treated as a direct transcript of Epicurean methodology. Specifically:

The claim that non-contestation is “the following of the non-apparent from the apparent” overstates the role of the formal inference step. For the Epicureans, the formal step “Since there is motion, there is void” is not in itself the epistemic achievement — the empirical establishment of the motion-void connection through the similarity method is.
The passage’s picture of non-contestation as the primary tool for discovering non-evident truths may reflect Antiochus projecting his own rationalistic leanings onto Epicurean methodology, assimilating it to a kind of a priori deduction from evident premises.
The passage does, however, preserve a genuine Epicurean distinction between things verifiable by direct perception (epimarturēsis) and things confirmed by absence of conflicting evidence (ouk antimarturēsis). This division is authentic; what Antiochus gets wrong is the relation of non-contestation to sign-inference.

What Epicurean Non-Contestation Actually Does

Drawing on Epicurus’ own letters and on the De Signis, Sedley reconstructs the proper role of non-contestation (pp. 267–272):

For basic physics (atoms, void): Non-contestation is a confirmatory check applied to theories that already have explanatory power. The void’s existence is posited to explain motion; non-contestation then confirms that this posit conflicts with no observable phenomenon, while the denial of void conflicts with the evident fact of motion. The result is genuine truth — not mere probability — because only one explanation is consistent with the full range of phenomena.

For celestial phenomena: Multiple explanations (all consistent with visible analogues in terrestrial experience) may each pass the non-contestation test. In this case, Epicurus accepts all of them as possibly true — probably in different worlds, given the infinity of the universe. Here the honest result is acknowledged plurality, not certainty. This is the “multiple explanations” principle of the Letter to Pythocles, and it is explicitly grounded in the availability of multiple non-contested alternatives, not in any deficiency of the method.

The key asymmetry: Contestation (a belief that conflicts with phenomena) proves falsehood. Non-contestation (a belief that conflicts with nothing) is a sufficient condition for truth when combined with explanatory power and the uniqueness of the non-contested explanation. This asymmetry between verification and falsification is, Sedley notes (p. 271), a genuine and important insight — Epicurus “can be congratulated on his insight that scientific theories lend themselves to falsification more readily than to verification” — and Antiochus’ conflation of non-contestation with discovery obscures it.

XII. EXPANDED ANALYSIS: THE THREE-WAY CONTROVERSY — STOICS, EPICUREANS, AND SCEPTICS

Introduction: Why the Three-Way Comparison Matters

The De Signis itself focuses on the Stoic-Epicurean controversy, but De Lacy’s Essay V (pp. 223–230) and Sedley’s broader analysis place the debate within a larger three-way conversation that includes the Empirical Sceptics, above all Sextus Empiricus. Understanding where the Sceptics stand illuminates both the Stoic and Epicurean positions by contrast, and clarifies what is genuinely at stake in the question of whether empirical inference can yield knowledge or only probability.

The Sceptic Position: Admonitive Signs Only

Sextus Empiricus accepts the following from the shared Hellenistic framework: all three schools divide things into the apparent (phainomena) and the non-apparent (adēla), and all agree that only the apparent needs no inference. Where they diverge is on whether the non-apparent can be known at all, and if so, by what means.

Sextus differentiates two kinds of signs corresponding to two sub-classes of the non-apparent (Adv. Math. VIII.152–158; Pyrrh. Hyp. II.100–101; De Lacy, Essay V, pp. 212–213, 223–224):

1. The admonitive sign (hypomnēstikon sēmeion): A sign that has been observed together with what it signifies in a clear situation, and subsequently serves as a reminder when the thing signified is not currently apparent. The standard example: smoke as the sign of fire, a scar as the sign of a past wound. The admonitive sign works by memory and association: having seen smoke and fire together before, smoke now reminds us of fire.

Sextus accepts admonitive signs as useful and legitimate. Without them, practical life (bios) would be impossible — skippers, farmers, and hunters all rely on them, as do animals (the hunting dog reads the track as a sign of the quarry). Their legitimacy does not depend on any philosophical theory; they are part of how living things navigate the world.

Crucially, Sextus does not claim that admonitive signs give us knowledge of fire — only that they lead us to expect fire. The relation between smoke and fire is a constant conjunction observed in experience; it does not assert a necessary connection, a causal relation, or anything that goes beyond the phenomenal level.

2. The indicative sign (endeiktikon sēmeion): A sign that, “from its own nature and constitution, all but saying the word, indicates the thing of which it is indicative” (Adv. Math. VIII.154). The indicative sign designates things that are by nature unperceivable — atoms, the void, the soul, pores in the flesh. It cannot have been observed together with what it signifies, since the thing signified is in principle inaccessible to perception. Its meaning must therefore be knowable a priori — or at least independently of any co-observation with what it signifies.

Sextus rejects indicative signs entirely. They are the invention of “dogmatic philosophers and rational physicians” (Adv. Math. VIII.156–158), who supposed they could provide knowledge of what is by nature beyond experience. Sextus’ arguments against them are numerous and various (De Lacy, Essay V, pp. 224–226):

A sign involves a relation between two things; you cannot know a relation unless you have apprehended both relata — but if both are apparent, no inference is needed; if one is by nature unperceivable, the relation cannot be established (Adv. Math. VIII.163–165, 171–175).
Philosophers disagree about whether signs are apprehended by sense-perception or thought. What is contested is thereby obscure; what is obscure requires another sign to clarify it; this generates an infinite regress (ibid. 176–182).
The Stoic theory that signs are propositions (lekta) confuses the logical level with the phenomenal level. Practical sign-users — sailors, hunters, animals — do not form propositions; yet they use signs expertly. Therefore the Stoic propositional analysis is wrong (ibid. 269–271). (De Lacy, Essay V, p. 226, notes that the hunting dog does not say “If this is the track, the animal is over there.”)
If a conditional is sound only when both protasis (the sign) and apodosis (the thing signified) are true, and the apodosis is non-apparent, we cannot determine the conditional’s soundness without already knowing what we are trying to learn (ibid. 266–268).

Sextus’ Critique of the Epicureans Specifically

While the Stoics are Sextus’ “arch opponents” (De Lacy, Essay V, p. 223), he also criticizes the Epicureans — not for their method, but for their conclusions. The Epicureans use a method (similarity-based inference confirmed by non-contestation) that Sextus regards as fine for practical purposes, but then extend it to establish a dogmatic metaphysics of atoms and void. This is precisely where, for Sextus, they overreach.

Sextus’ specific charge against inductive inference (relevant to the Epicurean position on analogy):

Induction from particulars to universals requires either examining all particulars (impossible, since their number is indefinitely large) or examining only some (insufficient, since unexamined ones might contradict the universal). (Pyrrh. Hyp. II.204; De Lacy, Essay V, p. 227)

This is essentially a version of the Stoic objection that Philodemus addresses at cols. xx.35–xxi.3 (not necessary to examine all cases; sufficient to examine many homogeneous and varied ones). Sextus presses harder: any extrapolation beyond examined cases is unjustified. He compares investigators of the non-evident to “persons aiming at a target in the dark — it is likely that someone will hit it, but there is no way of knowing who it is” (Adv. Math. VIII.325; De Lacy, Essay V, p. 227). In other words, even if the Epicureans happen to be right about atoms and void, they cannot know that they are right.

Sextus’ Alternative: Phenomenalism and the Practical Arts

Rejecting both Stoic rationalism and Epicurean empirical dogmatism, Sextus advocates a phenomenalistic empiricism (De Lacy, Essay V, pp. 228–230):

The arts are legitimate precisely because they do not claim knowledge of the hidden nature of things. They build their teachings from “things repeatedly observed or reported” (Adv. Math. VIII.291); their practitioners make predictions on the basis of admonitive signs — signs grounded purely in observed co-occurrence. Navigation, empirical medicine, even reading and writing — all are legitimate arts operating within the level of appearances.

The crucial limitation: none of these arts “permit the person trained in an art to make universally valid pronouncements about the hidden nature of things” (De Lacy, Essay V, p. 228). They give guidance for practical action; they do not give knowledge of causes or of the nature of things.

De Lacy compares Sextus’ position to positivism (Essay V, pp. 228–230): he combines a negative scepticism about metaphysical knowledge with positive empiricism about phenomena. He does not say the adēla are unknowable in a strong metaphysical sense (unlike the negative Sceptics who assert even this would be dogmatic); he simply follows appearances and suspends judgment about what lies behind them. “The laws” he recognizes are not absolute causal laws but empirical regularities subject to revision.

The Three Positions Compared

Question	Stoics	Epicureans (Philodemus)	Sceptics (Sextus)
Can non-evident things be known?	Yes — by a priori, analytic inference via contraposition	Yes — by properly-conducted empirical analogy + non-contestation	No — suspension of judgment; only appearances guide practice
What kind of sign reveals the non-evident?	Indicative (endeiktikon): reveals by its own nature	Particular (idion): established empirically through inconceivability	Only admonitive (hypomnēstikon): reminds of co-observed regularities
What is the status of similarity-based inference?	Pithanon only: convincing but fallible	Genuine knowledge when properly conducted	Useful practically; not knowledge of hidden things
Is there necessary connection between sign and signified?	Yes — analytic and a priori	Yes — but empirically established	No — only constant conjunction; necessity is not claimed
Role of induction/analogy	Insufficient for knowledge; yields at best pithanon	Primary method for knowledge of non-evident	Practically useful; epistemically limited to phenomenal level
Status of atoms, void, gods	Knowable via strict inference from concepts	Genuinely known via analogy + non-contestation	Not knowable; suspension of judgment
Relationship of formal deduction to experience	Primary; experience at best confirms formal truths	Derivative; all formal truths grounded in experience	Irrelevant to practical life; practically replaced by admonitive signs
Goal of the theory of signs	Establish a complete science grounded in a priori necessity	Establish empirical knowledge of nature, including physics	Practical guidance without metaphysical commitment

The Deep Difference between Epicureans and Sceptics

The Sceptics and Epicureans share important methodological ground: both are empiricists; both reject Stoic a priori necessity as the standard for legitimate inference; both ground their practice in appearances. But they differ on a fundamental question: whether properly-conducted inference from appearances can establish genuine truths about non-apparent things.

For Sextus, the answer is no — not because such truths do not exist, but because we have no way to verify that our inferences have reached them. Any inference that goes beyond observed co-occurrence claims more than experience can certify, and the multiplicity of conflicting philosophical theories about non-evident things proves that no such inference commands rational assent.

For Philodemus, the answer is yes — provided the inference is wide enough (many homogeneous and varied appearances), identifies the right qua-property, is checked against no conflicting appearance, and reaches a conclusion that is the unique explanation consistent with all known phenomena. When these conditions are met, the inference yields knowledge — not merely belief — and the resulting claim carries the same epistemic authority as direct perception.

The Sceptic challenges Philodemus on exactly this: he cannot be certain that his conditions have been met, cannot be certain that no unexamined case conflicts, cannot be certain that his “insofar as” is the right one. Philodemus’ response, implicit throughout the De Signis, is that these challenges apply equally to any claim to knowledge — including the claim that we cannot know the non-evident — and that the Sceptic’s own practical use of admonitive signs already implicitly commits him to more than mere phenomenalism. The practical craftsman who reads smoke as a sign of fire is making an inference that goes beyond the observed case; the question is only how far such inferences can legitimately extend.

The Sceptics’ Asymmetric Relationship to the Two Dogmatic Schools

De Lacy observes (Essay V, p. 223) that “though Sextus attacks both Epicureans and Stoics, he considers the Stoics his arch opponents.” This asymmetry is philosophically significant. Sextus’ method is, in its foundations, much closer to the Epicurean than to the Stoic. He accepts:

The primacy of appearances as the basis of all legitimate inquiry
The illegitimacy of purely a priori inference
The practical usefulness of sign-based reasoning grounded in observed regularities
The critique of Stoic conceptualism (signs as lekta)

What he rejects is only the Epicurean extension of empirical method to claim genuine knowledge of non-apparent things. In this sense, the De Signis debate, read alongside Sextus, presents a spectrum rather than a binary:

Stoics: a priori deduction → necessity → knowledge of the non-apparent (but only by analytic inference)
Epicureans: empirical analogy → necessity (via inconceivability) → genuine knowledge of atoms, void, nature (but the necessity is empirically grounded)
Sceptics: empirical observation → constant conjunction → practical guidance only (no claim to knowledge of the non-apparent; suspension of judgment)

Philodemus occupies the center of this spectrum — more epistemically ambitious than the Sceptics, but grounding his ambitions in experience rather than a priori reason. The De Signis is, among other things, an argument that this middle position is not merely a compromise but is epistemically superior to both extremes: more faithful to how we actually learn about the world than Stoic rationalism, and more intellectually honest about what properly-conducted empirical inquiry achieves than Sceptical suspension of judgment.

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