Saturday, December 25, 2010

Universally Quantified Quantified Statements

Quantification deals with statements about all, none, or some of a group.

One may indeed conclude that:

1) All Cats are black.
2) Sophie is a cat.
3) Therefore, Sophie is black.

BUT, not with any of the laws of Logic priorly taught. For symbolically, one can see that this wouldn't follow in any modus ponens kind of way.

1) P
2) Q
3) R

Obviously, this is an invalid argument. That's why we need Quantification!

This is not a new form of logic, it's just a bit of the science behind "Quantified Statements". In reality, Quantified statements turn out to be a form of the rules taught earlier.


Universally Quantified Statements


Universally Quantified Statements are statements about all or none of a group. These are actually, "if, then" statements disguised as "all x is y". For example, if I say, "All cats are black", I'm basically saying, "If anything is a Cat, it is black". Or if I say, "No dog is yellow", I'm saying, "If anything is a dog, it is not yellow".

"x" is used as the Variable to represent "Anything" in order to symbolize Quantified statements.
So, when I say, "All dogs are confused", I say, for any x, if x is a dog, it is confused.

To symbolize this, we say, "(x)(Dx->Cx). (x) represents the "For any X". "Dx" represents the antecedent clause, "If x is a dog", and "Cx" represents the Consequent clause, "x is confused".

This way, we can put a subject in as x:

(x)(Dx->Cx) (For any x, if x is a Dog, x is confused)

Let's say Sam is a Dog. Sam, then, becomes the subject for the argument to apply to.

1) (x)(Dx)->Cx)
2) Ds (Sam is symbolized as "s" attaching to the D "Dog")
3) Ds->Cs (Sam is symbolized as "s" attaching to the C "confused")

The only way you can learn these is through examples, so try some of these out:
1.
1) Every car is oily.
2) Sally is a car.
3) If Sally is a car, Sally is oily.
3) Therefore, Sally is Oily.

Symbolized
1) (x)(Cx->Ox)     (For any x, if x is a car, x is oily)
2) Cs     (Sally is a car)
3) Cs->Os    (If Sally is a car, Sally is Oily)
4) Os     (Therefore, Sally is Oily)


2.

1) No humans have wings.
2) Sam is a human.
3) If Sam is a human, Sam does not have wings.
4) Therefore, Sam does not have wings.

Symbolized:
1) (x)(Hx-> ¬Wx)     (For any x, if x is a human, x does not have wings)
2) Hs     (Sam is a human [Note how "H" represents the human and "s" represents Sam])
3) Hs -> ¬Ws     (If Sam is a human, then Sam does not have wings)
4) ¬Ws     (Sam doesn't have wings)


3.

1) All Christians are morally reprobate.
2) Evan is a Christian.
3) If Evan is a Christian, then Evan is morally reprobate.
4) Therefore, Evan is morally reprobate.

Symbolized
1) (x)(Cx->Mx)     (For any x, if x is a Christian, x is morally reprobate)
2) Ce     (Evan is a Christ [Evan is symbolized by "e"])
3) Ce->Me     (If Evan is a Christian, Evan is morally reprobate)
4) Me     (Therefore, Evan is morally reprobate.


One last and slightly more complicated example:

1) All bears have claws.
2) Everything that has claws can kill.
3) Bobby is a bear.
4) If Bobby is a bear, then Bobby has claws.
5) If Bobby has claws, then Bobby can kill.
6) Therefore, if Bobby is a bear, Bobby can kill.
8) Therefore, Bobby can kill.


Symbolized

1) (x)(Bx->Cx)    (For any x, if x is a bear, x has claws)
2) (x)(Cx->Kx)    (for any x, if x has claws, x can kill)
3) Bb     (Bobby is a bear [Bobby symbolized by "b"])
4) Bb->Cb     (If Bobby is a bear, then bobby has claws)
5) Cb->Kb     (If Bobby has claws, then Bobby can Kill)
6) Bb->Kb     (Therefore, if Bobby is a bear, Bobby can Kill)
7) Kb     (Therefore, Bobby can Kill)


If you have any questions, please comment on this post or send me an email. I'm more than willing to help, as I know these posts aren't as clear as a text book would have them.

Conditional Proof and Reductio Ad Adsurdum

Here are two types of argumentation which will prove incredibly useful.

The first is called a "Conditional Proof". A Conditional Proof isn't any special law of Logic, it's just a mode of reasoning. Many times when we lay out a set of premises which lead to a conclusion, there are some premises we actually "Suppose", which is another way of saying, "Suppose this is true". Instead of arguing, "This is true, and this is true, therefore this is true", with a conditional proof one can argue "If this is true, then these conclusions follow."

Here's an example.

1) Michael is either in the Library or at Sonic.
2)     Michael is not at Sonic
3)     Therefore, Michael is in the Library.


Ok, so look at the first premise. In this case, we're not supposing the first premise, so it's just like any old P->Q premise. But see how the next premise 2) is indented? This is a way of saying, "Suppose 2) is true". We may or may not know two is true, so we're supposing it to see which conclusions follow. The next most important thing to remember is that all following conclusions which result from the "supposed" premises must also be indented. That's why the third premise is indented in this argument.


Here's a more complicated example:

1) If God exists, he is timeless.
2) If God is timeless, he is unchanging.
3) If God is unchanging, he could not have created the Universe.
4)     God exists.
5)     Therefore, God is timeless. (MP 1,4)
6)     Therefore, God is unchanging (MP 2,5)
7)     Therefore, God could not have created the Universe. (MP 3,6)
8)Therefore, if God exists, he could not have created the universe.(CP 4-6)

Obviously, I take issue with 3), but this is a good argument for the sake of example. The last premise is NOT indented, because the CP (Conditional Premises) show that 7) results when God's existence is supposed. So one can conclude based on these premises that if indeed God does exist, he could not have created the Universe.



Reductio Ad Absurdum

The Technical meaning for this is "Reduction to Absurdity". You've probably used this a lot! A Reductio Ad Absurdum argument makes use of the Conditional Proof mode of argumentation to show that, if a certain premise is true, it entails contradictions. If a premise's truth entails contradictions, it necessarily cannot be true.

Here's an example:

1) If Humanism is true, God doesn't exist and we have a morale obligation to love other humans.
2) If God doesn't exist, all humans are just jelly bags with no more ontological value than rocks.
3) If all humans are just jelly bags with no more ontological value than rocks, then we have no morale obligation to love other humans.
4)     Humanism is true. (CP)
5)     Therefore God doesn't exist. (MP 1,4)
6)     Therefore, all humans are just jelly bags with no more ontological value than rocks. (MP 5, 2)
7)     Therefore, we have no morale obligation to love other humans. (MP 6,3)
8)     Therefore, we have a morale obligation to love other humans. (MP 4,1)
9)Therefore, if Humanism is true, we have a morale obligation to love other humans and we have no morale obligation to love other humans. (CP 4-8)
10) Therefore, humanism is not true. (RAA)


One can see that RAA arguments are very useful. Simply suppose that proposed premise is true, and allow it to contradict itself and show itself to be false.

Saturday, December 4, 2010

Shameless Venting

I feel as if I'm about to write one of those posts I'll regret later. It's one of the kinds you write when you're in a desperate mood and just want someone to listen to you. Well, hey. If you see this more than a day after I wrote it, I didn't regret writing it.

I want to take care not to become overly personal on this blog because I resolved to orient it towards apologetics months ago. I do, however, hold to a personal and heartfelt form of "counseling" apologetics. I do this because in the midst of the horrifying doubts I experienced, the thing I needed most was a friend to speak truth into me-- not arguments. Perhaps if people see that I've gone through the same struggles that they've been through and made it, it will give them strength. Alas, here I am, broken, confused, tired, mad, sad, frustrated, and everything on the list.

Is wrong to be frustrated with God? Or to want to pick a fight with Him? I don't necessarily think so. It's probably stupid looking to God, who has all of time in view. Job, in the midst of his trials, was pretty frustrated at God, and God basically tried to make it clear that he was being stupid to not trust Him. I do think that God can take our questions, though. I don't think he's offended when we yell at Him, telling him to clear away the confusion. It's not that it's not stupid, but I think God understands that we're human and have the desire to know everything when all we need to know is, "Be still and Know that I am God."

What I'm asking now is, "What is my life about?" I know the purpose of my life is to enjoy God and glorify Him forever. But how specifically do I do this?

Will my life ever amount to anything? Will I ever feel God again? Will the overwhelming anxiety which has plagued me the past few months ever be replaced by God-filled peace?

Will I ever overcome this unbelief? What's causing it? Unwillingness? All I want is to live a life; a beautiful life of God-filled happiness. What's stopping it?

I most of all do not want to waste this precious life I've been given.

Thursday, December 2, 2010

Why?

Who am I? Where am I going? I know God is there, but to what degree is he really there? Is Open theism true? Is Sovereignty only a human ascription to God? What does it even mean?! Does he really have a plan for my life? If he does, why on earth does everything seem so confusing right now? Why?

I know this seems a bit out of line as compared to the posts I usually put up on this blog since I decided to orient it towards apologetics. Right now, however, I need to be vulnerable; if not with anyone, to myself. I struggle with these ridiculous questions too, and right now my heart is in absolute anguish. Earlier in my life I thought to suffer was to experience physical pain, but now as I have lived through the past few months, I see that real suffering is the absence of God in one's heart. I can't imagine the cross, oh, I can't; I don't even want to think about it. In fact, the thing that is specifically bothering me right now is m unwillingness to think of the cross.

Why has my heart hardened so? Why do I not desire God? It would seem at the current moment that I do desire God, but I don't at the same time; I'm afraid of what he's going to do in my life. What has gotten into me? I know the wonder and joy that it is to be filled by God, but I don't want to go there, even though I do. Am I afraid of loss? But how could I lose anything when such a Great and Wonderful Heavenly father waits for me? Am I afraid that I'm making the wrong decision by deciding to live a life in America instead of being a full-time Missionary? Having made this decision, am I becoming less of a "living sacrifice?" Aren't there plenty more challenges to fight living in America? Just because I am not a full-time missionary doesn't mean I cannot be a warrior with a war to fight. Just because I plan on being married doesn't mean I can't have the heart of a lion and the flesh of a lamb. Just because I have someone to love dearly doesn't mean I'm cleaved to this world.

I feel, [gulp], like I am for some reason in rebellion against God because I'm unwilling to jump off the cliff and live. I'm doing everything "right", of course. No "big" sins; not even bad or impure thoughts (as far as willingness goes. I'm fully aware that my every thought is tainted by sin) But there's so, so much more than just abstaining from bad things. How much more should we indulge in the good? I feel the inability to indulge in the goodness, love, outrageous devotion, sacrifice, peace, wonder, awe, spontaneity, glory. What happened to the beautiful life I wanted to live? What happened to the life of praise mine was supposed to be?

In December of last year, I was filled to the brim with the Holy spirit. I was planning on heading to the 10/40 window to preach until I died a horrible, beautiful death. But then I began to experience a small doubt. Wasn't heaven too amazing to be true? To dance and sing, to breathe in and out the love of our Creator, Christ, in his very presence? Then Evolution entered my mind. Were we really evolved from apes? If so, how could we be dignified creatures at all? Was our world really created by God? Or did the Universe create itself ever so slowly? Is the bible reliable at all or even true? All of these led me into eight horrifying months of existential despair, depths of depression, suicidal thoughts, self-doubts, slippery reality, and unending questions about my world view. When it was all over and I came back to faith after hundreds of hours studying, my heart had lost almost every spiritual truth I had gained in the previous semester and summer at college. Although I have moved forward quite a bit from that loss, I still have very far to go.

Part of the battle, however, is an endless mental conflict. As I try to take baby steps to return to the faith I once had, all I can begin remember is how sanctified I once was and begin to beat myself up for my inability to see into these great spiritual truths. When I finally become settled on starting small and growing deeper into Christ, I begin to question myself and why I've allowed myself to become so backslidden through the doubts I had. I also beat myself up for not planning on being a missionary full time. Any of my brothers and sisters in Christ who read this, I would appreciate advice, prayers, anything. Its not on every occasion that I open myself up so, but I feel that the degree to which my heart aches for a taste of the reality of Christ requires my confessing these struggles.

Peace to you all