Posterior Analytics

1. Introduction

Posterior Analytics is Aristotle’s most systematic treatment of what it is to know something scientifically and how such knowledge is structured. Where the Prior Analytics develops a general theory of syllogistic inference, the Posterior Analytics asks under what additional conditions deductive inference yields epistēmē—a kind of understanding that is necessary, explanatory, and organized into sciences.

Aristotle presents scientific knowledge as a network of demonstrations (apodeixeis) that derive conclusions from first principles (archai). These principles are not themselves demonstrated but are nonetheless known; a central task of the work is to explain how such knowledge is possible without circularity or infinite regress. The treatise is therefore both a work in logic and a foundational text in epistemology and philosophy of science.

The work is tightly argued and often compressed, using the technical framework of Aristotelian logic. It presupposes familiarity with terms like syllogism, per se predication, and middle term, and it assumes the broader metaphysical backdrop of Aristotle’s account of substance, essence, and causality. Yet its guiding questions—what distinguishes scientific knowledge from mere opinion, how explanations work, and how basic truths are known—have been seen as of enduring philosophical interest.

Interpretive debates concern, among other things, how strictly Aristotle means to idealize science, how to understand the status of first principles, and how his account of induction and nous relates to later empiricist and rationalist traditions. The Posterior Analytics has thus been read both as a historical document mapping ancient ideals of demonstrative science and as a resource for contemporary discussions of explanation, justification, and theory structure.

2. Historical and Intellectual Context

2.1 Position in Classical Greek Thought

The Posterior Analytics, composed in the 4th century BCE, belongs to a period when Greek thinkers were increasingly reflecting on the nature of technai (arts) and epistēmai (sciences). Plato, in dialogues such as the Meno and Republic, had linked knowledge with stable, reasoned accounts and distinguished it from mere true belief. Aristotle’s treatise can be read as a systematic attempt to spell out the structure of such reasoned accounts in detail.

Predecessors in mathematics and astronomy, including Pythagoreans and figures associated with early geometry, provided models of rigorous proof. Many scholars hold that Aristotle is generalizing from such practices: Euclidean-style geometry, codified slightly later, exhibits the kind of axiomatic, demonstrative structure the Posterior Analytics describes.

2.2 Relation to Presocratic and Sophistic Traditions

Aristotle’s emphasis on necessity and explanation responds to Presocratic attempts to uncover invariant principles of nature (e.g., Parmenides, Anaxagoras) and to sophistic debates about argument and persuasion. The Organon as a whole is often seen as an answer to sophistic eristic: it distinguishes valid inference from mere verbal victory. The Posterior Analytics specifies how such valid inferences must be configured to yield genuine knowledge rather than dialectical success.

2.3 Cultural and Institutional Setting

The work emerged within the Lyceum, Aristotle’s school in Athens, which fostered empirical research in biology, cosmology, and politics alongside logical and metaphysical studies. Many commentators infer that the treatise was designed for advanced students already trained in syllogistic and familiar with ongoing investigations in particular sciences.

2.4 Hellenistic and Early Peripatetic Background

Aristotle’s immediate successors, such as Theophrastus and Eudemus, developed and sometimes modified his theory of demonstration. Later Hellenistic schools—Stoics, Epicureans, Skeptics—offered rival logical systems and epistemologies. Although these developments postdate the composition of the Posterior Analytics, they shaped how its ideas were received, critiqued, and transmitted, and they highlight the text’s role as a benchmark in subsequent debates about scientific method and certainty.

3. Author, Composition, and Place in the Organon

3.1 Authorship and Composition

The Posterior Analytics is universally attributed to Aristotle. Stylistic and doctrinal features align it with other logical works and with the mature phase of his philosophical output. Most scholars date its composition to roughly 350–335 BCE, though views differ on precise chronology and on whether the two books were composed together.

The work is generally regarded as a set of internal teaching materials or revised lecture notes. The compressed style, abrupt transitions, and occasional obscurities have been taken as evidence that Aristotle was writing for a specialized audience within the Lyceum rather than for a broader public.

3.2 Relationship between Book I and Book II

There is broad agreement that Books I and II form a unified project, but debate concerns the extent of their editorial coherence. Some interpreters propose that Book II may incorporate earlier or later material, or that certain chapters (especially II.19 on nous) reflect distinct stages of Aristotle’s thought. Others argue for substantial unity, emphasizing thematic continuities between the theory of demonstration in Book I and the treatment of definition, inquiry, and first principles in Book II.

3.3 Place within the Organon

Within the traditional Organon, the Posterior Analytics occupies a central position:

Some historians view the Organon as a later editorial construct and caution against reading too much systematic intent into this ordering. Nonetheless, most agree that the Posterior Analytics presupposes the Prior Analytics and is, in turn, presupposed by later discussions of scientific method in Aristotle’s physics, biology, and metaphysics.

4. Structure and Organization of Posterior Analytics

4.1 Overall Division

The Posterior Analytics is divided into two books (I and II), traditionally designated An. Post. I (71a1–85b2) and II (89b23–100b17 in Bekker pagination). Each book is composed of short chapters (approximately 34 in Book I, 19 in Book II), though chapter boundaries are a later editorial imposition and not always uncontroversial.

4.2 Thematic Arc of Book I

Book I is organized around the idea of demonstration as the core of scientific knowledge. Its progression can be schematized as follows:

While not all scholars agree on this subdivision, many note that Book I moves from a basic definition of scientific demonstration to increasingly fine-grained distinctions about priority, explanation, and the architecture of the sciences.

4.3 Thematic Arc of Book II

Book II shifts attention from the structure of completed demonstrations to the processes and forms of inquiry that lead to them:

This organization allows Aristotle to connect the formal conditions of demonstration with questions about how one arrives at definitions and first principles in the first place.

4.4 Perceived Compositional Tensions

Commentators note some tensions in the organization. For instance, II.1–3 revisit issues about per se predication and priority discussed in Book I, leading some to posit redactional layers or didactic repetition. Chapter II.19, with its highly compressed epistemological account, is often treated as climactic but has also been suspected of reflecting a slightly different agenda or stage of thought. Despite such issues, most interpretations treat the work as pursuing a continuous inquiry from conditions of scientific knowledge to the acquisition of its starting points.

5. Concept of Scientific Knowledge (Epistēmē)

5.1 Definition and Core Features

In An. Post. I.2 Aristotle characterizes epistēmē as knowledge of necessary truths together with their causes, achieved through demonstration:

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“We suppose ourselves to possess scientific knowledge of a thing… when we think that we know the cause on which the fact depends, as the cause of that fact and of no other, and, further, that the fact could not be otherwise.”

— Aristotle, Posterior Analytics I.2, 71b9–12 (trans. Barnes, modified)

On this account, to know scientifically is not merely to have a true belief, nor even a justified true belief in a modern sense, but to grasp a necessitated connection: why something must be the case.

Key features typically ascribed to epistēmē in the treatise include:

• Necessity: Its objects “cannot be otherwise.”
• Universality: It concerns universal propositions rather than isolated particulars.
• Explanatoriness: It involves knowing the middle term that explains the conclusion.
• Systematicity: It is embedded within organized bodies of knowledge (sciences).

5.2 Contrast with Other Cognitive States

Aristotle distinguishes epistēmē from:

There is debate over whether epistēmē can admit degrees (stronger vs weaker forms) or whether Aristotle reserves the term strictly for the ideal of apodictic knowledge. Some interpreters read the treatise as describing a rigorous ideal rarely, if ever, fully realized in empirical disciplines; others maintain that Aristotle intended large portions of mathematics and even parts of natural philosophy to meet these criteria.

5.3 Scope of Scientific Knowledge

Aristotle often uses examples from geometry and astronomy, but he also envisages epistēmē in domains like biology and psychology. Scholars disagree on how literally one should take his extension of the demonstrative ideal to such areas, especially given later Aristotelian writings that stress observation and variability in nature. The Posterior Analytics itself, however, presents epistēmē as a unified standard that can be instantiated in different subject-matters provided they are organized around stable natures and per se properties.

6. Demonstration, Syllogism, and First Principles

6.1 Demonstrative Syllogism

In the Posterior Analytics, a demonstration (apodeixis) is a special kind of syllogism that yields scientific knowledge. Whereas the Prior Analytics treats syllogisms in general, here Aristotle restricts attention to those whose premises satisfy stringent conditions. A standard formulation is:

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“By demonstration I mean a scientific syllogism, and by scientific I mean one in virtue of which, by having it, we understand something.”

— Posterior Analytics I.2, 71b17–19

A demonstrative syllogism must have premises that are:

• True
• Primary and immediate (indemonstrable)
• Prior to and better known than the conclusion
• Causally explanatory of the conclusion
• Universal and necessary, typically in per se form

The middle term expresses the cause: it is through the middle that the major term belongs to the minor, thereby explaining the conclusion.

6.2 Regress Problem and Need for First Principles

In I.3 Aristotle addresses the apparent regress problem: if every piece of knowledge requires a demonstration, then either there is an infinite chain of demonstrations, or a circular one, or demonstrations terminate. Aristotle rejects infinite regress and circularity, arguing that scientific chains must terminate in first principles (archai), which are indemonstrable but known.

Different types of first principles are distinguished:

6.3 Priority and Explanatory Order

Aristotle connects logical derivation with metaphysical priority: premises should be prior “by nature” and “better known in themselves” than conclusions. This priority is not merely epistemic (what we happen to know first) but tied to what grounds or causes what. Demonstration ideally mirrors the ontological and causal structure of reality.

There is significant interpretive disagreement over how strictly this mirroring is required and over whether all demonstrations must ultimately rest on purely intuitive knowledge (nous) of principles, topics taken up more fully in discussions of Book II.

7. Definition, Essence, and Explanatory Priority

7.1 Definitions and Essences

In Book II Aristotle focuses on definition (horismos) as a statement of essence (to ti ēn einai). A correct definition gives what something is, typically via genus and differentia (e.g., “human is rational animal”). Definitions are central to science because they identify the natures that ground the properties demonstrated about things.

7.2 Relations between Definition and Demonstration

A central question in II.2–3 is whether there can be a demonstration of what something is or only of properties that follow from what it is. Aristotle explores several possibilities:

• That a definition itself might be the conclusion of a demonstration.
• That one might demonstrate that a given account is the definition.
• That definition and demonstration are related but irreducible: definition states essence; demonstration shows that certain features belong because of that essence.

Aristotle appears to deny that essence as such is demonstrable, because demonstration presupposes that the subject of predication already exists and is understood. Instead, he often presents essence as what explains why certain attributes belong per se.

7.3 Explanatory and Ontological Priority

Definition is linked to explanatory priority. The essence of a thing is prior to its “proper attributes” (idia) and other per se accidents, in that these attributes are explained by the essence. For instance, in a canonical example, the definition of eclipse (the earth’s blocking the light of the moon) explains why certain observational features (the moon’s darkening) occur.

Some commentators construe this as a tight essentialist model: every genuine scientific proposition is grounded in essences that definitions capture. Others emphasize more modest claims: definitions provide focal points for explanation without necessarily underwriting a fully essentialist metaphysics in every science.

7.4 Debates on the Epistemic Status of Definitions

There is disagreement over how we know definitions:

• One line of interpretation stresses that definitions are first principles known by nous and not derived from demonstration.
• Another emphasizes inductive and investigative procedures—discussed later in Book II—through which definitions are gradually refined.

Aristotle’s text suggests a complex interaction: inquiry may begin with rough accounts, which are then adjusted in light of explanatory successes and failures, while fully correct definitions function as indemonstrable starting points for demonstrative science.

8. Induction, Perception, and the Role of Nous

8.1 The Epistemological Problem of First Principles

Since first principles cannot be demonstrated (on pain of regress or circularity), Aristotle asks in II.19 how they are known. His answer invokes a progression from perception to nous, with induction (epagōgē) and experience as intermediate stages.

8.2 From Perception to Experience

Aristotle sketches a developmental sequence:

1. Perception of particular instances (e.g., seeing many individual humans).
2. Memory (mnēmē), a retention of perceptual impressions.
3. Experience (empeiria), built from many memories of the same kind of thing.

This transition is presented as natural and quasi-psychological rather than purely logical.

8.3 Induction and the Emergence of Universals

From experience, the mind is said to arrive at universal concepts and principles “all at once” in a kind of intuitive generalization. Aristotle calls this process induction, but he does not describe it in terms of enumerative or probabilistic reasoning. Instead, the text suggests that when enough particular cases are grasped, the universal becomes manifest to the intellect.

Interpreters diverge on how to understand this:

8.4 Nous as Intuitive Grasp of Principles

The final stage is nous, often translated “intellect” or “intuitive understanding.” Aristotle writes that nous grasps first principles as self-evident once the mind is adequately prepared:

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“It is clear, then, that we must get to know the primary premises by induction; for this is the way in which perception instils universals in us.”

— Posterior Analytics II.19, 100b3–5

Nous is distinguished from discursive reasoning; it is immediate and non-inferential. Yet it is not purely innate: it arises from the structured interaction of the mind with the world.

Debates focus on whether nous is a mysterious, quasi-mystical faculty or a naturalized intellectual capacity grounded in cognitive development. Some modern readers see Aristotle as proposing an early foundationalism in which basic beliefs are secured by intuitive insight; others emphasize the continuity between empirical observation, rational pattern-recognition, and intuitive grasp.

9. Types of Inquiry: That, Whether, What, and Why

9.1 The Four Central Questions

In Book II Aristotle classifies scientific inquiry through four principal kinds of question:

This classification structures Aristotle’s account of how different cognitive aims relate to demonstration and definition.

9.2 From “That” to “Why”

Aristotle distinguishes knowledge that something is the case (e.g., that the moon is eclipsed) from knowledge why it is (e.g., because the earth is interposed). Demonstration ideally provides dioti: the middle term reveals the cause, upgrading bare fact-knowledge to explanatory understanding.

However, inquiry often begins with hoti: observation of phenomena or empirical regularities. Scientific investigation then seeks the explanatory middle term that would answer the corresponding dioti question.

9.3 Whether and What

The questions whether something is and what it is are associated with existence and essence:

• Whether (ei) it is: Establishing that there is such an object or phenomenon.
• What (ti) it is: Determining its essence and giving a definition.

Aristotle often portrays inquiry as proceeding from the more indeterminate to the more determinate: from asking whether something exists, to recognizing that it exists, to identifying what it is, and finally to explaining why it has its characteristic features.

9.4 Links to Demonstration and Definition

Different types of inquiry correlate with different argumentative goals:

Commentators debate the exact order and dependence of these questions. Some treat the sequence as a strict logical progression; others see it as a flexible heuristic reflecting how different sciences may, in practice, alternate between establishing facts, discerning essences, and discovering causes.

10. Key Concepts and Technical Vocabulary

The Posterior Analytics relies on a dense network of technical terms. The following table highlights several of the most important, complementing the entry’s glossary with a focus on how they function within the treatise.

Scholars sometimes diverge in translating and systematizing these terms. For example, kath’ hauto has been rendered “essentially,” “in itself,” or “per se,” with differing emphases on metaphysical versus logical readings. Similarly, nous is variously interpreted as a basic faculty of rational intuition, as a stage in cognitive development, or as a normative ideal of understanding.

11. Famous Passages and Central Doctrines

11.1 Definition of Scientific Knowledge (I.2)

One of the most cited passages is Aristotle’s characterisation of epistēmē in I.2 (71b9–12), where he states that to have scientific knowledge is to know the cause and to grasp that the thing could not be otherwise. This passage has become a touchstone for interpretations of Aristotelian explanatory knowledge and for debates about the role of necessity in science.

11.2 The Regress Problem and First Principles (I.3)

In I.3 (72b5–73b26) Aristotle formulates and addresses the regress problem: if every piece of knowledge requires a demonstration, there is a danger of infinite regress or circularity. His solution—appealing to indemonstrable first principles known by nous—is often regarded as a classic statement of a foundationalist response to epistemic regress.

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“Not all knowledge is demonstrative: knowledge of the immediate premises is indemonstrable.”

— Posterior Analytics I.3, 72b20–21

11.3 Better Known to Us vs. Better Known by Nature (I.2)

Another influential doctrine appears in I.2 (71b33–72a5), where Aristotle distinguishes what is better known to us (often more particular, accessible to perception) from what is better known by nature (more universal, explanatory). This distinction underpins his account of learning, which moves from the former to the latter, and it shapes subsequent philosophy of science concerning discovery vs. justification.

11.4 Demonstration and Definition (II.2–3)

In II.2–3 (90a14–93b38) Aristotle explores whether there is demonstration of essence and how definition relates to demonstration. These chapters have been crucial for later discussions of analytic vs. synthetic truths, the status of definitions in mathematics and metaphysics, and the nature of essentialist explanation.

11.5 Nous and the Acquisition of First Principles (II.19)

II.19 (99b15–100b17) presents Aristotle’s brief but influential sketch of how perception, memory, experience, induction, and nous combine to yield knowledge of first principles. The passage has inspired a wide range of interpretations, from empiricist to rationalist, and has been central in assessing whether Aristotle offers a naturalized account of basic knowledge.

These passages, taken together, articulate the treatise’s most prominent doctrines: that science is demonstrative and explanatory, grounded in first principles, and connected to human cognitive capacities through a structured developmental process.

12. Philosophical Method and Scientific Explanation

12.1 Demonstration as Method

In the Posterior Analytics, Aristotle proposes demonstration as the characteristic method of science. The method is not merely to derive conclusions from premises, but to select premises that capture genuine causal relations. The form of explanation is syllogistic, but its success depends on suitable content—propositions expressing per se, necessary connections.

12.2 Causal-Explanatory Model

Aristotle often illustrates explanation with cases where the middle term expresses a cause:

• Explaining why the interior angles of a triangle equal two right angles by appealing to properties of parallel lines.
• Explaining an eclipse by the interposition of the earth blocking the sun’s light from the moon.

In such examples, the structure of the syllogism mirrors the structure of the cause. Many interpreters see here an early version of a “covering-law” model: the explanandum is subsumed under a universal law-like statement. Others stress differences: Aristotle’s explanations are tied to essences and natures, not to generalizations alone.

12.3 Methodological Constraints on Sciences

The treatise also outlines methodological constraints:

• Each science must have a determinate subject-matter and first principles appropriate to it.
• Demonstrations should proceed within a science; cross-scientific demonstrations are limited and carefully regulated.
• The organization of a science reflects priority relations: more fundamental propositions explain less fundamental ones.

This yields a hierarchical picture of scientific knowledge, with upper levels providing deeper explanations.

12.4 Interplay of Analysis and Synthesis

Aristotle’s method involves both analysis (breaking down complex phenomena into simpler explanatory factors) and synthesis (reconstructing the phenomena via demonstration). Inquiry often starts from observed facts (hoti) and, via analysis, uncovers the relevant middle terms (causes). Once these are identified, synthesis yields demonstrations answering the dioti question (“why?”).

Some modern interpreters emphasize the exploratory, problem-solving character of this method, aligning it with contemporary views of theory construction. Others regard the account as primarily normative, presenting an ideal of scientific explanation that actual practices approximate to varying degrees.

13. Ancient, Medieval, and Islamic Commentarial Traditions

13.1 Ancient Peripatetic and Late Antique Commentaries

Early Peripatetics such as Theophrastus and Eudemus are reported to have engaged with the Posterior Analytics, though their works survive only fragmentarily. Systematic surviving commentaries begin in late antiquity:

These commentators focus on clarifying technical vocabulary, resolving apparent contradictions, and relating the text to broader Aristotelian metaphysics and psychology. They also develop extensive discussions of nous, induction, and the classification of sciences.

13.2 Islamic Philosophical Tradition

In the medieval Islamic world, the Posterior Analytics was transmitted in Arabic translation and became central to philosophical treatments of logic and scientific method.

Key figures include:

Islamic philosophers often used the Posterior Analytics as a foundation for their own encyclopedic systems of the sciences, while also adapting elements to Islamic theological and cosmological concerns.

13.3 Byzantine and Latin Scholastic Commentaries

In Byzantium, figures such as Ps.-Philoponus and later scholars kept the commentary tradition alive. In the Latin West, the Posterior Analytics became widely known in the 12th–13th centuries via translations from Arabic and Greek.

Major Latin commentators include:

Medieval scholastics used the treatise to articulate an ideal of scientia applied both to natural philosophy and to theology. They debated the extent to which theological articles could be demonstrative and how first principles related to faith and revelation.

13.4 Continuity and Divergence

Across these traditions, commentators generally endorsed the centrality of demonstration and first principles, but diverged in:

• How strictly to interpret necessity in natural sciences.
• The status and accessibility of nous.
• The classification and interrelation of particular sciences.

These long-standing debates shaped the text’s transmission into the early modern period and conditioned later philosophical responses.

14. Modern Interpretations and Critiques

14.1 Logical and Analytic Reconstructions

Twentieth-century analytic philosophers and logicians, such as Jan Łukasiewicz and Jonathan Barnes, have sought to reconstruct Aristotle’s theory of demonstration in modern logical terms. They typically:

• Clarify the structure of syllogistic reasoning.
• Examine the role of per se predication and middle terms.
• Evaluate whether Aristotle’s ideal corresponds to axiomatic systems in mathematics and logic.

Some argue that Aristotle anticipates formal axiomatic theories, while others stress limitations of syllogistic logic compared to modern predicate calculus.

14.2 Epistemological Debates: Foundationalism and Regress

The Posterior Analytics has been central in contemporary discussions of epistemic foundationalism. Proponents of this reading maintain that Aristotle offers a canonical response to the regress problem by positing basic beliefs grounded in nous. Critics question:

• Whether nous provides an adequate, non-circular justification.
• How basic principles are distinguished from non-basic ones.
• Whether Aristotle’s view is vulnerable to skeptical challenges.

Some alternative interpretations portray Aristotle as a contextualist or moderate foundationalist, allowing for interlocking support among beliefs while still positing some non-inferential starting points.

14.3 Philosophy of Science: Idealization vs Practice

Philosophers of science have asked how Aristotle’s model relates to actual scientific practice:

These discussions often compare Aristotelian demonstration with contemporary ideas of explanation, lawlikeness, and theory-ladenness.

14.4 Debates on Definition, Essence, and Essentialism

Modern metaphysics and philosophy of language have revisited Aristotle’s linkage of definition, essence, and scientific explanation. Some neo-Aristotelian metaphysicians see the treatise as an early articulation of essentialist metaphysics, where laws and explanations are grounded in the natures of things. Others regard the essentialist language as heuristic or domain-relative, arguing that many sciences do not operate with stable essences in Aristotle’s sense.

14.5 Induction and Naturalized Epistemology

Finally, Aristotle’s account of induction and nous has been scrutinized in light of modern empiricism and cognitive science. Interpretations range from reading Aristotle as proposing a primitive, non-probabilistic induction, to seeing in his account an early attempt at naturalized epistemology in which basic knowledge arises from the structured functioning of human cognitive capacities. Disagreements persist over how to reconcile the apparent immediacy of nous with the empirical, developmental story that precedes it.

15. Legacy and Historical Significance

15.1 Influence on Ancient and Medieval Science

The Posterior Analytics profoundly shaped ancient and medieval conceptions of scientia. Its model of demonstrative science influenced:

• The axiomatic structure of Greek mathematics, as seen in Euclid’s Elements.
• Late antique and medieval classifications of the sciences into theoretical, practical, and productive domains.
• Scholastic treatments of theology and metaphysics as sciences organized around first principles.

Through commentaries and curricular use, it became a standard reference for what it meant to “know scientifically.”

15.2 Transmission into Early Modern Thought

Early modern philosophers engaged extensively—sometimes indirectly—with Aristotelian ideas of demonstration, first principles, and certainty:

At the same time, the rise of experimental and probabilistic methods led many to question the universality of Aristotelian demonstration for natural science.

15.3 Role in the Development of Logic and Philosophy of Science

Modern logic largely superseded syllogistic, yet the Posterior Analytics remains a landmark in the history of:

• Proof theory: articulating conditions on valid and knowledge-yielding arguments.
• Philosophy of explanation: anticipating structural accounts where explanation involves subsumption under general principles.
• Theory of scientific method: framing issues about axiomatization, hierarchy of theories, and the relation between data and theory.

The treatise has also influenced 20th-century models of explanation, including Hempel’s covering-law model, which some view as a distant descendant of Aristotelian demonstration.

15.4 Contemporary Relevance

In current philosophy, the Posterior Analytics serves multiple roles:

• As a historical document illuminating ancient scientific ideals and educational practices.
• As a source for neo-Aristotelian approaches to metaphysics, essentialism, and explanation.
• As a reference point in ongoing debates about foundationalism, induction, and the nature of scientific understanding.

While few contemporary scientists would describe their work using Aristotelian syllogisms, many philosophers continue to draw on Aristotle’s insights into the relations between knowledge, cause, essence, and method, ensuring the treatise’s continued significance in discussions of how and why science explains.