Deduction: Deductively Valid & Deductively Sound

Deduction is the process of reasoning from one or more premises to reach a logically certain conclusion. Hence, a deductive argument is one in which if the premises were true, then the conclusion must also be true. This certainty is what distinguishes deductive arguments from other argument forms.

In informal logic circles, the term cogent is typically used to describe a good argument. To some degree, this seems to be an attempt to accommodate deductive and inductive reasoning with a simple set of common terms. Among formal logicians, the word cogent is not commonly used. Instead the terms valid and sound are the standard. 

Deductively Valid Arguments - A valid deductive argument is one in which, if the premises were true, then the conclusion must also be true. The premises deductively entail the conclusion so that it would be impossible for it to be false.  Another way to think about it is to say that with deductively valid arguments, the premises support the conclusion 100%. If the argument does not meet these conditions then it is said to be deductively invalid. The terms valid and invalid refer to the relationship between the premises and the conclusion refereed to as the inference.

To asses whether an argument is valid, simply assume that the premises are all true (whether they are or not) and consider if it would still be possible for the conclusion to be false. If it is possible for the conclusion to be false, the argument is invalid. If it is not possible, it is a deductively valid argument.

Applying this concept to our informal logic model we find that a deductively valid argument is one in which the relevancy and sufficient grounds criteria are completely satisfied.


Deductively Sound Arguments - A deductively sound argument is one in which the argument is valid and all of it's premises are actually true. Hence, the arguments conclusion is true.

If the argument has one or more false premises, is invalid, or both, it is deductively unsound.

For instance, if I present the argument:

P1 If I can fly over this building, I am Superman.
P2 I can fly over this building.
C  I am Superman.

This is a deductively valid argument since the form of the argument is such that if the premises were true, the conclusion must also be true. It is of course an unsound argument since one or more of it's premises are not true.

Applying the concept of soundness to the informal logic model we find that arguments that are sound qualify as cogent. There are, however, arguments that qualify as cogent in the ARG sense and do not qualify as sound in the classical sense. One reason is that the standard used to evaluate premises in formal logic is whether they are true or not true. In informal logic, premises are judged by the less stringent criteria of being either acceptable or unacceptable.

The two types of deductive arguments are categorical syllogisms and propositional arguments.

Deductive Reasoning: Wikipedia
Internet Encyclopedia of Philosophy: Validity and Soundness
A Practical Study of Arguments, Trudy Govier

The Price of Education (revisited)

Back in 2011 I wrote blog entry on how the average cost of a four year degree had tripled in inflation adjusted dollars from 1980 to 2010. So has there been any change in the three years since? For the most part, not really.

The following table from collegeboard.org provides the average tuition/fees and room/board charges from 1971-72 to 2013-14. The data is provides in inflation adjusted 2013 dollars.



As the bottom line indicates, over the last five years average tuition and fees increased another 27%. I seem to remember reading an article within the last year which indicated there was a slowdown in tuition increases which this data doesn't jive with, so I took a glance at the full report and found that there has been a trend of decreasing annual rate increases. The one year change from 2009-10 was 9.5%, 2010-11 6.5%, 2011-12 4.7%, 2012-13 3.1%, 2013-14 0.9%. Does this mean tuition has now leveled out and will just keep pace with inflation? Not necessarily. If you look at the data from my original post you find that annual rate increases do jump around. For instance, in 2008-09 the percentage change was 0.8% only to be followed with a whopping 9.3% increase the next year.

Even if education prices level out it is already an incredibly expensive investment and the young people who have to decide whether to make it are typically ill equipped to do so. Though many of them have financially experienced, caring parents who will help guide them along, it is probably true that just as many do not. And the complete lack of financial/accounting education in high school means that these youngsters typically have no ability to understand the long term effects of having this amount of debt.

BOUNCE: Guillaume Blanchet

Blend two years of traveling, a soccer ball, lots of editing and what do you get? If you're Guillaume Blanchet the result is a happiness producing, brilliant short film.

Find more about  Guillaume Blanchet here.


BOUNCE - This is not a freestyle movie from Guillaume Blanchet I Filmmaker on Vimeo.

Accidental/Perspective Illusions

Image dump of various accidental or timing illusions.

2014 Illusion of the Year Winner: Dynamic Ebbinghaus

The winner of the Best Illusion of the Year contest goes to Christopher D. Blair, Gideon P. Caplovitz, and Ryan E.B. Mruczek of the University of Nevada for an animated version of the Ebbinghaus illusion.

The classic Ebbinghaus is an illusion of relative size perception in which two identical circles are placed near to each other with one surrounded by large circles and the other surrounded by small circles. The size difference between the surrounding circles causes the center circles to appear to be different sizes.



The new version referred to as the Dynamic Ebbinghaus, takes the classic static illusion and turns it into a moving display where the central circle stays the same but the surrounding circles continually grow and shrink.

Here's a video showcasing the development of the illusion.

Chess Pieces Illusion

One set of white chess pieces and the other black. The difference is easy to see. Right? Well believe it or not, only the background surrounding the two set of pieces is different. The pieces themselves are identical. Yep, that's right. They are exactly the same shades of white and gray.



This illusion was created by Barton L. Anderson and Jonathan Winawer and published in Nature, 434 in 2005, Image segmentation and lightness.

Here is a nifty video which allows you to see that they are in fact the same.

Aurora Australis From Space

Cool video of the Aurora Australis created from various images and videos taken from the International Space Station.



NASA ISS : Aurora Australis from space from FullWerks on Vimeo.

Is it racist to not want to judge by race?

Last month the Supreme Court, in a 6-2 decision, upheld a Michigan Constitutional amendment banning the use of race as a factor in college admissions. It was a controversial decision which sparked a great deal of debate among both opponents and supporters of affirmative action.

One of these debates occurred on Fox News Sunday between Jennifer Gratz and Shanta Driver. I had seen the two present their views before and both pretty much stuck to their normal scripts, at least until the very end when Driver dropped a bombshell by saying "this is a racist decision that takes us back to an era of states rights where white majorities can disenfranchise minority communities and now prevent us from getting higher education."

So, if I understand correctly, Driver believes that the members of the Supreme Court who voted to allow the amendment to stand are essentially being racist because they are not in favor of discriminating on the basis of race.

You might think that perhaps Ms. Driver let her emotions get the better of her during the interview and that she doesn't really think that it was a "racist decision"...except that there is a very long quote of her responding to the decision on BAMN (By All Means Necessary) which starts by saying "Today's Supreme Court decision upholding the ban on affirmative action in Michigan is a racist decision."

Jennifer Gratz gave what I thought was a perfect response to Driver's cheap tactics saying "I think it is unbelievable that someone would sit here today and say prohibiting racial discrimination is a racist decision, I think that that tells us where the level of discourse is today. Look, good people can disagree. But we can’t have name-calling and baiting like this.” Couldn't have said it better.