Get acquainted with predicate logic in one sitting

The Logic Ninja

Thank you, Professor Baber, for teaching me the basics of predicate logic in one sitting.

Losing my marbles over Mawson

Mawson introduces philosophy of religion with nuance and style, and with plenty of his own authentic recipes. However, I can't make heads or tails of this passage:

"God might have chosen not to create a world but rather have remained the sole existent thing, in which case he would not have had the property of being creator, although strictly speaking, he would still have created everything other than himself."

Mawson, T.J. Belief in God: An Introduction to the Philosophy of Religion. Clarendon Press, 2005. 81.

I am assuming he means, "could still have created everything other than himself."  Let's take "could" and "might have" as synonyms for "true in at least one (logically) possible world."

God might have chosen not to create a world. But even a for creationless reality it holds that God could have chosen to create everything other than himself.

The fog hasn't lifted yet though, since "everything other than himself" picks out different items in different worlds (perhaps God only creates sea monkeys in some world). Mawson is probably referring to the contents of the actual world when he says "everything other than himself." But this led me to some interesting conclusions, which I'm have likely been mapped out and explored in more detail in advanced logical systems.

My general conclusion: it is necessarily true that p is true in some W so long as p is possibly true or necessarily true.

More specifically:
(1) Possibly, God has the property of being creator.
(2) Necessarily, it's possible that God has the property of being creator.

Any statement expressing a possible-world indexed proposition, like (1), will itself give rise to a statement that expresses a necessary truth. On the other hand, if (1) is false then it would be false in all possible worlds. Why is this? Here is my unprofessional attempt at finding out:

(3) It will snow in June next year
(4) It will snow in some month next year

If (3) is true, then obviously (4) is true. More generally, as long as at least one month has snow, then (4) is true. On the other hand, it must (*actually*) snow in June for (3) to be true. This example isn't perfect, but it helps me see why we should affirm this:

(5) If p is true in some possible world, then that p is true in some possible world is necessarily true.

Let's see if we can stretch it even further here.

(6) p is true in this world (the actual world)
(7) therefore, p is true in some possible world
(8) that p is true in some possible world is true in all possible worlds

So perhaps Mawson is trying to say something very precise here (I'm switching from possible words back to good ol' fashioned possible here just to make the sentences less awkward)

(6') in this world, God created something
Therefore
(7') it is possible that God created something
(8) necessarily, it is possible that God created something

Moral of the story: even in worlds where (6') is false, (7') is true

"God might have chosen not to create a world ... [but] ... he could still have created everything other than himself."

Am I stretching this too far? Probably so. But at least I didn't completely waste my morning on a typo.

Corn-fed cattle

- Posted using BlogPress from my iPad

Physicists are drama queens

Scientists at CERN, the world's largest physics lab near Geneva, stunned the world of science on Thursday night by announcing they had observed tiny particles known as neutrinos travelling slightly faster than light.

Wouldn't "recorded" be a little less misleading than "observed?"

Brian Cox, the TV presenter and physicist, told BBC Radio 6 Music: "If it is confirmed it will be the most important discovery in physics in at least the past 100 years.
"It is a very big deal, it requires a complete rewriting of our understanding of the universe ... it is such an extraordinary claim that it is difficult to believe."

Extraordinary claims require extraordinary evidence!

http://www.telegraph.co.uk/science/science-news/8785366/Science-world-in-shock-after-Cern-light-speed-claim.html

Mapping the Conceptual Terrain

A recurring theme in philosophy is something like this: philosopher x proposes some properties that constitute concept C (more specifically I guess we'd say that the possession of said properties is individually necessary and jointly sufficient to constitute C).  Ahh yes, but philosopher y has an example that shows that our intuitions about C go further; philosopher x's account leaves something important out!

This came to mind while watching an episode of The Twilight Zone this evening. The inmate's robot has all the qualities that (we think) a mental life comprises: rationality, learning abilities, emotions, qualitative conscious experiences like perception, pain and hunger.  So does the robot have a mind?  Well, perhaps some will disqualify the robot on account of lacking a soul. Regardless, if you feel the chill at the conclusion of the episode, ask yourself why.

Naturalism and the scientific spirit

http://opinionator.blogs.nytimes.com/2011/09/04/what-is-naturalism/

Dreaming of the Will to Live

A slight headache from too many dark beers rolled me out of bed this morning.  On the way to the kitchen cabinet, I rehearsed the dream which had just abruptly ended.  This dream was powerful and affected my emotional status the rest of the day.

Dream scenery is often not shocking until recalled during waking hours.  Walking down a busy street inside your high school, cars cruising by while you head to your locker.  This is pretty normal--and seems normal--in a dream.  Incidentally, I've developed a habit of recalling dreams in the morning to better retain them.  This habit came out of a fascination with lucid dreaming, inspired by The Waking Life.

Now, about last night's dream: it manages to bring together some powerful subjective elements into the same scene.  I found myself sitting on stage in a large church, playing the piano.  Looking around, there were friends from past and present.  Some of them looked to be behind the stage in a choir.  Others were in the audience.  A dozen well-adorned couples marched in an elated progression down the center aisle.  Was this a wedding?  If so, it was quite a rowdy one. This video comes pretty close to capturing it:



(The scene of this dream may very well have been supplemented my memory of this video, who knows).  All my friends are in this big church with me onstage playing music.  Believe it or not, I cannot remember who was walking down the aisle!  I only remember observing how happy we all were on this occasion.

Weddings always bring out a sentimental side: friends and family from all stages of life gravitating around the imminent married couple.  Celebration and nostalgia.  Vicariously watching our lives unfold in a communal moment.  Chairs of people bowed out in neat little rows, pointed at the front center-stage.  Why do we like ceremonial entrances so much?  Probably because they grant us permission to drift into abstraction.  To ponder our way past a marriage into the deepness of marriage.

So, I am on stage at this crazy ceremony, what to do next?  Make something musical happen!  Thinking to myself, "The intensity needs to escalate here so it settles at the appropriate time," I began clapping and the whole room joined right in.  What a rush of energy!  Here we are in this happy moment, and we are all thinking about the transition to adulthood.  We are nostalgic and hopeful.  Much life is still ahead.

Just when the sweetness of this scenery had enveloped me, a strange thought dislodged my attention: "How could this all truly end?"  "How can there be an end to this?"  "Will this really just fade away?"  My dream-self tried imagining a dark, empty void.  Perhaps to see what it would be like to be permanently unconscious.  Could I discover any communicability between the wonderful scene and the dark, empty void?  Not at all.  The idea of  a truly empty void was simply not available for me to compare.  No matter how hard my mind focused: there was still a spark, a soft whisper of existence.  And yet this unimaginable void was so terrible, issuing anger within me towards its possible but inconceivable finality.  How deeply unjust to think that all sentient creatures will pass away.  Rage, rage against the dying of the light.

That was my dream.  Hoping to think about it more this week.

Wilson on Witch Trials

What do you think of the Salem Witch Trials from Canon Wired on Vimeo.

“Are there Good Reasons for Abortion?” Wendy Savage and Madeleine Flannagan Debate on Unbelievable?

“Are there Good Reasons for Abortion?” Wendy Savage and Madeleine Flannagan Debate on Unbelievable?

Free Will, Moral Responsibility, and Reformed Theology: A Contemporary Introduction

Paul Manata has written a full-length introduction to the topic of free will and moral responsibility from a Reformed perspective.