## Wednesday, June 30, 2010

### Why the Universe is the Way it is

This is a great book. I've only read the first chapter or so but it's great!

Needless to say, I need an accountability partner with my addiction to buying books off of amazon kindle. Either that or a leash. :P

## Wednesday, June 16, 2010

### C.S. Lewis on Joy

The past two days have been laden with convictions. I want to quote C.S. Lewis to kind of sum up my opinion about myself recently.

“If we consider the unblushing promises of reward and the staggering nature of the rewards promised in the Gospels, it would seem that Our Lord finds our desire, not too strong, but too weak. We are half-hearted creatures, fooling about with drink and sex and ambition when infinite joy is offered us, like an ignorant child who wants to go on making mud pies in a slum because he cannot imagine what is meant by the offer of a holiday at the sea. We are far too easily pleased.” C.S. Lewis

It's good to reflect on this.

I also want to add some song lyrics to this. "See the Glory" is a song by Steven Curtis Chapman that I've not come to understand until recent years. It's so powerful when you think about it!

“If we consider the unblushing promises of reward and the staggering nature of the rewards promised in the Gospels, it would seem that Our Lord finds our desire, not too strong, but too weak. We are half-hearted creatures, fooling about with drink and sex and ambition when infinite joy is offered us, like an ignorant child who wants to go on making mud pies in a slum because he cannot imagine what is meant by the offer of a holiday at the sea. We are far too easily pleased.” C.S. Lewis

It's good to reflect on this.

I also want to add some song lyrics to this. "See the Glory" is a song by Steven Curtis Chapman that I've not come to understand until recent years. It's so powerful when you think about it!

So what is this thing I see

Going on inside of me?

When it comes to the grace of God

Sometimes it’s like …

I’m playing Gameboy standing in

the middle of the Grand Canyon

I’m eating candy sittin’ at a gourmet feast

I’m wading in a puddle when I

could be swimming in the ocean

Tell me what’s the deal with me

(I know the time has come for me to)

Wake up and see the glory

Ever star in the sky tells His story, oh

And every breeze is singing His song

All of creation is imploring

Hey, come see this grand phenomenon

The wonder of His grace

Should take my breath away

I miss so many things when I’m consumed with …

How could I trivialize it

This awesome gift of God’s grace?

Once I have come to realize it

I should be speechless and amazed

Wake up and see the glory

Open your eyes and take it in

Wake up and be amazed

Over and over againSo what is this thing I see

Going on inside of me?

When it comes to the grace of God

Sometimes it’s like …

I’m playing Gameboy standing in

the middle of the Grand Canyon

I’m eating candy sittin’ at a gourmet feast

I’m wading in a puddle when I

could be swimming in the ocean

Tell me what’s the deal with me

(I know the time has come for me to)

Wake up and see the glory

Ever star in the sky tells His story, oh

And every breeze is singing His song

All of creation is imploring

Hey, come see this grand phenomenon

The wonder of His grace

Should take my breath away

I miss so many things when I’m consumed with …

How could I trivialize it

This awesome gift of God’s grace?

Once I have come to realize it

I should be speechless and amazed

Wake up and see the glory

Open your eyes and take it in

Wake up and be amazed

Over and over again

## Tuesday, June 15, 2010

### Sentential Logic Rule # 7 & 8- Addition & Disjunctive Syllogism

This is part of the Lessons in Logic Series.

The 7th rule of Logic is called Addition.

It's kind of weird and funny.

First, let me define disjunction in this sense. When we use verbal logic, a disjunction is a divide between two statements, or, a parting. "Either I will go here, or I will go there." A disjunction has two possibilities within one statement. In many cases these possibilities can both be true at the same time, but in all cases, they cannot both be untrue (if it is a true statement). For example, the two disjunctions in the statement, "Tonight, either I'll go bowling or Susan will go bowling." could both be true. But, if one of them is false, then we can rightly conclude that the other must be true. If the aforementioned statement is a true disjunction, then if I don't go bowling, Susan must have gone bowling. It's the same vice versa- If Susan didn't go bowling, then I must have gone bowling. Though it might be tempting, we can't conclude anything from knowing that one of them is true, since it is logically possible that the other is true at the same time.

Some more examples:

"On this fishing trip, I'll either catch a blue fish, or I'll catch a Bass."

Notice how, above, both of statements could be true. I could catch a bluefish and a bass at the same time on the fishing trip. But, if the disjunction is true (which means I'm going to catch something), then if I don't catch a bluefish, I'll catch a bass. And vice versa

"I'll either go to the prom, or I won't."

Now it's clearly obvious that this is a case where only one of the disjunctive statements/possibilities can be true. If I know that I didn't go to the prom, then the disjunct, "I'll go to the prom" has been negated and is not true. If one of the statements is not true, then the other is true.

Rule # 7 , or, Addition (add.) states that, if you know one thing to be true, then it can be put in a disjunction with an outrageous truth and be a true disjunction. For example: I know I am a man. So I can say, "Either I am a man, or my car is made of green cheese." It's a bit weird, but it is a valid conclusion. We know that I am a man, so if I'm not, we can suggest any other ridiculous truth to be it's disjunct if it isn't true.

Addition:

1. P

2. (P v Q)

Rule # 8, or, Disjunctive Syllogism (DS) states that, if there is a true disjunction, then if one of the possibilities is not true, then the other must be true. I've outlined this law in the above writing.

1. Either I will go to the gas station or go straight home

2. I didn't go to the gas station

3. Therefore, I went straight home.

1. (P v Q)

2. ¬Q

3. P

What you

1. (P v Q)

2. Q

3. ¬P

This can't be concluded, since it is logically possible in some cases (not this one) that both (either/or) statements can be true.

Addition isn't used very much in arguments, so it's not necessary that any examples be given.

Here's a more complicated example of Hypothetical syllogism.

1. P -> Q

2. Q -> (R v S)

3. S -> T

4. R -> U

5. P

6. ¬S

7. P-----(Given)

8. Q-----(MP)

9. (R v S)-----(MP)

10. (¬S)-----(Given)

11. R-----(DS)

12. U-----(MP)

13. ¬ T (MT)

:P

The 7th rule of Logic is called Addition.

It's kind of weird and funny.

First, let me define disjunction in this sense. When we use verbal logic, a disjunction is a divide between two statements, or, a parting. "Either I will go here, or I will go there." A disjunction has two possibilities within one statement. In many cases these possibilities can both be true at the same time, but in all cases, they cannot both be untrue (if it is a true statement). For example, the two disjunctions in the statement, "Tonight, either I'll go bowling or Susan will go bowling." could both be true. But, if one of them is false, then we can rightly conclude that the other must be true. If the aforementioned statement is a true disjunction, then if I don't go bowling, Susan must have gone bowling. It's the same vice versa- If Susan didn't go bowling, then I must have gone bowling. Though it might be tempting, we can't conclude anything from knowing that one of them is true, since it is logically possible that the other is true at the same time.

Some more examples:

"On this fishing trip, I'll either catch a blue fish, or I'll catch a Bass."

Notice how, above, both of statements could be true. I could catch a bluefish and a bass at the same time on the fishing trip. But, if the disjunction is true (which means I'm going to catch something), then if I don't catch a bluefish, I'll catch a bass. And vice versa

"I'll either go to the prom, or I won't."

Now it's clearly obvious that this is a case where only one of the disjunctive statements/possibilities can be true. If I know that I didn't go to the prom, then the disjunct, "I'll go to the prom" has been negated and is not true. If one of the statements is not true, then the other is true.

Rule # 7 , or, Addition (add.) states that, if you know one thing to be true, then it can be put in a disjunction with an outrageous truth and be a true disjunction. For example: I know I am a man. So I can say, "Either I am a man, or my car is made of green cheese." It's a bit weird, but it is a valid conclusion. We know that I am a man, so if I'm not, we can suggest any other ridiculous truth to be it's disjunct if it isn't true.

Addition:

1. P

2. (P v Q)

Rule # 8, or, Disjunctive Syllogism (DS) states that, if there is a true disjunction, then if one of the possibilities is not true, then the other must be true. I've outlined this law in the above writing.

1. Either I will go to the gas station or go straight home

2. I didn't go to the gas station

3. Therefore, I went straight home.

**Disjunctive Syllogism**1. (P v Q)

2. ¬Q

3. P

What you

*can't*conclude with hypothetical syllogism.1. (P v Q)

2. Q

3. ¬P

This can't be concluded, since it is logically possible in some cases (not this one) that both (either/or) statements can be true.

Addition isn't used very much in arguments, so it's not necessary that any examples be given.

Here's a more complicated example of Hypothetical syllogism.

1. P -> Q

2. Q -> (R v S)

3. S -> T

4. R -> U

5. P

6. ¬S

7. P-----(Given)

8. Q-----(MP)

9. (R v S)-----(MP)

10. (¬S)-----(Given)

11. R-----(DS)

12. U-----(MP)

13. ¬ T (MT)

:P

### Sentential Logic Rule #6 - Absorption

This is part of the Lessons in logic Series.

The next rule I want to summarize is called absorption. (absp.)

This rule is kind of peculiar, yet pretty simple I think. The law of absorption states that , if P implies Q, and P is true, then P and Q are true.

Logical Form:

1. P -> Q

2. P

3. P & Q

Why is this true? Well, we know this: (P -> Q), or, that P implies Q. That means that if P is true, then Q is true. But if we know P is true, and we know that P -> Q, then by knowing P is true, we also know Q is true. So if we know P and Q are true, we can conclude : P & Q.

Here's a verbal form.

1. If I am a soccer player, I am an athlete.

2. I am a soccer player.

3. Therefore, I am a soccer player and an athlete.

Seems pretty simple!! Here's a more complicated argument that it's useful in.

1. P -> Q

2. Q -> R

3. (P & R) -> S

4. P

5. P-------- (Given)

6. P -> R--------(Hyp. Syllogism)

7. (P & R)--------(Absp.) (If P is true, then R is true. P is true, therefore P and R are true.)

8. S--------(MP)

:)

The next rule I want to summarize is called absorption. (absp.)

This rule is kind of peculiar, yet pretty simple I think. The law of absorption states that , if P implies Q, and P is true, then P and Q are true.

Logical Form:

1. P -> Q

2. P

3. P & Q

Why is this true? Well, we know this: (P -> Q), or, that P implies Q. That means that if P is true, then Q is true. But if we know P is true, and we know that P -> Q, then by knowing P is true, we also know Q is true. So if we know P and Q are true, we can conclude : P & Q.

Here's a verbal form.

1. If I am a soccer player, I am an athlete.

2. I am a soccer player.

3. Therefore, I am a soccer player and an athlete.

Seems pretty simple!! Here's a more complicated argument that it's useful in.

1. P -> Q

2. Q -> R

3. (P & R) -> S

4. P

5. P-------- (Given)

6. P -> R--------(Hyp. Syllogism)

7. (P & R)--------(Absp.) (If P is true, then R is true. P is true, therefore P and R are true.)

8. S--------(MP)

:)

## Sunday, June 6, 2010

### Idols

"When you cry out, let your collection of idols deliver you! The wind will carry them off, a breath will take them away. But he who takes refuge in me shall possess the land and shall inherit my holy mountain." - Isaiah 57

Oh Lord, my God! Be my true God! Be my object of worship, that all can see the glorious freedom that it brings! Rid me of my idols, for they will not satisfy the deepest longings of my heart..

Oh Lord, my God! Be my true God! Be my object of worship, that all can see the glorious freedom that it brings! Rid me of my idols, for they will not satisfy the deepest longings of my heart..

### Sentential Logic Rule #5 - Simplification

This is post number 5 of the Lessons in Logic Series.

The 5th rule of Sentential logic is called "simplification", or, "Simp."

Simplification, like Conjunction, is very simple. If there is a sentence that contains multiple truth statements, the law of Simplification states that you may derive each truth statement into a single proposition. For example: "I have a car, a plane, and an apple." can be derived into- "I have a Car. I have a plane. I have an apple".

The Logical form--

1. P & Q

2. P (Simp. 1)

3. Q (Simp. 1)

Since we knew that P and Q were true in one statement, we could derive it into multiple statements.

A more complicated argument involving Simplification would look like this:

1. P -> Q----- If P is true, then Q is true

2. (P & R)-----P and R are true

3. P-----(Simp., 2) ----- Therefore, P is true.

4. R-----(Simp., 2) ----- Therefore, R is true.

5. Q-----(MP 1,3) ------- Therefore, Q is true.

The 5th rule of Sentential logic is called "simplification", or, "Simp."

Simplification, like Conjunction, is very simple. If there is a sentence that contains multiple truth statements, the law of Simplification states that you may derive each truth statement into a single proposition. For example: "I have a car, a plane, and an apple." can be derived into- "I have a Car. I have a plane. I have an apple".

The Logical form--

1. P & Q

2. P (Simp. 1)

3. Q (Simp. 1)

Since we knew that P and Q were true in one statement, we could derive it into multiple statements.

A more complicated argument involving Simplification would look like this:

1. P -> Q----- If P is true, then Q is true

2. (P & R)-----P and R are true

3. P-----(Simp., 2) ----- Therefore, P is true.

4. R-----(Simp., 2) ----- Therefore, R is true.

5. Q-----(MP 1,3) ------- Therefore, Q is true.

## Saturday, June 5, 2010

### Sentential Logic Rule #4 - Conjunction

This is Post #4 in the Lessons in Logic Series.

The next few laws of logic are pretty simple, after getting past necessary and sufficient truths.

Rule #4 is called "Conjunction", or, abbreviated: "Conj."

Conjunction is simply adding two(or more) propositions together to make a statement which contains both truths. For example: I am a Parrot. I am Green. -> I am green, and I am a Parrot. Or you could say I am a green Parrot.

1. P

2. Q

3. P & Q

P is true. Q is true. Therefore, P and Q are true.

A more complicated argument this could be used in looks a little bit like this.

1. (P & Q) -> R-------(If P and Q are true, then R is true)

2. S -> P-------------(If S is true, then P is true)

3. T -> Q-------------(If T is true, then Q is true)

4. S------------------(S is true)

5. T------------------(T is true)

6. S-----------(#4)-------------------------S is true (taken from the given truth)

7. T-----------(#5)-------------------------T is true (taken from the given truth)

8. P-----------((MP-modus ponens) #2, #6)---Therefore, P is true

9. Q-----------((MP-modus ponens) #3, #7)---Therefore, Q is true

10. P & Q------(Conj. 8,9)------------------Therefore, P and Q are true

11. R----------(MP 1,10)--------------------Therefore, R is true.

Any questions just add a comment! If you're learning these, make sure you try making up your own situation and arguments and try practicing them!

The next few laws of logic are pretty simple, after getting past necessary and sufficient truths.

Rule #4 is called "Conjunction", or, abbreviated: "Conj."

Conjunction is simply adding two(or more) propositions together to make a statement which contains both truths. For example: I am a Parrot. I am Green. -> I am green, and I am a Parrot. Or you could say I am a green Parrot.

1. P

2. Q

3. P & Q

P is true. Q is true. Therefore, P and Q are true.

A more complicated argument this could be used in looks a little bit like this.

1. (P & Q) -> R-------(If P and Q are true, then R is true)

2. S -> P-------------(If S is true, then P is true)

3. T -> Q-------------(If T is true, then Q is true)

4. S------------------(S is true)

5. T------------------(T is true)

6. S-----------(#4)-------------------------S is true (taken from the given truth)

7. T-----------(#5)-------------------------T is true (taken from the given truth)

8. P-----------((MP-modus ponens) #2, #6)---Therefore, P is true

9. Q-----------((MP-modus ponens) #3, #7)---Therefore, Q is true

10. P & Q------(Conj. 8,9)------------------Therefore, P and Q are true

11. R----------(MP 1,10)--------------------Therefore, R is true.

Any questions just add a comment! If you're learning these, make sure you try making up your own situation and arguments and try practicing them!

## Wednesday, June 2, 2010

### Look out for the Holy Spirit

Careful... convictions of the Holy spirit will hit you like a train wreck, cause you to burst into tears of sorrow, effect in you the most painful, yet willful repentance, seize you with daggers of unrelenting sorrow and pain, and assure of future joy. Jesus wasn't kidding.

"I have much more to say to you, more than you can now bear. 13But when he, the Spirit of truth, comes, he will guide you into all truth. He will not speak on his own; he will speak only what he hears, and he will tell you what is yet to come. 14He will bring glory to me by taking from what is mine and making it known to you. 15All that belongs to the Father is mine. That is why I said the Spirit will take from what is mine and make it known to you."

## Tuesday, June 1, 2010

### Lessons in Sentential Logic, Rule # 3 Hypothetical Syllogism

This is post number three in the Lessons in logic series.

Hypothetical Syllogism is very simple. It's almost like an identity rule, which is very natural to us.

This is the Logical Form:

1. P -> Q

2. Q -> R

3. P -> R

1. If I wake up, I will go to work.

2. If I go to work, I will get paid.

3. Therefore, if I wake up, I will get paid.

1.If I am dog, I am an animal.

2.If I am an animal, then I am a physical entity.

3. Therefore, if I am a dog, I am a physical entity.

Simple enough?

Thus, Hypothetical Syllogism! or (HS)

Here's a more complicated argument that you could use (HS) in.

1. P -> Q

2. Q -> R

3. ¬ R

What Happens?

Well, if R isn't true, we know that if Q -> R, and ¬R, then Q can't be true. And if P -> Q, and ¬Q, then P can't be true. Therefore, if we have the above listed information, we can conclude:

4. ¬ P

Any questions let me know!

Hypothetical Syllogism is very simple. It's almost like an identity rule, which is very natural to us.

This is the Logical Form:

1. P -> Q

2. Q -> R

3. P -> R

1. If I wake up, I will go to work.

2. If I go to work, I will get paid.

3. Therefore, if I wake up, I will get paid.

1.If I am dog, I am an animal.

2.If I am an animal, then I am a physical entity.

3. Therefore, if I am a dog, I am a physical entity.

Simple enough?

Thus, Hypothetical Syllogism! or (HS)

Here's a more complicated argument that you could use (HS) in.

1. P -> Q

2. Q -> R

3. ¬ R

What Happens?

Well, if R isn't true, we know that if Q -> R, and ¬R, then Q can't be true. And if P -> Q, and ¬Q, then P can't be true. Therefore, if we have the above listed information, we can conclude:

4. ¬ P

Any questions let me know!

### Lessons in Sentential Logic - Rule # 2 Modus Tollens

Ok, so this is going to be the next post about "Lessons in Logic".

Last post, I covered the first rule of Sentential logic,

What MP stated was, if Q's truth logically follows from P's truth, and if P is true, then Q is true.

1. P -> Q

2. P

3. Q

So, according to (MP), if P -> Q (if P's truth implies Q's truth) , and P (P is true), then Q (Q is true).

Before I go onto the next rule of Logic, I want to talk more about

In the last post, I described a sufficient cause as a something which, if true, implies certain truths which are necessary.

For Example: If it is true that I am a soccer player, then that naturally

I'll list a few of these things which must be true if I am a soccer player:

1. I must be an athlete.

2. I must play a sport.

3. I must be alive.

4. I must have touched a soccer ball.

So, If I am a common soccer player, then ALL of these truths listed above naturally follow. You'll notice that the truth of my being a soccer player is

Here's an interesting way I like to think about it: A truth is like a house, resting 10 feet in the air. If the house is up in the air, you must ask, "How in the world is it resting 10 feet in the air? There must be something supporting it!" Then you notice that the house (or, the truth) is resting on four columns. These columns are sturdy and are strong enough to keep the house stable at 10 feet in the air.

But what happens if one of the columns breaks down and falls over? The house will fall over! The house's altitude is absolutely dependent on each column, and if even one of them falls, then the house will topple. A logical truth is very similar! You have a sufficient cause: a house, ten feet up in the air. If the house is ten feet in the air, then you

Here's a picture I attempted to draw to illustrate it (have mercy on my bad art skills!):

So, observe from this pictures that you've first got P, the house. If P is true, or, the house is sitting up 10 feet in the air, then that means necessarily that Q1, Q2, Q3, and Q4 are true, or, there are 4 columns supporting it. That means that the house, P, is the sufficient condition, and that the four Qs are the necessary conditions.

Here's where I'm going to introduce the next rule of logic,

Notice that, if any of the columns falls down, the house will topple also. If the house is sitting up in the air, that means that all four columns MUST be supporting it. (remember this is an illustration, there are certainly more Q's that could be added as necessarily implied truths from/supporting the truth of my being a soccer player)

But, if one of the columns falls down, then the house must fall, and P must not be true.

Logical Form:

1. P -> Q

2. ¬ Q

3. ¬ P

So, let's return to the soccer player example.

We know that, if I am a soccer player, it logically follows that I am these things:

(labeling them as the necessary truths they represent)

1. I must be an athlete. (Q1)

2. I must play a sport. (Q2)

3. I must be alive. (Q3)

4. I must have touched a soccer ball. (Q4)

So, P implies these four Q's (and more, but I'm not adding these).

Let's try taking out the columns underneath the house, or, "P", or, "I am a soccer player".

1. If I am not an athlete, then I cannot be a soccer player. (¬ Q1 -> ¬P)

Even if this Q1 column is taken from underneath the foundation, P's truth cripples, or, is "¬", negated.

2. If I don't play a sport, I don't play soccer. (¬ Q2 -> ¬ P)

The same for the second one. If I don't play a sport, I don't play soccer!

It's the same for the rest of them. You may be wondering why I'm using 4 Q's instead of just one like you've seen in arguments, but no worries: you select one of the Q's and deal with them.

For Ex:

1. If I am a soccer player, I play a sport.

2. I don't play a sport.

3. Therefore, I am not a soccer player.

But remember! Just because you have one or two columns, that doesn't mean the house is up there! Just because I am a alive, or because I am alive and I play a sport, does not mean I am a soccer player. In other words, If (P -> Q) and you know Q is true, you can't conclude anything.

So, now you know...

1. (P -> Q)

2. ¬ Q

3. ¬ P

Peace!

Last post, I covered the first rule of Sentential logic,

*modus ponens*. (Hereafter to be substituted as (MP).What MP stated was, if Q's truth logically follows from P's truth, and if P is true, then Q is true.

**The Logical Form**:1. P -> Q

2. P

3. Q

So, according to (MP), if P -> Q (if P's truth implies Q's truth) , and P (P is true), then Q (Q is true).

Before I go onto the next rule of Logic, I want to talk more about

*sufficient causes/conditions*and*necessary truths*.In the last post, I described a sufficient cause as a something which, if true, implies certain truths which are necessary.

For Example: If it is true that I am a soccer player, then that naturally

*requires*that several things*have*to be true.I'll list a few of these things which must be true if I am a soccer player:

1. I must be an athlete.

2. I must play a sport.

3. I must be alive.

4. I must have touched a soccer ball.

So, If I am a common soccer player, then ALL of these truths listed above naturally follow. You'll notice that the truth of my being a soccer player is

*sufficient*to cause all of the above to*necessarily*follow.Here's an interesting way I like to think about it: A truth is like a house, resting 10 feet in the air. If the house is up in the air, you must ask, "How in the world is it resting 10 feet in the air? There must be something supporting it!" Then you notice that the house (or, the truth) is resting on four columns. These columns are sturdy and are strong enough to keep the house stable at 10 feet in the air.

But what happens if one of the columns breaks down and falls over? The house will fall over! The house's altitude is absolutely dependent on each column, and if even one of them falls, then the house will topple. A logical truth is very similar! You have a sufficient cause: a house, ten feet up in the air. If the house is ten feet in the air, then you

*know*it is necessary that there are columns supporting it. These columns are the necessary truths which not only logically follow from an argument, but also support its truth.Here's a picture I attempted to draw to illustrate it (have mercy on my bad art skills!):

So, observe from this pictures that you've first got P, the house. If P is true, or, the house is sitting up 10 feet in the air, then that means necessarily that Q1, Q2, Q3, and Q4 are true, or, there are 4 columns supporting it. That means that the house, P, is the sufficient condition, and that the four Qs are the necessary conditions.

Here's where I'm going to introduce the next rule of logic,

*modus tollens*.Notice that, if any of the columns falls down, the house will topple also. If the house is sitting up in the air, that means that all four columns MUST be supporting it. (remember this is an illustration, there are certainly more Q's that could be added as necessarily implied truths from/supporting the truth of my being a soccer player)

But, if one of the columns falls down, then the house must fall, and P must not be true.

*Modus Tollens*, or (MT), states that, if Q's truth is implied by P's truth, and if Q is not true, then P can't be true. (note that "¬P" means, "not" P, or, "P is not true". Or, you could say, "¬¬P" means "not not P", which is the same thing as "P".Logical Form:

1. P -> Q

2. ¬ Q

3. ¬ P

So, let's return to the soccer player example.

We know that, if I am a soccer player, it logically follows that I am these things:

(labeling them as the necessary truths they represent)

1. I must be an athlete. (Q1)

2. I must play a sport. (Q2)

3. I must be alive. (Q3)

4. I must have touched a soccer ball. (Q4)

So, P implies these four Q's (and more, but I'm not adding these).

Let's try taking out the columns underneath the house, or, "P", or, "I am a soccer player".

1. If I am not an athlete, then I cannot be a soccer player. (¬ Q1 -> ¬P)

Even if this Q1 column is taken from underneath the foundation, P's truth cripples, or, is "¬", negated.

2. If I don't play a sport, I don't play soccer. (¬ Q2 -> ¬ P)

The same for the second one. If I don't play a sport, I don't play soccer!

It's the same for the rest of them. You may be wondering why I'm using 4 Q's instead of just one like you've seen in arguments, but no worries: you select one of the Q's and deal with them.

For Ex:

1. If I am a soccer player, I play a sport.

2. I don't play a sport.

3. Therefore, I am not a soccer player.

But remember! Just because you have one or two columns, that doesn't mean the house is up there! Just because I am a alive, or because I am alive and I play a sport, does not mean I am a soccer player. In other words, If (P -> Q) and you know Q is true, you can't conclude anything.

So, now you know...

1. (P -> Q)

2. ¬ Q

3. ¬ P

Peace!

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