Graphs and paradoxes

A directed graph is a pair where N is any collection or set of objects (the nodes of the graph) and E is a relation on N (the edges). Intuitively speaking, we can think of a directed graph in terms
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A directed graph is a pair <N, E> where N is any collection or set of objects (the nodes of the graph) and E is a relation on N (the edges). Intuitively speaking, we can think of a directed graph in terms of a dot-and-arrow diagram, where the nodes are represented as dots, and the edges are represented as arrows. For example, in the following figure we have a graph that consists of three nodes–A, B, and C, and four edges: one from A to A, one from A to B, one from B to C, and one from C to B. Image courtesy of author. Note that with directed graphs we distinguish between those cases where a node has an arrow from itself to itself and those cases where it does not, and we also take into account the direction of the edge–that is, the edge from B to C is distinct from the edge from C to B (we do, however, represent cases where we have arrows going in both directions with a single line with two “arrowheads”). In the diagram above, the nodes might represent Alice, Betty,. . .

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News source: OUPblog » Philosophy

Immunology in perspective

Among students of science, in contrast to those who do science, the dominant discussion revolves around the degree to which scientific interpretations are subject to extra-curricular influences,
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Among students of science, in contrast to those who do science, the dominant discussion revolves around the degree to which scientific interpretations are subject to extra-curricular influences, specifically, to what extent are facts independent of the larger political context in which science resides. (Political refers to the economic costs and benefits measured as improved health, productivity, military defense, etc.; promotion of ideological commitments; corporate advancement; social flourishing, and the like.) The question is not just applicable to understanding how science makes its truth claims, but represents a general quandary: Scientists, historians, lawyers–all citizens–constantly face the task of drawing the line around credible disputes over the standing of facts and their meaning, which ultimately determines their status as “true.” This matter is posed throughout our culture. Indeed, in whatever endeavor we engage, assumptions are made about the reality of our. . .

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News source: OUPblog » Philosophy

Voltaire thought Shakespeare "a drunken savage&rdquo;; Mencken dismissed Gatsby as a "glorified anecdote." Why <strong>great critics make terrible judgments</strong>

Voltaire thought Shakespeare &quot;a drunken savage&amp;rdquo;; Mencken dismissed Gatsby as a &quot;glorified anecdote.&quot; Why great critics make terrible
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Voltaire thought Shakespeare "a drunken savage”; Mencken dismissed Gatsby as a "glorified anecdote." Why great critics make terrible judgments

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News source: Arts & Letters Daily

At 15, he was a member of the Hitler Youth. At 24, he attacked Heidegger for sympathizing with Nazism. The complicated moral development of <strong>J&uuml;rgen Habermas</strong>

At 15, he was a member of the Hitler Youth. At 24, he attacked Heidegger for sympathizing with Nazism. The complicated moral development of J&amp;uuml;rgen
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At 15, he was a member of the Hitler Youth. At 24, he attacked Heidegger for sympathizing with Nazism. The complicated moral development of Jürgen Habermas

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News source: Arts & Letters Daily

In the mid-60s, <strong>Norman Podhoretz</strong> gave up on becoming the next Lionel Trilling. Instead he wrote about ambition, alienating almost everyone he knew

In the mid-60s, Norman Podhoretz gave up on becoming the next Lionel Trilling. Instead he wrote about ambition, alienating almost everyone he
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In the mid-60s, Norman Podhoretz gave up on becoming the next Lionel Trilling. Instead he wrote about ambition, alienating almost everyone he knew

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News source: Arts & Letters Daily

Sanctuary & Religious Liberty

Embed from Getty Images As the Trump administration steps up the enforcement of immigration law, some illegal immigrants have engaged in the time-honored tradition of seeking sanctuary in churches.
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Embed from Getty Images As the Trump administration steps up the enforcement of immigration law, some illegal immigrants have engaged in the time-honored tradition of seeking sanctuary in churches. The idea of churches serving as sanctuary from the state was developed in Western Europe during the Middle Ages and has become embedded in western culture. As would be expected, the granting of sanctuary has created considerable controversy. Being familiar with the history of oppressive states and injustice, I generally support the idea of sanctuary in its role of providing the individual with another defense against the potential tyranny of the state. Because of this view, I hold that sanctuary should be limited to those who need protection from injustice on the part of the state rather than endorsing blanket sanctuary for anyone for any reason. Judging who is thus worthy of sanctuary (as with any moral assessment) can be rather complicated, but the basic principle is clear enough.. . .

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News source: Talking Philosophy

Formal Learning Theory

[Revised entry by Oliver Schulte on February 17, 2017. Changes to: Main text, Bibliography] Formal learning theory is the mathematical embodiment of a normative epistemology. It deals with the
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[Revised entry by Oliver Schulte on February 17, 2017. Changes to: Main text, Bibliography] Formal learning theory is the mathematical embodiment of a normative epistemology. It deals with the question of how an agent should use observations about her environment to arrive at correct and informative conclusions. Philosophers such as Putnam, Glymour and Kelly have developed learning theory as a normative framework for scientific reasoning and inductive inference....

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News source: Stanford Encyclopedia of Philosophy

Virtual Colloquium: Craig E. Bacon, “Proportionality, Maximization, and the Highest Good”

Welcome again to the Prosblogion Virtual Colloquium! This week&amp;#8217;s paper is &amp;#8220;Proportionality, Maximization, and the Highest Good&amp;#8221; by Craig E. Bacon. Bacon is a PhD candidate at the
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Welcome again to the Prosblogion Virtual Colloquium! This week’s paper is “Proportionality, Maximization, and the Highest Good” by Craig E. Bacon. Bacon is a PhD candidate at the University of South Carolina. His dissertation is entitled The Life of Virtue: Moral Progress and Kant’s Idea of the Highest Good, and is scheduled to be defended [...]

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News source: The Prosblogion

Juan Luis Vives in Paris, Erasmus in Venice. Does the <strong>mobility of 16th-century intellectuals</strong> explain Europe&rsquo;s rise in fortunes?

Juan Luis Vives in Paris, Erasmus in Venice. Does the mobility of 16th-century intellectuals explain Europe&amp;rsquo;s rise in
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Juan Luis Vives in Paris, Erasmus in Venice. Does the mobility of 16th-century intellectuals explain Europe’s rise in fortunes?

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News source: Arts & Letters Daily

The self-righteousness of <strong>literary style guides</strong>. They offer advice like &ldquo;avoid fancy words&rdquo; but often fail to practice what they preach

The self-righteousness of literary style guides. They offer advice like &amp;ldquo;avoid fancy words&amp;rdquo; but often fail to practice what they
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The self-righteousness of literary style guides. They offer advice like “avoid fancy words” but often fail to practice what they preach

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News source: Arts & Letters Daily