Aesthetic Judgment First published Fri Feb 28, 2003; substantive revision Thu Jul 22, 2010 Beauty is an important part of our lives. Ugliness too. It is no surprise then that philosophers since antiquity have been interested in our experiences of and judgments about beauty and ugliness. 1. What is a judgment of taste? 1.1 Subjectivity The first necessary condition of a judgment of taste is that it is essentially subjective. This subjectivist thesis would be over-strict if it were interpreted in an “atomistic” fashion, so that some subjective response corresponds to every judgment of taste, and vice versa. However, it is not obvious what to make of the subjectivity of the judgment of taste. Beyond a certain point, this issue cannot be pursued independently of metaphysical issues about realism, for the metaphysics we favor is bound to affect our view of the nature of the pleasure we take in beauty. This is all important as far as it goes, but it is all negative. 1.2 Normativity 1.3 Recasting Normativity 2.
Set Theory First published Thu Jul 11, 2002 Set Theory is the mathematical science of the infinite. It studies properties of sets, abstract objects that pervade the whole of modern mathematics. The language of set theory, in its simplicity, is sufficiently universal to formalize all mathematical concepts and thus set theory, along with Predicate Calculus, constitutes the true Foundations of Mathematics. 1. The objects of study of Set Theory are sets. The language of set theory is based on a single fundamental relation, called membership. Basic Set Theory for further discussion. When dealing with sets informally, such operations on sets are self-evident; with the axiomatic approach, it is postulated that such operations can be applied: for instance, one postulates that for any sets A and B, the set {A,B} exists. One of the basic principles of set theory is the existence of an infinite set. for further discussion. The fundamental concept in the theory of infinite sets is the cardinality of a set. 2.
Definitions First published Thu Apr 10, 2008 Definitions have interested philosophers since ancient times. Plato's early dialogues portray Socrates raising questions about definitions (e.g., in the Euthyphro, “What is piety?”)—questions that seem at once profound and elusive. 1. Ordinary discourse recognizes several different kinds of things as possible objects of definition, and it recognizes several kinds of activity as defining a thing. In philosophy, too, several different kinds of definitions are often in play, and definitions can serve a variety of different functions (e.g., to enhance precision and clarity). 1.1 Real and nominal definitions John Locke distinguished, in his Essay, “real essence” from “nominal essence.” This characterization of the distinction is rough because a zoologist's definition of “tiger” should count as a real definition, even though it may fail to provide “the constitution of the insensible parts” of the tiger. 1.2 Dictionary definitions and ostensive definitions 2.
Cusanus, Nicolaus [Nicolas of Cusa] 1. Biography Nicholas of Cusa (Nikolaus Cryfftz or Krebs in German, then Nicolaus Cusanus in Latin) was born in 1401 in Kues (now Bernkastel-Kues) on the Moselle River between Koblenz and Trier. He was one of four children in a bourgeois family. His father, Johan Cryfftz, was a prosperous merchant who became one of the landed gentry in Trier. The first record we have of Nicholas' early education comes from his study of the liberal arts at University of Heidelburg in 1416–17. In 1425 he entered the service of the archbishop of Trier and, as his secretary, received income from several benefices. Ordained a priest sometime during the 1430s, Nicholas first gained wider notice for his work as a conciliarist at the Council of Basel. Nicholas' most important philosophical works were written in the twenty-four years between the appearance of De docta ignorantia and his death. In 1450 he was named bishop of Brixen in the Tirol. 2. 2.1 Metaphysics and ontology 2.2 The Mind and Human Knowing
Parmenides First published Fri Feb 8, 2008; substantive revision Sun Jun 3, 2012 Parmenides of Elea, active in the earlier part of the 5th c. BCE, authored a difficult metaphysical poem that has earned him a reputation as early Greek philosophy's most profound and challenging thinker. His philosophical stance has typically been understood as at once extremely paradoxical and yet crucial for the broader development of Greek natural philosophy and metaphysics. He has been seen as a metaphysical monist (of one stripe or another) who so challenged the naïve cosmological theories of his predecessors that his major successors among the Presocratics were all driven to develop more sophisticated physical theories in response to his arguments. 1. The dramatic occasion of Plato's dialogue, Parmenides, is a fictionalized visit to Athens by the eminent Parmenides and his younger associate, Zeno, to attend the festival of the Great Panathenaea. 2. 2.1 The Proem 2.2 The Ways of Inquiry 2.3 The Way of Conviction
Zeno of Elea First published Wed Jan 9, 2008; substantive revision Wed Jan 11, 2012 Zeno of Elea, 5th c. B.C.E. thinker, is known exclusively for propounding a number of ingenious paradoxes. 1. The dramatic occasion of Plato's dialogue, Parmenides, is a visit to Athens by the eminent philosopher Parmenides and Zeno, his younger associate, to attend the festival of the Great Panathenaea. Plato's Parmenides depicts Socrates going as a young man to hear Zeno reading from the famous book he has brought to Athens for the first time. Once Socrates had heard it, he asked Zeno to read the first hypothesis of the first argument again, and, after it was read, he said: “What do you mean by this, Zeno? While the later tradition unreliably ascribes other works to Zeno, there is some interesting evidence in the commentary on the Parmenides by the Athenian Neoplatonist Proclus (5th c. 2. 2.1 The Arguments Against Plurality 2.1.1 The Antinomy of Limited and Unlimited 2.1.2 The Antinomy of Large and Small
Aristotle First published Thu Sep 25, 2008 Aristotle (384–322 B.C.E.) numbers among the greatest philosophers of all time. Judged solely in terms of his philosophical influence, only Plato is his peer: Aristotle's works shaped centuries of philosophy from Late Antiquity through the Renaissance, and even today continue to be studied with keen, non-antiquarian interest. A prodigious researcher and writer, Aristotle left a great body of work, perhaps numbering as many as two-hundred treatises, from which approximately thirty-one survive.[1] His extant writings span a wide range of disciplines, from logic, metaphysics and philosophy of mind, through ethics, political theory, aesthetics and rhetoric, and into such primarily non-philosophical fields as empirical biology, where he excelled at detailed plant and animal observation and taxonomy. Because of its wide range and its remoteness in time, Aristotle's philosophy defies easy encapsulation. 1. 2. Organon Categories (Cat.) 3.
Aristotle's Logic 1. Introduction Aristotle’s logical works contain the earliest formal study of logic that we have. It is therefore all the more remarkable that together they comprise a highly developed logical theory, one that was able to command immense respect for many centuries: Kant, who was ten times more distant from Aristotle than we are from him, even held that nothing significant had been added to Aristotle’s views in the intervening two millennia. In the last century, Aristotle’s reputation as a logician has undergone two remarkable reversals. 2. The ancient commentators grouped together several of Aristotle’s treatises under the title Organon (“Instrument”) and regarded them as comprising his logical works: Categories On Interpretation Prior Analytics Posterior Analytics Topics On Sophistical Refutations 3. All Aristotle’s logic revolves around one notion: the deduction (sullogismos). The core of this definition is the notion of “resulting of necessity” (ex anankês sumbainein). 4. 4.1 Terms 5.
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