Caturday’s Astronomy Pix for September 23-29, 2012


English: Computer simulation of the heating of...

English: Computer simulation of the heating of a space shuttle orbiter upon reentry. Temperatures on the exterior of the shuttle can reach during this phase of flight. (Photo credit: Wikipedia)

Equinox: The Sun from Solstice to Solstice

NGC 2736: The Pencil Nebula

Unusual Spheres on Mars

A Space Shuttle Over Los Angeles

Stars and Dust Across Corona Australis

Stars in a Dusty Sky

NGC 7023: The Iris Nebula

English: The Space Shuttle Atlantis atop the S...

English: The Space Shuttle Atlantis atop the Shuttle Carrier Aircraft (SCA) returns to the Kennedy Space Center after a ten month refurbishment. (Photo credit: Wikipedia)

Caturday’s Astronomy Pix is a weekly installment, published each weekend with links to each daily entry on NASA’s website Astronomy Picture of the Day. I hope you enjoy looking at these often breathtaking images as much as I do.

Fractal of the Week: Vermessika


Yes, I know that the title of this post is a silly neologism. But there are some nights when my faculty for made-up words needs to be sated.

This, though, is one of my favorites from the last few days, and needed something…different for me to call it. So take away my skeptic card and sue me.

I’d like to give a shoutout to my fractalizing friend Janet Russell at BuddhaKat, and offer my condolences of her losses on this date, and thanks for brightening my own evening with the images posted in her entry linked to below.

All images in this post are original works by the author, and are copyright 2012 Troy Loy

How to Argue: A Sample Argument Evaluation


G’day. I’m foregoing the usual news item post for this updated completion to my earlier How to Argue post, in which I wrote on formally setting out arguments, and how we must analyze them, only evaluating them afterward to see whether the truth of the conclusion follows from the premises when an argument is either inductive or deductive in nature.

Here, we’ll evaluate an argument, and I want to use the argument I set out last time, and first going over the argument itself using a truth table to determine it’s validity as given. We’ll also note any insufficiencies of this argument immediately following, and how we can make it better.

Here it is as last time, in one row in formal notation. We are using sentential logic, or basic symbolic logic for simplicity…

P, Q, (P & Q)→R : R→S

And in English, the variables are repeated here from the previous post…

  • P – Expressions of belief are claims.
  • Q – No claim should get a free pass.
  • R – If you express your claims, but don’t like criticism, then you have two choices.
  • S – Your choices are to make better claims or to defend your claims.

…where commas are used to separate the premises, a colon to separate the premises from the conclusion, the “&” sign to join premises “P” and “Q” together as sub-premises with “R” in a complex premise, and the “→” sign to designate hypothetical or “If/Then” conditional statements into the 3rd premise, “(P & Q)→R” and the complex conclusion, “R→S.”

Note first that the truth of “R” depends upon the truth of “P” and “Q” together, and that of “S” depends on that of “R.” Already you might suspect that this doesn’t look promising, but let’s work that out, using all four variables and the full argument to see all of the possible worlds that the argument could pertain to, all possible situations, to see if there are any of these in which the premises may be true and the conclusion false.

That would show it to be invalid.

From a filled in truth table, we need find only one row where this is the case, and as we shall see, a truth table’s number of rows, or possible situations, doubles for each variable after the first. This one will have 16 such rows beneath the header showing the guide-columns for the variables and the guide-columns for the argument itself.

Each row on the table shows a possible variation of the truth values of the premises and the conclusion.

For ease of reading the table, I’ll use binary notation, with “1” for true, and “0” for false for the truth values of the variables and their operator symbols.

Well, glancing at the table, we don’t have to look far to see, at row 2 marked in red, that there does exist a possible combination of values in which all of the premises are true and the conclusion false.

P Q R S P, Q, (P & Q) R, R S
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 1 1 1 1 1 1 1 1 0 0
1 1 0 1 1 1 1 1 1 0 0 0 1 1
1 1 0 0 1 1 1 1 1 0 0 0 1 0
1 0 1 1 1 0 1 0 0 1 1 1 1 1
1 0 1 0 1 0 1 0 0 1 1 1 0 0
1 0 0 1 1 0 1 0 0 1 0 0 1 1
1 0 0 0 1 0 1 0 0 1 0 0 1 0
0 1 1 1 0 1 0 0 1 1 1 1 1 1
0 1 1 0 0 1 0 0 1 1 1 1 0 0
0 1 0 1 0 1 0 0 1 1 0 0 1 1
0 1 0 0 0 1 0 0 1 1 0 0 1 0
0 0 1 1 0 0 0 0 0 1 1 1 1 1
0 0 1 0 0 0 0 0 0 1 1 1 0 0
0 0 0 1 0 0 0 0 0 1 0 0 1 1
0 0 0 0 0 0 0 0 0 1 0 0 1 0

Sadly, despite any merits at all of it, it’s not a good argument, because as good logic students will quickly notice, it’s not complete.

What’s up with this? What’s wrong with it?

First, the original conclusion, “R→S” is better as the premise “R→S,” followed by the premise “R”, and the conclusion “S,” and the argument in full as follows:

P, Q, (P & Q)→R, R→S, R: S

So, let’s look at the truth table with this argument now completed, and see if it’s any better, with the added columns marked in green…

P Q R S P, Q, (P & Q) R, R S, R: S
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0
1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1
1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1
1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0
1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1
1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0
0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1
0 1 1 0 0 1 0 0 1 1 1 1 0 0 1 0
0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1
0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0
0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1
0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0
0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1
0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0

Much better.

This is a valid argument, though that’s no guarantee of the truth of the conclusion, only of the conclusion’s truth if the premises are likewise true. What’s important to logicians is the truth-preserving qualities of such arguments.

On this now-completed truth table, there exists no possible situation, no possible world in which both the premises’ truth and the conclusions falsehood occur, no small matter even by itself for anybody concerned with truth in whatever form it takes.

Fractals of the Midweek: Pareidolia Fest I


Pareidolia…The natural tendency for human beings to see meaningful patterns in random data — where no such patterns nor meaning actually exists — just by virtue of humans being what we are. We learn through noting and recognizing patterns. For example, it is advantageous for us to recognize faces, especially human ones. Sometimes we make false positives — picking out these faces in ambiguous visual stimuli….

…and we are are particularly likely to see them in the oddest places; clouds, tortillas, engravings on coins, product logos, in television static; and that’s just visual pareidolia.

There are other sorts as well, such as seemingly picking out snatches of speech from recordings played backward, or voices from random radio static, so-called electronic voice phenomenon, or EVP. Those would be audio pareidolia.

So it also is with art, and so here I present a set of images from my collection that have evoked in others and myself the seeing of faces, and other, stranger sorts of things, that can be seen in fractals as with any visual or other sensory medium…

All images in this post are original works by the author, and are copyright 2012 Troy Loy

“The problem with ideology…


…is, if you’ve got an ideology, you’ve already got your mind made up. You know all the answers and that makes evidence irrelevant and arguments a waste of time. You tend to govern by assertion and attacks.”

~ Bill Clinton former president of the USA, 18th Oct 2006 , at an event sponsored by the Center for American Progress. (unsourced)

An ideology is essentially a collection of ideas, often consisting as a body of personal truth claims, knowledge and values, with values being themselves based on truth claims, claims as to what states of affairs are to be preferred over others.

While I wouldn’t put things quite the way Mr. Clinton did, it is the case that most ideologies, because of the nature of their truth claims and value beliefs, are in large part unsuited for objective inquiry into how things really are.

This applies especially to partisan political, economic, and religious ideologies, and those of other sorts whose constituent ideas do not hold up to objective scrutiny, or which contain those that, seen from outside that ideology, can be clearly seen as non-factual and even mutually inconsistent or contradictory.

There is a danger in holding our ideas too closely, and by extension, our bodies of them, and in thinking ourselves to already have the truth without an honest attempt to actually find it first.

Critical examination of ideas, especially our own, is exactly what ideologues with an agenda would much rather we not do.

Credulity, especially concerning political loyalties, sows the seeds of political manipulation. So rather than be first to point fingers and make accusations of skewed views to those who disagree with us, I think it more useful, more honest to scrutinize our own potential for bias.

Unless we want to get taken in by our own opinions, and those who cynically exploit them, it’s important to critically examine what we believe, why we believe it, what we think we know, and to be as sure as we can that we have good reasons for both, to have good “whys” for our ideas, and to make sure that our “whys” also have good reasons for them.

Metacognition, “thinking about thinking” lets us account for our motivations, our biases, our numerous cognitive and reasoning errors, though I don’t think it’s humanly possible to completely avoid them.

But briefly stepping outside of our ideological bubbles is possible when we allow ourselves the honesty and freedom to doubt, to consider and evaluate our thoughts and the evidence for our claims without reflexive rejection or uncritical acceptance.

We needn’t do this to feel intellectually superior to others or to pat ourselves on the back for being such great objective thinkers, but to exercise due care in not holding our ideas too close to our breast, to not hold them so dogmatically (and I’m not aware of any civilization whose people actually prospered from adherence to dogma and suppression of freedom of thought) that those ideas blinker us from seeing and accepting what’s demonstrably true when it disagrees with our pet prejudices and cherished notions of Truth™.

Toeing the party line because it reassures us of our own subjective and often shared sense of rightness and righteousness, and avoiding self-scrutiny because it makes us uncomfortable is dangerous.

Not all sets of ideas are equally valid or useful for reliably and effectively solving our problems, especially when those ideas involve denial of the very existence of the problems we face. The very best ideas are those that lead us to recognizing difficulties and to best let us find solutions to them.

It’s not difficult to imagine that the deceptive promotion of ignorance, fact-denial, over-dependence on authority and dogmatic thinking are only useful if one has a political axe to grind, as a means to control others and not as an attempt to seek the truth, whatever it may be.

These more often than not lead to many of us being blindsided by the new, the unusual, the anomalous, the unexpected and unknown, and this is not a situation conducive to one’s benefit, much less in a world in which we do not and cannot control absolutely everything, or worse, someone else controls us when we fall for fallacious appeals to emotion, to patriotism, to party loyalty, to our desire for security and not a careful examination of the issues.

If some want to be among the intellectually deprived and politically disenfranchised, that’s fine. They should then feel free to confuse opinion with facts, ignorance and obstinacy with virtue, partisanship with truth, but should not presume to do the same for others. Leave the rest of us to go to the stars, not back to the caves.