LogicINTUITIONISM
November 15, 2023

INTUITIONISM

One of the most familiar non-classical logics is intuitionism, which, in simple terms, is based upon the rejection of the law of excluded middle: (P ∨ ¬P). There are both…
Modern Branches of PhilosophyPhilosophy BranchesPHILOSOPHY OF MATHEMATICS
November 14, 2023

PHILOSOPHY OF MATHEMATICS

The philosophy of mathematics is traditionally concerned with the ontological and epistemological foundations of mathematics. The two questions, of ontology and epistemology, are intimately related, as a satisfactory account of…
ANALYTIC PHILOSOPHYHistory Of PhilosophyANALYTIC PHILOSOPHY IN THE TWENTIETH CENTURY
November 15, 2023

ANALYTIC PHILOSOPHY IN THE TWENTIETH CENTURY

The analytic tradition arose partly as a rejection of Hegelian idealism in favor of what George Edward Moore (1873–1958) called a “common sense” view of the world, alongside developments in…
FORMS OF PHILOSOPHICAL WRITINGWriting PhilosophyTHE EXPOSITORY PAPER
November 19, 2023

THE EXPOSITORY PAPER

We have already touched on the expository paper, but let’s discuss it briefly here. Look at the adjective expository. It is derived from the noun exposition, which is the noun…
WHAT IS PHILOSOPHY?PHILOSOPHICAL FILMS AND TV SHOWS
November 24, 2023

PHILOSOPHICAL FILMS AND TV SHOWS

Note: Some of these titles may be difficult to find, either in DVD format or streaming. Film Animation Animal Farm (1954)Based on George Orwell’s novel of the same name, farm…
THE EARLY MODERN PERIODHistory Of PhilosophyRATIONALISM
November 15, 2023

RATIONALISM

Rationalism designates a variety of philosophical schools maintaining that reason, as opposed to empirical investigation, is the most important method of acquiring knowledge.
LogicHIGHER-ORDER LOGICS
November 15, 2023

HIGHER-ORDER LOGICS

The language sketched above is better referred to as first-order predicate calculus, as the language only quantifies over (first-order) individuals. A stronger language, second-order predicate calculus, can therefore be constructed…
MEDIEVAL PHILOSOPHYHistory Of PhilosophySCHOLASTICISM
November 15, 2023

SCHOLASTICISM

A general term for those philosophers influenced by the medieval rediscovery of classic texts, Scholasticism is broadly characterized by an interest in logic and disputation and is motivated to resolve…
Writing PhilosophyESSENTIAL WRITING SKILLS
November 21, 2023

ESSENTIAL WRITING SKILLS

Having just walked through the basic process of writing a philosophy paper, we turn now to the essential skillset you should develop and apply not only to the writing of…
FORMS OF PHILOSOPHICAL WRITINGTHE PERSONAL ESSAY
November 20, 2023

THE PERSONAL ESSAY

The personal essay is a self-reflective search for meaning. Unlike most philosophical writing, it is not argumentative. Instead, it is exploratory and speculative, often even somewhat confessional. It is typically…
CLASSICAL PHILOSOPHYHistory Of PhilosophySTOICISM
November 15, 2023

STOICISM

Founded by Zeno of Citium (334–262 BC), early Stoicism shared many similarities with Epicureanism, including the belief that the world was largely deterministic and that the overall goal of the…
History Of PhilosophyPYTHAGOREANISM
November 15, 2023

PYTHAGOREANISM

Based on the teachings of Pythagoras (c. 570–495 BC) and the school he established inCroton in southern Italy, we may conclude that, in many ways, Pythagoreanism was more ofa mystery…
LogicPREDICATE CALCULUS (PREDICATE LOGIC)
November 15, 2023

PREDICATE CALCULUS (PREDICATE LOGIC)

The next development of the propositional calculus is the predicate calculus. This considers the logical relationships that hold between predicate expressions, along with the quantifiers ∃x (“there is at least…
FORMS OF PHILOSOPHICAL WRITINGWriting PhilosophyTHE POSITION PAPER
November 19, 2023

THE POSITION PAPER

A position paper may be viewed as a type of argumentative paper in that it states a claim—your position—concerning a topic, issue, or question and presents a justification for that…
STRATEGIC WRITING CHOICESWriting PhilosophySTRATEGIC WRITING CHOICES FOR PHILOSOPHY CLASS
November 18, 2023

STRATEGIC WRITING CHOICES FOR PHILOSOPHY CLASS

Writing philosophy should not be easy, but you cannot allow it to become impossible. Here are five strategic rules of thumb for embarking on a successful writing project for philosophy…

Books

  • Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets

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  • The Impact of Identity: The Power of Knowing Who You Are

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  • Creative Mythology: The Masks of God, Volume IV

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  • Meditations

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  • Why Good People Do Bad Things: Understanding Our Darker Selves

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  • Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets (Incerto)

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  • Right Thing, Right Now: Justice in an Unjust World (The Stoic Virtues Series)

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  • Ethics (Penguin Classics)

    $12.39
  • The Meditations of the Emperor Marcus Aurelius Antonius

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  • The Republic (Penguin Classics)

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  • Hospitality, Volume I (The Seminars of Jacques Derrida)

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  • Anatomy of the Spirit: The Seven Stages of Power and Healing

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  • The Call to God: An Arabic Critical Edition and English Translation of Epistle 48 (Epistles of the Brethren of Purity)

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  • My Big TOE: Discovery: Book 2 of a Trilogy Unifying Philosophy, Physics, and Metaphysics: Discovery

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  • Schopenhauer Collection: World as Will and Idea Volumes 1-3, Wisdom of Life, Counsels and Maxims, and The Art of Being Right

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The Atomos Blog

Can Math Prove Its Own Sanity? — A Deep Dive into Artemov’s Landmark Paper

Can Math Prove Its Own Sanity? — A Deep Dive into Artemov’s Landmark Paper

Philosophy StudentPhilosophy Student
Can Math Prove Its Own Sanity? — A Deep Dive into Artemov’s Landmark PaperProof TheoryUncategorized

Can Math Prove Its Own Sanity? — A Deep Dive into Artemov’s Landmark Paper

Philosophy StudentPhilosophy StudentApril 14, 2026
Philosophy of Law: An IntroductionAtomosPHILOSOPHY OF LAW

Philosophy of Law: An Introduction

Atomos EditorAtomos EditorJanuary 10, 2026
Philosophy of Science: An IntroductionAtomosPHILOSOPHY OF SCIENCE

Philosophy of Science: An Introduction

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Aesthetics: An IntroductionAESTHETICSAtomos

Aesthetics: An Introduction

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Epistemology: An IntroductionAtomosEPISTEMOLOGY

Epistemology: An Introduction

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Ethics: An IntroductionAtomosETHICS

Ethics: An Introduction

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Logic: An IntroductionAtomosLOGIC

Logic: An Introduction

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Metaphysics: An IntroductionAtomosMETAPHYSICS

Metaphysics: An Introduction

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Philosophy of History: An IntroductionAtomosPHILOSOPHY OF HISTORY

Philosophy of History: An Introduction

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Philosophy of Language: An IntroductionAtomosPHILOSOPHY OF LANGUAGE

Philosophy of Language: An Introduction

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Philosophy of Mind: An IntroductionAtomosPHILOSOPHY OF MIND

Philosophy of Mind: An Introduction

Atomos EditorAtomos EditorJanuary 10, 2026

Terms & Concepts

C

Communitarian ethic

An ethical theory that values community and communal relationships, whichform individuals. https://youtube.com/shorts/D5QXiE6fwHc?feature=share
H

Historicism

Originally the view that all human knowledge is irreducibly historical, and thus to some extent relativistic, historicism increasingly came to mean the (largely unfalsifiable) view that historical development is subject…
U

Underdetermination

A theory is said to be under determined by evidence if that evidence would provide the same degree of confirmation for a rival theory; in particular, a scientific theory that…
I
I-proposition
H
Human rights
U
Upanishads
I
Immaterialism
C
Counterfactual
H
Hume’s fork
L
Logical necessity
B
Bayes’s Theorem
S
Sorites Paradox
View All