This Sentence Is False. True Or false? (Conclusion)

For convenience, I’ll repeat the sentence in question, immediately below this one.

This sentence is false.

The sentence in bold-face immediately above this one is not true, and is not false. It is “undecidable,” and has no “truth value.” The reason is rooted in its self-referential nature.

Here it is:

According to classical Aristotelian logic, what we call “common sense,” a statement cannot be both true and false. It must be one or the other.

If the sentence we’re considering is true, then it is false (after all, that’s what it directly states, that it is a false sentence). It's impossible for a sentence to be both true and false, and so we can rule out the possibility that the sentence is true.

So, the sentence in question must be false (which aside from "true," our initial assumption, is the only remaining alternative).

However, the sentence in question cannot be false either. If the sentence is false, then it is a lie, and the opposite of what it states must in fact be true. Since the sentence in question states that it is a false sentence, the opposite must in fact be the case – i.e. the sentence must be true. Again, no statement can be false AND true, so we must also throw out the possibility that the sentence in question is false.

The sentence in question is therefore demonstrably not true AND also not false – according the rules of “common sense” logic.

Weird. Apparently, logic is sometimes illogical (another strangely self-referential idea)!

If you like this kind of thing, you’ll love Hofstadter’s book (see part 1 of this investigation, here). However, be forewarned. It’s easily the "thickest” book I’ve ever attempted to read. I’m not just referring here to the length of this prodigious tome, but mainly to the difficulty of grappling with the ideas presented within it. Reading that book is like trying to step on your right foot with your right foot, nearly every page of it! It’s about radical, "outside the box" observation and expansion of the human mind – literally thinking hard about thinking hard. An intellectual challenge of the first order, this meta-logical journey will be truly maddening for most mere mortals, but is a sublimely rewarding experience for those brave and stout enough to make the trip.

For further study or additional masochism, try a google search on “self reference” or “fuzzy logic.”

Good luck!

(Click here to go to Part 1.)

-----

Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Harvard Chooses Female Head

It only took 371 years, 27 previous presidents, and a LOT of coaxing, but Harvard finally has a woman as top banana.

Ms. Drew Faust, a Civil War historian, will take the place of discredited former head Lawrence Summers, who left as Harvard's head amid contentious relationships with faculty and after making controversial remarks about the inherent inability of women to do world-class research in the sciences.

With seven U.S. presidents as alumni, and over 40 Nobel Prize winners on its cumulative list of faculty members, Harvard occupies a singular place in the roster of great American universities, and Faust's appointment is sending a powerful shockwave throughout academia in this country and within the iconic institution itself.

From a recent Washington Post article:

"Harvard is making a statement at a critical time when we are seeing student bodies [at many schools] that are well over 50 percent women," said Claire van Ummersen, director of the Office of Women in Higher Education at the American Council on Education. "We see women faculty increasing in number, and the place where we have lagged most is in research institutions having women at the executive level. . . . Hopefully, this will have some influence on boards of trustees or overseers of other institutions."

Faust's selection comes as Harvard moves to modernize its more than 30-year-old undergraduate curriculum, a move that's being closely watched by institutes of higher education throughout the U.S.

Read the rest of the article here.

-----

Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Test Dates: 2007-2008

Having a clear test preparation plan is crucial in achieving success on major standardized tests like the SAT, SAT2, ACT, PSAT, SSAT, and HSPT.

Testing dates scheduled during the 2007-2008 school year have now been released for most of these tests.

It's time to select the test dates that work best from the list below, and arrange your plans accordingly.

"Plan your work, and work your plan."

---

ACT Dates: 2007-2008

6/9/07 (Registration: 5/4/07; late registration: 5/18/07.)

9/15/07 (Registration: 8/10/07; late registration: 8/24/07.)

10/27/07 (Registration: 9/21/07; late registration: 10/5/07.)

12/8/07 (Registration: 11/2/07; late registration: 11/15/07.)

2/9/08 (Registration: 1/4/08; late registration: 1/18/08.)

4/12/08 (Registration: 3/7/08; late registration: 3/21/08.)

6/14/08 (Registration: 5/9/08; late registration: 5/23/08.)

---

HSPT Dates: 2007-2008

Test dates vary. The most common dates are in the fall and spring.

Contact high school admissions departments to confirm test and registration dates.

---

PSAT Dates: 2007-2008

10/17/07 or 10/20/07

Contact high school to confirm test and registration dates.

---

SAT Dates: 2007-2008

10/6/07 (Registration: 9/10/07; late registration: 9/14/07.)

11/3/07 (Registration: 10/2/07; late registration: 10/11/07.)

12/1/07 (Registration: 10/30/07; late registration: 11/8/07.)

1/26/08 (Registration: 12/26/07; late registration: 1/4/08.)

3/1/08 (Registration: 1/29/08; late registration: 2/7/08.)

5/3/08 (Registration: 4/1/08; late registration: 4/10/08.)

6/7/08 (Registration: 5/6/08; late registration: 5/15/08.)

---

SAT2 Dates: 2007-2008

10/6/07 (Registration: 9/10/07; late registration: 9/14/07.)

11/3/07 (Registration: 10/2/07; late registration: 10/11/07.)

12/1/07 (Registration: 10/30/07; late registration: 11/8/07.)

1/26/08 (Registration: 12/26/07; late registration: 1/4/08.)

5/3/08 (Registration: 4/1/08; late registration: 4/10/08.)

6/7/08 (Registration: 5/6/08; late registration: 5/15/08.)

---

SSAT Dates: 2007-2008

10/18/07

11/10/07

12/8/07

1/12/08

2/9/08

3/8/08

4/12/08

6/14/08

(Registration and late registration dates to be announced.)

-----

Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Biggest SAT Score Dip In 31 Years

Are recently released national score results an anomaly, or further evidence that the SAT is a on the way out?

My vote is with the latter conclusion.

Ever since the Princeton Review and others began to expose the glaring weaknesses and basic uselessness of the SAT as an assessment of “college readiness” two decades ago, this dinosaur of the standardized testing universe has been racing toward extinction at an ever-increasing pace.

The administrators of the SAT1 recently debuted another major rewrite of the test (the third such revision in approximately 20 years undertaken) out of frustration with truth tellers like the Princeton Review and desperation caused by threats from the likes of U.C. Berkeley and others to drop the SAT from their admission requirements.

There’s still a bit of life in the old beast ... but the writing is on the wall. I give the SAT around 10 years to go the way of the Dodo. We shall see.

A Washington Post article begins:

“The first national results from the revamped SAT show the biggest annual drop in reading scores in 31 years and a significant edge for female students over males on the new writing section of the test, the College Board reported yesterday.

The report on SAT scores for the high school Class of 2006 illuminated how the introduction of the writing section – including a much-dreaded essay question – and revisions to the mathematics and reading sections have changed an assessment tool still used for admissions by most colleges and universities.”

For the complete text of the article, click here.

Another article on the same news item is found here.

-----

Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Are Public Schools Outperforming Private Schools?

A recent article in the San Francisco Chronicle reported findings indicating that the significant extra expense involved in sending children to private schools could, in fact, be a waste of money.

Apparently, test scores are showing that public school students may actually be getting a better education than those attending private schools, (especially conservative Christian schools).

While this seems to fly in the face of “common sense,” the numbers are what they are, and they don’t seem to support the notion that (generally speaking) private schools are better than public schools; indeed, they seem to support the opposite conclusion.

Below is an excerpt from the beginning of the article:

“(07-15) 04:00 PDT Washington - The federal Education Department reported Friday that, in reading and math, children attending public schools generally do as well as or better than comparable children in private schools. The exception was in eighth-grade reading, where the private-school children did better.

The report, which compared fourth- and eighth-grade reading and math scores from nearly 7,000 public schools and more than 530 private schools in 2003, also found that conservative Christian schools lagged significantly behind public schools when it came to eighth-grade math.” 

To read the article in its entirety, click here.

-----

Contact Chris

borlandeducational.com

Copyright © 2006-present: Christopher R. Borland. All rights reserved.