Apparently, based on this (sort of) clever weave of semantics “The logical conclusion of atheism is that it’s illogical.” … If you abuse logic enough you can twist pretty much anything into a “truth” statement. You could very well, in mathematical and formal logic, make a statement claiming blue is red and still have it manage to actually equate to be “true”… that is if you do enough twisty bullshit in the middle.

Reading that post even someone how has never taken a logic course can see the problems, there are assumptions, jumps and irrational conclusions (mostly due to the fact that he had a predetermined statement in mind). It the atheist’s turn to play! yay!:

1. An extensional analytic sentence is one that, through substitution of synonyms for synonyms, results in a narrowly logical truth, e.g., a truth in “standard” propositional logic.

2. The sentence-scheme “c causes e” analytically entails (but is not synonymous with) “c and e exist; e’s existence stands to c in the relation of being the result of c’s existence, such that this relation is not that of e being narrowly, logically necessitated by c.” The reason there is no synonymy is that there are other features of the causal relation, features not mentioned in the entailed sentence.

3. The sentence-schema “x is omnipotent” analytically implies “for any possible existent y, necessarily, if x wills that y exist, y exists.”

4. The relation expressed by “x wills that y exist and y exists as a consequence of this willing” is a species of the relation expressed by “x causes y to exist.”

5. If God exists, God is omnipotent and the cause of the universe that exists.

6. If the universe is willed to exist by God and the universe does not exist, then it is the case that [by (3), (4) and (5)]

• (a) God wills the universe to exist and the universe exists and
• (b) God wills the universe to exist and the universe does not exist.

7. The proposition expressed by the sentence, “God wills the universe to exist and the universe exists, and God wills the universe to exist and the universe does not exist,” is a negation of a theorem of standard propositional logic, namely, that it is not the case that both p and not-p.

8. Therefore, God narrowly logically necessitates whatever possibility he causes to exist.

9. Therefore, it is not the case that the universe is caused to exist by God [from (2)].

10. Therefore, God does not exist [from (5) and (9)].

=D LoLz

�

I woke up this morning incredibly happy - mostly because I didn’t have to work today and I didn’t really have anything too overly strenuous planned. And then I saw a lecture by Janna Levin and it made me even happy. She is now my new hero - I even bought her new book A Madmad Dreams of Turing Machines.

There is something about a woman who talks mathematical logic that just turns my crank. Her introduction about the book is absolutely fascinating - I hope the book is even half as good. The book is about Alan Turing and Kurt Godel. Although they never met in person they both dealt with the truths and lies in mathematics. One making a statement equivalent to “this sentence is a lie” in mathematics and the other creating the computer - more or less. Turing is slightly more well known than Godel (out side of the math world, anyway) but I think he’s far more interesting.

Godel was insane - he died by starving himself to death. (Where in direct opposition to that Turing ate a poison apple.) I think what I find most interesting about them is that although they both came to the conclusion that mathematics is essentially infinite and unprovable (no “theory of everything”) they took it entirely different ways in their outlook on life.

Godel …somehow… had it confirm his religion even deeper where as Turing denied religion entirely. Turing called humans biological machines, that are essentially soulless - just as artificial intelligence would be soulless.

Anyway - I’m super excited to read the book. It’s fiction but non-fiction, which is really cool. And I think it’ll be well written. I’ll do a post about it when I finish reading it. But until I read it and end up disappointed Janna will remain my new favorite person on the planet.

I didn’t bring my camera - and Ang has yet to upload the photos - but Dr. Jeffrey Shallit spoke at Guelph last night about misinformation theory. I am much to tired to go into why this next statement is true, so you’ll just have to take my word for it:

Jeffrey Shallit is by far the best speaker I have ever seen as a skeptics event. Including all CFI events, UTSA, Guelph - all of them. He was by far - the best. He was interesting, entertaining, informative and hilarious. He brought prizes for the crowd, which was the cutest thing ever. (Even cuter was that they were really geeky prizes and we all thought they were so incredibly awesome.)

If you ever have a chance to go and see him - goooo! It was so good. I appreciated his talk a lot… I wish we could have pulled in more people for him to talk to (we had just over 60). Hopefully I’ll be able to post a picture of two eventually. I feel like a doofus - I totally forgot my voice recorder and it would have been a great lecture to have recorded because it was super entertaining.

Also - for all you 9/11 crazies (aka my brother) you should head over to his blog and check out all his posts on 9/11 conspiracy theories - they show a ton of great arguments that you should be reading.

Unfortunately Kirk Durston didn’t show up to put on a good debate for us - but he did agree to do a talk on information theory for us in the fall - so I look forward to hearing why the disgusting display of “math” is actually okay in his world.

Okay, now for a bit of a blog round-up of awesomeness.

I’m not gonna lie, I’m not a HUGE fan of 3QD, but Azra puts up this post that I thought was pretty interesting. I think the thing I don’t like the most about 3QD is the huge lack of personal opinion. But whateves.

You are a tree is right up there on my ‘new favorite blogs’ list. The Nerd Test looked fun, then I regreted taking it.

Oh dear.

At good math bad math there is a post that I’ve been waiting for forever. I was talking to someone about the logic of numbers and the reasoning behind their positions and stuff, and now I finally have someone a lot more coherent than me helping.

I’d like to go out for drinks with Shelly. She’s humorous. Especially in this post about African Orphans being the new cool accessory.

The previous paragraph was meant to be sarcastic—however the media,
and several adoption activists, genuinely seem to feel that the
motivation behind celebrity adoptions is positive PR. This is
ridiculous. Although I am no starry-eyed celeb fanatic, I can admire
their desire to share an immense fortune with those less fortunate, and
to adopt a child who would face a miserable, and likely short, life
without intervention.

hardy har is a very serious way. Its so scary that its true though. …Everyone wants one.

I really like this peice at Subversive Inc. So much that I’ll post it here.

fragmentations of a feminist

   

sometimes you’ll find her
waving posterboard into
whips of wind,
sharpy letters smooth
precision cut, inked with
pink glitter and moon stars
signs signifying, mouths chanting
my body, my choice
take back the night
out of the kitchens and into the streets
or
until the violence stops

sometimes,
she kneads bread in a blistering kitchen,
yeast and steam rising
like hot sidewalks breathe after cool rains.
she wears that old denim mini skirt
that makes love to her hips like saran wrap
and stiletto heels
the black ones–
because when the flour makes paste
near the edge of her ankle
her lips curve like
she’s keeping secrets.

sometimes,
she studies the women like she studied men
in those naïve days–those
fools drunk on power
and pretense
chasing phalluses with spatulas
melted around the edges,
and bobby pins made shiny
with aerosol cans.

sometimes,
wrists red,
thighs spread or sewn
with purple tape to match
the next morning’s bruises.

How are earthquakes related? I could tell you - but then you’d just know even less. So go here to read an intelligent description of it.

UTI has a new front pager. I dont know if I like him yet. one post isn’t enough to decide. But, I will welcome him anyway.

Elron started a new online mag that he’s asked me to contribute to. I said sure. So… uh yeah. Go here to see it yo! Its got a bit more a serious attitude than my blog but most do.

Soooo this time ‘round I will be working with making some of
the questions I’ve faced in the past a little more precise and how to get some
actual answers.

First consider an informal example. We could expand the
language by adding a three-lace sentential connective symbol #, called the
majority symbol. We allow now as a wff expression (#αβγ) when ever α, β and γ
are wffs. In other words, we add a sixth formula building operation to our list:

Є#(α,β,γ) = (#αβγ).

Then we must give the interpretation of this symbol. That
is, we must say how to compute v|((#αβγ)), given the values v|(α), v|(β) and v|(γ).
We choose to define

V|((#αβγ)) is to agree with the majority of v|(α), v|(β),
v|(γ).

We claim thatthis extension has gained us nothing, in the
following precise sense: For any wff I the extended language, there is a
tautologically equivalent wff in the original language. (On the other hand, the
wff in the original language may be much longer than the wff in the extended
language.) We will prove this (in a more general situation) below; here we just
not that it relies on the fact that (#αβγ) is tautologically equivalent to

(α^β) V (α^γ) V (β^γ). 

(We note parenthetically that our insistence that v|((#αβγ))
be calculable from (v|(α), v|(β), v|(γ)) plays a definite role here. In
everyday speech, there are unary operators like “it is possible that” or “I
believe that.” We can apply one of these operators to a sentence, producing a
new sentence whose truth or falsity cannot be determined solely on the basis of
the truth or falsity of the original one.)

In generalizing the foregoing example, the formal language
will be more of a hindrance than a help. We can restate everything using only
functions. Say that a k-place Boolean
function is a function from {F,T}^k
into {F,T}. (A Boolean function is then anything which k-place Boolean function for some k. We stretch this slightly by permitting F and T themselves to be
0-place Boolean functions.) Some Boolean functions are defined by the equations
(where X Є {T,F}) 

I^n(X1,…Xn) = Xi,

N(F) = T, N(T) = F,

K(T, T) = T, K(F, X) = K(X, F) = F,

A(F, F) = F, A(T, X) = A(X, T) = T,

C(T, F) = F, C(F, X) = C(X, T) = T,

E(X, X) = T, E(T, F) = E(F, T) = F. 

From a wff α we can extract a Boolean function. For example,
if α is the wff A1^A2, then we can make a table (below). The 2^2 lines of the
table correspond to the 2^2 truth assignments for {A1, A2}. For each of the 2^2
pairs X, we set Bα(X) equal to the truth value α receives when its sentence symbols
are given the values indicated by X.

In general, suppose that α is a wff whose sentence symbols
are at most A1,…,An. We define an n-place
Boolean function Bα^n (just Bα if n
seems unnecessary), the Boolean function realized by α, by 

Bα^n(X1,…,Xn)= the truth value given to α when

 A1,…,An
are given the values X1,…,Xn.

Or in other words Bα^n(X1,…,Xn) = |v(α), where v is the
truth assignment for {A1,…,An} for which v(Ai) = Xi. Thus Bα^n comes from
looking at |v(α) as a function of v, with α fixed.

…There, I’d do some proofs, but its 2:40 am and I have class
in the morning, so you’ll just have to trust me, because I probably won’t do
proofs tomorrow. I will however probably do 0-ary Connectives and Ternary
Connectives. 

Okay fine one quickly:
Let α and β be wffs whose sentence symbols are among A1,…,An.
Then 

a) α
|= β for all X {F,T}^n, Bα (X) (less than or equal to) Bβ(X)

b) α
|= =| iff Bα = Bβ

c) |=
α if Bα is the constant function with value T.

Proof α |= β iff for all 2^n truth assignments v for A1,…,An.
Whenever |v(α) = T, then also |v(β) = T. (this is true even if the sentence
symbols in α and β do not include all of A1,…,An) Thus

Α |= β  iff for all 2^n
assignments v,  |v(α) = T => v|(β) = T

 Iff for all
2^n n-tuples X,  Bα^n(X) = T => Bα^n(X)
= T

 Iff for all
2^n n-tuples X,  Bα^n(X) (less than
or equal to) Bβ^n(X),

Where F < T.

In addition to identifying tautologically equivalent wffs,
we have freed ourselves from the formal language. We are now at liberty to
consider any Boolean function, whether it is realized or not.