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Viewing: Blog Posts Tagged with: logic, Most Recent at Top [Help]
Results 1 - 18 of 18
1. A Puzzle for the Senses

casesense_cover

When you visit your favorite restaurant can you smell the food even before walking inside? Can you feel the difference between the soft fur of a puppy and the cold wet nose? If a bright red bird swoops by, can you identify what kind of bird it is just by color? Should you pay to use your senses?

That is the premise for A Case of Sense; a new book by author Songju Ma Daemicke illustrated by Shennen Bersani. The book opens with a young boy playing outside, and greedy Fu Wang has cooked wonderful Chinese dishes with the smells wafting throughout town. He announces that the townspeople must pay for the smells and when they don’t he takes everyone to court! The judge has a clever way to deal with the case and readers might use a little logical reasoning to figure out the puzzle.

Saturday, Songju will be signing at the ISLMA conference in Tinley Park, IL from 2pm-4pm. In celebration, we have a fun little puzzle in logic and sight that might keep kids coloring for a little while!

rainbow-sudoku

Get out the markers or the crayons and color in the missing spaces. Remember that all the colors will be rows, columns, and squares of 9 without repeating!

Download the printable PDF version! 

Download the answers here!


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2. A person-less variant of the Bernadete paradox

Before looking at the person-less variant of the Bernedete paradox, lets review the original: Imagine that Alice is walking towards a point – call it A – and will continue walking past A unless something prevents her from progressing further.

The post A person-less variant of the Bernadete paradox appeared first on OUPblog.

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3. Is “Nothing nothings” true?

In a 1929 lecture, Martin Heidegger argued that the following claim is true: Nothing nothings. In German: “Das Nichts nichtet”. Years later Rudolph Carnap ridiculed this statement as the worst sort of meaningless metaphysical nonsense in an essay titled “Overcoming of Metaphysics Through Logical Analysis of Language”. But is this positivistic attitude reasonable?

The post Is “Nothing nothings” true? appeared first on OUPblog.

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4. What might superintelligences value?

If there were superintelligent beings – creatures as far above the smartest human as that person is above a worm – what would they value? And what would they think of us? Would they treasure, tolerate, ignore, or eradicate us?

The post What might superintelligences value? appeared first on OUPblog.

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5. Paradoxes logical and literary

For many months now this column has been examining logical/mathematical paradoxes. Strictly speaking, a paradox is a kind of argument. In literary theory, some sentences are also called paradoxes, but the meaning of the term is significantly different.

The post Paradoxes logical and literary appeared first on OUPblog.

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6. The strange case of the missing non-existent objects

Alexius Meinong (1853-1920) was an Austrian psychologist and systematic philosopher working in Graz around the turn of the 20th century. Part of his work was to put forward a sophisticated analysis of the content of thought. A notable aspect of this was as follows. If you are thinking of the Taj Mahal, you are thinking of something, and that something exists.

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7. Deductive Detectives

Image

“Eliminate all other factors, and the one which remains must be the truth,” Sherlock Holmes has said about his method of detective work. In Sylvan Dell’s new picture book, Deductive Detective, our hero Detective Duck shows that he’s learned from the best! He dons his best deerstalker hat, his much-too-big magnifying glass, and solves the case of the missing cake with the same methods the pros use!

That is, a style of logical thinking called “deductive reasoning.” In deductive reasoning, someone finds an answer they’re looking for by first finding out what the answer isn’t. When Detective Duck examines the clues and finds out which of his friends couldn’t have stolen the cake, it leads him closer to what really happened!

Of course, you don’t need a weird hat and a magnifying glass to use deductive reasoning. These methods come in handy every day! If you lose a toy, for example (or car keys), you may make your search easier by determining where the item isn’t.

“Oh yeah,” you may say, “I didn’t bring it to my friend’s house; I wasn’t holding it when I walked to the living room, or landed on the moon. I wouldn’t have brought it to my parents’ room or under the ocean or into Mordor.” By deciding where you shouldn’t look, you now have a better idea of where you should.

This kind of logic process happens throughout the day, sometimes without you even being aware of it; you might say your brain is always on the case as much as any detective!

Apply deductive reasoning the next time you’re in the bookstore: subtract the books that don’t meet the highest educational standards, offer pages of activities and facts, offer online supplements, are fun to look at and fun to read! You’ll be left with books by Sylvan Dell like The Deductive Detective!


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8. Cloak, Cape or Hood: Writing Consistent Fiction


Goodreads Book Giveaway

Start Your Novel by Darcy Pattison

Start Your Novel

by Darcy Pattison

Giveaway ends October 01, 2013.

See the giveaway details at Goodreads.

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In this January 6, 2013 NPR interview, John Sandys talks about inconsistencies in movies that were released in 2012:

Well, I think ’cause “Men in Black 3″ travels back and forth in time, it means you’ve got a whole host of factual mistakes as well, which it opens itself up to. One which jumped at me was in Cape Canaveral in 1969, we see the flag of Spain waving, but it’s the wrong flag. It’s the current era flag, not the 1969-era flag. I mean, it’s hardly a major research job. I don’t know whether they thought it wasn’t worth looking into or they just thought, well, no one will care.

This week, I am doing a final pass through of a novel and finding tons of inconsistencies.

For example, the main character shows up in a cloak and a scarf wrapped around her head. But at the beginning of the next scene, which is a direct follow-up, she throws back her hood and takes off her cloak. In another scene, she is described as wearing a cape.

(I know: Capes are soooo out of style.)

Reading and revising for consistency of details is different than reading for story. Here are a few tips:

  1. Put on your editor’s hat. This isn’t the time to worry about the story line, characterization, plot or those other big issues. Instead, you need to be very logical and you need to pay attention. That requires a different mindset.
  2. Take notes. I use sticky notes, but you could use just a sheet of paper to jot notes. As I read along, I jot down anything that sounds fishy to me, or I am uncertain of consistency through out the manuscript: numbers, names, eye color, hair color, peculiar or unusual wordings, etc. For complicated books or series, some suggest a Story Bible, or a place where you record all such details. For this story, I didn’t feel the need for something that structured. But in an upcoming series, I will definitely go that route.
  3. Timeline. Lots of what I am doing this week is tightening the time line. I had to cut some scenes and that left my character at a loss for an afternoon and evening. So, I moved some scenes to fill in those spaces. Often, I will literally fill in a calendar for the final timeline (after the major revisions), and often it will be hour by hour. I know I planned it all out before, but the revisions make a difference. So, I do it again.
  4. Words and phrases. I also make sure I haven’t repeated a word or phrase too often. It’s hard to describe how this one works, but you sorta have a watcher in your head paying attention to how a story is told. And it will go, “Whoa! Stop right there, little missy.” So, I stop and correct. It’s paying attention to the difference between work table and workbench.
  5. Logic. It’s important for every action to be in the correct time order and to be logical. Clarity rules on this pass through. You can’t hit a ball with a bat if you haven’t picked up a bat first.

Of course, I am making these types of decisions as I write the manuscript, but I’ve found I need one last run through. What else do you check for in your last pass through a manuscript?

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9. Why study paradoxes?

Why should you study paradoxes? The easiest way to answer this question is with a story:

In 2002 I was attending a conference on self-reference in Copenhagen, Denmark. During one of the breaks I got a chance to chat with Raymond Smullyan, who is amongst other things an accomplished magician, a distinguished mathematical logician, and perhaps the most well-known popularizer of `Knight and Knave’ (K&K) puzzles.

K&K puzzles involve an imaginary island populated by two tribes: the Knights and the Knaves. Knights always tell the truth, and Knaves always lie (further, members of both tribes are forbidden to engage in activities that might lead to paradoxes or situations that break these rules). Other than their linguistic behavior, there is nothing that distinguishes Knights from Knaves.

Typically, K&K puzzles involve trying to answer questions based on assertions made by, or questions answered by, an inhabitant of the island. For example, a classic K&K puzzle involves meeting an islander at a fork in the road, where one path leads to riches and success and the other leads to pain and ruin. You are allowed to ask the islander one question, after which you must pick a path. Not knowing to which tribe the islander belongs, and hence whether she will lie or tell the truth, what question should you ask?

(Answer: You should ask “Which path would someone from the other tribe say was the one leading to riches and success?”, and then take the path not indicated by the islander).

Back to Copenhagen in 2002: Seizing my chance, I challenged Smullyan with the following K&K puzzle, of my own devising:

There is a nightclub on the island of Knights and Knaves, known as the Prime Club. The Prime Club has one strict rule: the number of occupants in the club must be a prime number at all times.

Pythagoras paradox.png
Pythagoras paradox, by Jan Arkesteijn (own work). Public domain via Wikimedia Commons.

The Prime Club also has strict bouncers (who stand outside the doors and do not count as occupants) enforcing this rule. In addition, a strange tradition has become customary at the Prime Club: Every so often the occupants form a conga line, and sing a song. The first lyric of the song is:

“At least one of us in the club is a Knave.”

and is sung by the first person in the line. The second lyric of the song is:

“At least two of us in the club are Knaves.”

and is sung by the second person in the line. The third person (if there is one) sings:

“At least three of us in the club are Knaves.”

And so on down the line, until everyone has sung a verse.

One day you walk by the club, and hear the song being sung. How many people are in the club?

Smullyan’s immediate response to this puzzle was something like “That can’t be solved – there isn’t enough information”. But he then stood alone in the corner of the reception area for about five minutes, thinking, before returning to confidently (and correctly, of course) answer “Two!”

I won’t spoil things by giving away the solution – I’ll leave that mystery for interested readers to solve on their own. (Hint: if the song is sung with any other prime number of islanders in the club, a paradox results!) I will note that the song is equivalent to a more formal construction involving a list of sentences of the form:

At least one of sentences S1 – Sn is false.

At least two of sentences S1 – Sn is false.

————————————————

At least n of sentences S1 – Sn is false.

The point of this story isn’t to brag about having stumped a famous logician (even for a mere five minutes), although I admit that this episode (not only stumping Smullyan, but meeting him in the first place) is still one of the highlights of my academic career.

Frances MacDonald - A Paradox 1905.jpg
Frances MacDonald – A Paradox 1905, by Frances MacDonald McNair. Public domain via Wikimedia Commons.

Instead, the story, and the puzzle at the center of it, illustrates the reasons why I find paradoxes so fascinating and worthy of serious intellectual effort. The standard story regarding why paradoxes are so important is that, although they are sometimes silly in-and-of-themselves, paradoxes indicate that there is something deeply flawed in our understanding of some basic philosophical notion (truth, in the case of the semantic paradoxes linked to K&K puzzles).

Another reason for their popularity is that they are a lot of fun. Both of these are really good reasons for thinking deeply about paradoxes. But neither is the real reason why I find them so fascinating. The real reason I find paradoxes so captivating is that they are much more mathematically complicated, and as a result much more mathematically interesting, than standard accounts (which typically equate paradoxes with the presence of some sort of circularity) might have you believe.

The Prime Club puzzle demonstrates that whether a particular collection of sentences is or is not paradoxical can depend on all sorts of surprising mathematical properties, such as whether there is an even or odd number of sentences in the collection, or whether the number of sentences in the collection is prime or composite, or all sorts of even weirder and more surprising conditions.

Other examples demonstrate that whether a construction (or, equivalently, a K&K story) is paradoxical can depend on whether the referential relation involved in the construction (i.e. the relation that holds between two sentences if one refers to the other) is symmetric, or is transitive.

The paradoxicality of still another type of construction, involving infinitely many sentences, depends on whether cofinitely many of the sentences each refer to cofinitely many of the other sentences in the construction (a set is cofinite if its complement is finite). And this only scratches the surface!

The more I think about and work on paradoxes, the more I marvel at how complicated the mathematical conditions for generating paradoxes are: it takes a lot more than the mere presence of circularity to generate a mathematical or semantic paradox, and stating exactly what is minimally required is still too difficult a question to answer precisely. And that’s why I work on paradoxes: their surprising mathematical complexity and mathematical beauty. Fortunately for me, there is still a lot of work remains to be done, and a lot of complexity and beauty remaining to be discovered.

The post Why study paradoxes? appeared first on OUPblog.

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10. The construction of the Cartesian System as a rival to the Scholastic Summa

René Descartes wrote his third book, Principles of Philosophy, as something of a rival to scholastic textbooks. He prided himself in ‘that those who have not yet learned the philosophy of the schools will learn it more easily from this book than from their teachers, because by the same means they will learn to scorn it, and even the most mediocre teachers will be capable of teaching my philosophy by means of this book alone’ (Descartes to Marin Mersenne, December 1640).

Still, what Descartes produced was inadequate for the task. The topics of scholastic textbooks ranged much more broadly than those of Descartes’ Principles; they usually had four-part arrangements mirroring the structure of the collegiate curriculum, divided as they typically were into logic, ethics, physics, and metaphysics.

But Descartes produced at best only what could be called a general metaphysics and a partial physics.

Knowing what a scholastic course in physics would look like, Descartes understood that he needed to write at least two further parts to his Principles of Philosophy: a fifth part on living things, i.e., animals and plants, and a sixth part on man. And he did not issue what would be called a particular metaphysics.

Frans_Hals_-_Portret_van_René_Descartes
Portrait of René Descartes by Frans Hans. Public domain via Wikimedia Commons.

Descartes, of course, saw himself as presenting Cartesian metaphysics as well as physics, both the roots and trunk of his tree of philosophy.

But from the point of view of school texts, the metaphysical elements of physics (general metaphysics) that Descartes discussed—such as the principles of bodies: matter, form, and privation; causation; motion: generation and corruption, growth and diminution; place, void, infinity, and time—were usually taught at the beginning of the course on physics.

The scholastic course on metaphysics—particular metaphysics—dealt with other topics, not discussed directly in the Principles, such as: being, existence, and essence; unity, quantity, and individuation; truth and falsity; good and evil.

Such courses usually ended up with questions about knowledge of God, names or attributes of God, God’s will and power, and God’s goodness.

Thus the Principles of Philosophy by itself was not sufficient as a text for the standard course in metaphysics. And Descartes also did not produce texts in ethics or logic for his followers to use or to teach from.

These must have been perceived as glaring deficiencies in the Cartesian program and in the aspiration to replace Aristotelian philosophy in the schools.

So the Cartesians rushed in to fill the voids. One could mention their attempts to complete the physics—Louis de la Forge’s additions to the Treatise on Man, for example—or to produce more conventional-looking metaphysics—such as Johann Clauberg’s later editions of his Ontosophia or Baruch Spinoza’s Metaphysical Thoughts.

Cartesians in the 17th century began to supplement the Principles and to produce the kinds of texts not normally associated with their intellectual movement, that is treatises on ethics and logic, the most prominent of the latter being the Port-Royal Logic (Paris, 1662).

By the end of the 17th century, the Cartesians, having lost many battles, ulti­mately won the war against the Scholastics.

The attempt to publish a Cartesian textbook that would mirror what was taught in the schools culminated in the famous multi-volume works of Pierre-Sylvain Régis and of Antoine Le Grand.

The Franciscan friar Le Grand initially published a popular version of Descartes’ philosophy in the form of a scholastic textbook, expanding it in the 1670s and 1680s; the work, Institution of Philosophy, was then translated into English together with other texts of Le Grand and published as An Entire Body of Philosophy according to the Principles of the famous Renate Descartes (London, 1694).

On the Continent, Régis issued his General System According to the Principles of Descartes at about the same time (Amsterdam, 1691), having had difficulties receiving permission to publish. Ultimately, Régis’ oddly unsystematic (and very often un-Cartesian) System set the standard for Cartesian textbooks.

By the end of the 17th century, the Cartesians, having lost many battles, ulti­mately won the war against the Scholastics. The changes in the contents of textbooks from the scholastic Summa at beginning of the 17th century to the Cartesian System at the end can enable one to demonstrate the full range of the attempted Cartesian revolution whose scope was not limited to physics (narrowly conceived) and its epistemology, but included logic, ethics, physics (more broadly conceived), and metaphysics.

Headline image credit: Dispute of Queen Cristina Vasa and René Descartes, by Nils Forsberg (1842-1934) after Pierre-Louis Dumesnil the Younger (1698-1781). Public domain via Wikimedia Commons.

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11. The paradox of generalizations about generalizations

A generalization is a claim of the form: (1) All A’s are B’s. A generalization about generalizations is thus a claim of the form: (2) All generalizations are B. Some generalizations about generalizations are true. For example: (3) All generalizations are generalizations. And some generalizations about generalizations are false. For example: (4) All generalizations are false. In order to see that (4) is false, we could just note that (3) is a counterexample to (4).

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12. What made Russell feel ready for suicide?

In early May 1913 Bertrand Russell sat down to write a book on the theory of knowledge, his first major philosophical work after Principia Mathematica. He set a brisk pace for himself – ten pages a day at first, up to twelve by mid-May. He was “bursting with work” and “felt happy as king”. By early June he had 350 pages. 350 pages in one month!He never finished the manuscript. Some parts of it were published as journal articles, but the book itself was never completed. (It was later published posthumously under the title Theory of Knowledge.) What went wrong?

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13. The role of logic in philosophy: A Q&A with Elijah Millgram

Elijah Millgram, author of The Great Endarkenment, Svantje Guinebert, of the University of Bremen, to answer his questions and discuss the role of logic in philosophy. On other occasions, you’ve said that logic, at least the logic that most philosophers are taught, is stale science, and that it’s getting in the way of philosophers learning about newer developments. But surely logic is important for philosophers. Would you like to speak to the role of logic in philosophy?

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14. A Yabloesque variant of the Bernardete Paradox

Here I want to present a novel version of a paradox first formulated by José Bernardete in the 1960s – one that makes its connections to the Yablo paradox explicit by building in the latter puzzle as a ‘part’. This is not the first time connections between Yablo’s and Bernardete’s puzzles have been noted (in fact, Yablo himself has discussed such links). But the version given here makes these connections particularly explicit.

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15. Brain Twisters of a Different Kind

 

I thought I’d share a few thoughts with you today about those wee niggling puzzles that we all run around inside our heads when they’re brought to our attention.

Oh, don’t worry. I’m not going to go through the whole catalogue of examples. No. I will only choose a few, just to get people thinking about how we communicate with each other and the world and question how figures of speech get created.

Yes, you guessed it. I refer to those pesky oxymorons that tend to make us all look like morons when we use them. Oh, I know. Army Intelligence is one of the best examples around and one of the most widely used.

I want to talk about some of the frequently overlooked, but just as viable, examples instead.

First one up–Is it good if a vacuum really sucks? Now think about this. Is it? Of course, you say. That’s its function–sucking up the dirt. But, I say, that’s not the point. If it really sucks, it’s not doing its job, now is it? And yet, looked at from a different angle with a different tone of voice, it could mean that’s exceptionally efficient. So, which is meant here with the original question?

Second up–If a word is misspelled in the dictionary, how would we ever know? Now I admit, this one takes some consideration. It asks a legitimate question related to language. If the premier dictionary has always spelled a word a certain way with a specific definition, can we really be sure that it’s truly supposed to be spelled that way? What if the thesaurus spells it a different way. Isn’t it a case of tear and tier. The words mean entirely different things. Yet, how can we be certain that the word originally used for that meaning was spelled that way. Language evolves over time, after all. Just saying…

Next up–What is a whack and how can something be out of it? Anyone know? Please, clue me in. I’ve always wanted to know what a whack looked like.

Going on to–Doesn’t “expecting the unexpected” make the unexpected expected? Tongue twister time. Logic dictates that this is an impossibility, yet we use it, understand it’s meaning and directive. Then again, perhaps as we began to live by this motto, we also began our slide into nervous exhaustion, insomnia, paranoia, and assorted other disturbing conditions. If you’re always expecting something to happen without warning, aren’t you constantly in fight/flight response mode? Therefore, the very act of being prepared brings us to our knees with a variety of psychological problems.

And last for today–If all the world’s a stage, where is the audience sitting? This one is a real teaser in its own way. It’s very meaning says that each of us is both actor and audience member in the same instant. How can we possibly criticize those around us, or applaud them, if we are being judged for each moment of our own lives at the same time? Makes a person think, doesn’t it?

So consider some of those oxymorons that have cluttered your brain’s logic center for a while. Decide just what they ask, how they ask the question–if there is one–and how people respond to them. I’d be willing to bet that the average person doesn’t recognize them most of the time, much less think about them.

While you’re doing that, I’ll say a bientot,

Clauds


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16. Don’t Lose It—Use It! Practice Math Thinking in the Summer


The beginning of summer is the season of reading lists. You can find them everywhere, suggestions of media with which students and other active thinkers can exercise their minds free from the confines of a syllabus. Novels will help you develop reading and English skills. Anything from podcasts to comic books can support your learning of a foreign language. But how can students of mathematics develop, refine, and utilize math skills independently? It probably seems more difficult to practice math during the summer months.

Here are five fun, engaging activities to nourish your mind’s mathematical needs.

1. Sudoku and KenKen
Celebrated and distributed by many newspapers, including The New York Times, Sudoku and KenKen are mathematical grid-based games that develop skills of analytical assessment, logical thinking, and the very useful process of elimination. KenKen has the added bonus of using calculations. These puzzles are plentiful (and usually free) online and in collections in book stores, and they can be found in every degree of difficulty from very simple to extremely difficult.

2. Books by Louis Sachar
For elementary and middle school students with a wacky sense of humor, try Louis Sachar’s Sideways Arithmetic from Wayside School, a delightfully mathematical companion to his zany and entertaining story collection Sideways Stories from Wayside School. Sideways Arithmetic and its sequel are dense with clever, challenging puzzles that demand creativity and logic and elegantly set a basis for algebraic rigor.

3. Sets game
The Sets game is rich with mathematical thought, yet completely free of calculations. It involves matching sets of three cards which are either all the same or all different in each of four categories: shading, shape, cardinality, and color. It can be played alone or with any number of friends. The New York Times also offers free daily Sets puzzles.


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17. Logical Nonfiction

Anastasia Suen answers the question, "What Do Editors Want to See?" in Chapter Three of Picture Writing: A New Approach to Writing for Kids and Teens. On page 72 she says: When it comes to nonfiction, editors want to see logic. For a nonfiction book to work, it needs to be well organized. Simply gathering lots of information is not enough. To share information with your readers, you must

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18. Infinite Space, Infinite God II: An Exercise in Logic

 12 days of sci-fi day 3:

Nuns are people too, and we are given a view of the diversity of personalities who are called to the religious life as the stories move from Antivenin to An Exercise in Logic. Parents should be apprised that the salty ship commander engages in mild cussing akin to a John Wayne style character, but only a few instances…

 An Exercise in Logic by Barton Paul Levenson

RESPECT FOR OTHERS

 Editor’s comment: “She holds herself with the dignity of her position as both a nun and a diplomat, yet is willing to bend–whether that means by sneaking out in defiance of the mission  commander’s orders or going to her knees to pray when logic seems to fail her. “

 How many times, when trying to get a point across in a conversation with someone of a totally different life experience, we have said it to be alien or foreign to them? In this story, trying to explain Christianity to people raised in secluded colonies is a bit like trying to explain a life of freedom to someone whose lifelong existence has been dictated under communist rule. But even more difficult is being the foreigner…the one who cannot comprehend the faith belief being explained. A nun and expert on alien religions, Sr. Julian is called in to negotiate with a group of aliens whose obedience to the decisions and words of their ancestors is taken to the extreme, and she has a short time to learn their religion in order to prove them illogical.  Aristotle is oft quoted as saying “It is the mark of an educated mind to be able to entertain a thought without accepting it.”, and this story demonstrates how respectful discourse rather than angry debate can lead to Truth. For those who like stories of intellect and strategy, this one is for you! Pick up the entire anthology at Amazon http://ow.ly/4F48e .

 (About the author: Barton has a degree in physics. Happily married to genre poet Elizabeth Penrose, he confuses everybody by being both a born-again Christian and a liberal Democrat. His work has appeared in Marion Zimmer Bradley’s Fantasy Magazine, ChiZine, Cricket, Cicada, The New York Review of Science Fiction and many small press markets. His e-novels, “Ella the Vampire,” “Parole,” and “Max and Me” can be downloaded now from Lyrical Press or amazon.com, and his first paperback, “I Will” is available from Virtual Tales (or amazon).   Barton was prohibited from entering the Confluence Short Story Contest again after winning first prize two years in a row.)

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