Friday, December 23, 2005
Learn Something New Every Day
I was going to write this post on what I thought was a grammar mistake on the front page of CNN's website. Under a picture of travelers at LAX, the caption reads, "Travelers cue up at Los Angeles International Airport today." I was going to say that the proper word is "queue" not "cue," but then I double checked with Merriam-Webster. Sure enough, "cue" (main entry #5) is an alternate spelling for "queue."
Wednesday, December 21, 2005
Logic Lesson: The Four Forms of Propositions
In Aristotelian logic, there are four forms of propositions: universal affirmative, universal negative, particular affirmative, and particular negative. All declarative sentences can be properly characterized as one of these four forms.
For brevity, we may refer to each of these forms by a system of abbreviation, which was codified during the Middle Ages. The abbreviations are as follows: A = universal affirmative, E = universal negative, I = particular affirmative, and O = particular negative.*
If we use the letter "S" to stand for the logical subject and the letter "P" to stand for the logical predicate, the forms of the four propositions can be given as follows:
A: All S is P.
E: No S is P.
I: Some S is P.
O: Some S is not P.
Some examples: "All men are mortal" is in A form; that is, it is a universal affirmative proposition. "No ravens are white" is in E form. "Some politicians are corrupt" is in I form. And "Some politicians are not corrupt" is in O form.**
When we say a proposition is universal or particular, we are describing its quantity; when we say it is affirmative or negative, we refer to its quality. So, for example, how do we know that "All men are mortal" is a universal affirmative proposition? It is universal because it refers to all men, and it is affirmative because it says that all men are such and such, as opposed to saying that all men are not such and such. "Some politicians are not corrupt" is in O form because it talks about some politicians and says that they are not corrupt.
There are other finer details to go into, but we will put them off until later. Try your hand at some exercises given in the post below. Answers to the exercises appear when you click "Read more."
* The reasoning behind the abbreviations is that the Latin affirmo has as its first two vowels "a" and "i", and the Latin nego has as its first two vowels "e" and "o".
** More on the O in the answer to exercise 12.
For brevity, we may refer to each of these forms by a system of abbreviation, which was codified during the Middle Ages. The abbreviations are as follows: A = universal affirmative, E = universal negative, I = particular affirmative, and O = particular negative.*
If we use the letter "S" to stand for the logical subject and the letter "P" to stand for the logical predicate, the forms of the four propositions can be given as follows:
A: All S is P.
E: No S is P.
I: Some S is P.
O: Some S is not P.
Some examples: "All men are mortal" is in A form; that is, it is a universal affirmative proposition. "No ravens are white" is in E form. "Some politicians are corrupt" is in I form. And "Some politicians are not corrupt" is in O form.**
When we say a proposition is universal or particular, we are describing its quantity; when we say it is affirmative or negative, we refer to its quality. So, for example, how do we know that "All men are mortal" is a universal affirmative proposition? It is universal because it refers to all men, and it is affirmative because it says that all men are such and such, as opposed to saying that all men are not such and such. "Some politicians are not corrupt" is in O form because it talks about some politicians and says that they are not corrupt.
There are other finer details to go into, but we will put them off until later. Try your hand at some exercises given in the post below. Answers to the exercises appear when you click "Read more."
* The reasoning behind the abbreviations is that the Latin affirmo has as its first two vowels "a" and "i", and the Latin nego has as its first two vowels "e" and "o".
** More on the O in the answer to exercise 12.
Logic Exercises: The Four Forms of Propositions
These are excercises to accompany this post. Identify the form of each proposition. Answers appear when you click "Read more."
Easy ones:
1. Some pens are blue.
2. All cows are brown.
3. All philosophers with a PhD are poor.
4. Nobody is worth talking to.
5. Some books worth reading are worth buying.
6. All those who shop at Trader Joes are gourmands.
A little more difficult:
7. Most academics are liberal.
8. Most academics are conservative.
9. Everyone from New Jersey loves Bruce Springsteen.
Still more difficult:
10. Some wise guys are unwise.
11. All gods are immortal.
Tricky:
12. All ravens are not white.
13. Nobody doesn't like Sara Lee.
Answers
1. I
2. A
3. A (This is universal even though the "all" is qualified by "with a PhD." A proposition is universal if it refers to all the members of the class with which it is concerned. So even though "all philosophers with a PhD" does not include every philosopher (e.g., Richard Swinburne, who is a philosopher, does not have a PhD), the quantity is universal because with respect to philosophers with a PhD, it refers to all of them.)
4. E
5. I
6. A
7. I ("Most" still falls short of being all, and so logically indicates a particular quantity.)
8. I (Don't want to be accused of inserting bias into logic examples.)
9. A
10. I (You might think that since the predicate is "unwise" the quality would be negative, thus giving us an O. But the quality of the proposition is not negative -- it says that some wise guys are such and such -- even though the quality of the predicate is negative. Distinguishing between a negative proposition and a negative predicate is one of the trickiest parts of Aristotelian logic.)
11. A (Same reason as above.)
12. E or O. (The English in this sentence is ambiguous. In English, when we say "All ravens are not white" we could mean that there are no ravens whatsoever that are white. This would be consistent with the E form: No S is P. If we were trying to weasel out of something, we could also take "All ravens are not white" to mean that there are some ravens that are white. In other words we would emphasize the "all" in "All ravens are not white." It is because of this ambiguity that we give the E form as "No S is P" instead of "All S is not P," which is what one might have expected given the form of A, "All S is P."
13. E. (In logical form, this sentence would be "Nobody [is] [that which] doesn't like Sara Lee." For reasons discussed in answer 10, this makes the answer here E.)
Easy ones:
1. Some pens are blue.
2. All cows are brown.
3. All philosophers with a PhD are poor.
4. Nobody is worth talking to.
5. Some books worth reading are worth buying.
6. All those who shop at Trader Joes are gourmands.
A little more difficult:
7. Most academics are liberal.
8. Most academics are conservative.
9. Everyone from New Jersey loves Bruce Springsteen.
Still more difficult:
10. Some wise guys are unwise.
11. All gods are immortal.
Tricky:
12. All ravens are not white.
13. Nobody doesn't like Sara Lee.
Answers
1. I
2. A
3. A (This is universal even though the "all" is qualified by "with a PhD." A proposition is universal if it refers to all the members of the class with which it is concerned. So even though "all philosophers with a PhD" does not include every philosopher (e.g., Richard Swinburne, who is a philosopher, does not have a PhD), the quantity is universal because with respect to philosophers with a PhD, it refers to all of them.)
4. E
5. I
6. A
7. I ("Most" still falls short of being all, and so logically indicates a particular quantity.)
8. I (Don't want to be accused of inserting bias into logic examples.)
9. A
10. I (You might think that since the predicate is "unwise" the quality would be negative, thus giving us an O. But the quality of the proposition is not negative -- it says that some wise guys are such and such -- even though the quality of the predicate is negative. Distinguishing between a negative proposition and a negative predicate is one of the trickiest parts of Aristotelian logic.)
11. A (Same reason as above.)
12. E or O. (The English in this sentence is ambiguous. In English, when we say "All ravens are not white" we could mean that there are no ravens whatsoever that are white. This would be consistent with the E form: No S is P. If we were trying to weasel out of something, we could also take "All ravens are not white" to mean that there are some ravens that are white. In other words we would emphasize the "all" in "All ravens are not white." It is because of this ambiguity that we give the E form as "No S is P" instead of "All S is not P," which is what one might have expected given the form of A, "All S is P."
13. E. (In logical form, this sentence would be "Nobody [is] [that which] doesn't like Sara Lee." For reasons discussed in answer 10, this makes the answer here E.)
Tuesday, December 20, 2005
Monday, December 19, 2005
Faith & Philosophy: A Short Spiel
What is a philosopher? A philosopher is a person who has an interest in studying the really permanent things, things that will last more than a few hours or days or years. So studying philosophy is time well spent because you know the subject matter really isn’t going to change in the next few years. And not a lot of other areas of study can actually say that.
Now being a philosopher doesn't make you boring. You might think otherwise because when you think of "philosophy" you think of old guys in tweed jackets talking in long, confusing sentences about whether the table really exists. No, no, no. That's a caricature of philosophy. It's what Susan Pevensie is like at the beginning of The Lion, the Witch, and the Wardrobe. She wants to be realistic about everything and think things through, which are good things in and of themselves, but in trying to be grown up she's also become boring. Lucky for Susan, she realizes this and sees that she can be both realistic and jolly. As Aslan says in The Magician’s Nephew, "Jokes as well as justice come in with speech."
So a philosopher is not necessarily boring. But a philosopher is necessarily curious -- about the world and what it's really like.
Christians have always been interested in philosophy, not only for its own sake but for what it can help us understand about our faith. Many of the great philosophers have also been Christian, and many of these Christian philosophers have also been great Christians. In fact, in not a few cases, these Christians were great Christians -- real heroes of the faith -- not in spite of but because they were good philosophers: St. Augustine, St. Thomas Aquinas, Pascal, even C. S. Lewis.
Philosophy is known in the Christian tradition as the handmaiden to philosophy. What's a handmaiden? A handmaiden is a person who serves another, greater person. In the case of philosophy, philosophy is a servant to theology. Philosophy helps us to understand theology -- our Christian faith -- better. So for Christians, studying philosophy is a way of helping us increase our knowledge of God. And why is that important? Because knowledge and love go hand in hand. The more you know about God, the more you are able to love him. You can't increase in love without increasing in knowledge.
But why would you want to study Plato? After all, he wasn't a Christian, and doesn't the apostle Paul tell us to avoid vain philosophy?
We have to keep in mind that the same apostle who asked the Colossians to avoid vain philosophy is the same one who also eloquently and knowledgeably addressed the best philosophy of his time when he visited Athens. So Paul was no stranger to philosophy, and he most likely knew some Plato, too.
And as for Plato, a twentieth-century philosopher has said that all philosophy is a footnote to Plato. Plato is the real beginning of philosophy. There isn't much in philosophy that Plato didn't intelligently comment about. So if we want to follow in the footsteps of the great philosophers, we'll want to begin with Plato.
Thirty or forty years ago, a common attitude of Christians to philosophy was "Bah, philosophy." But then some Christians began to realize that the alternative to philosophy was not to not have a philosophy at all, the "alternative" to philosophy was to have a bad philosophy. And studying philosophy doesn't necessarily make you proud. As Christians we want to develop the virtue of humility, but the opposite of humility is pride, not ignorance. Lewis says in one of his most famous books that God requires us to love him with all that we are, and that includes our mind. The command to be good requires that we be as intelligent as we can.
In college, almost all of the criticisms you'll hear about Christianity will be philosophical ones. It might seem otherwise but it's not. Has science really shown that Christianity is false? Well, that's a philosophical question, not a scientific one. Can we really understand the text of the Bible because, after all, don't we have biases when reading the Bible? Again, that's a philosophical question, not a literary one. Is there such a thing as the soul, or can I be just reduced to my brain and nervous system? A philosophical question, not a psychological or neuroscientific one.
So can studying Plato help you in your Christian walk? Yes, most definitely. Will an understanding of good philosophy help you become a better disciple of Jesus Christ. Yes, most definitely. And that will be a very exciting thing; it won't be boring at all.
Now being a philosopher doesn't make you boring. You might think otherwise because when you think of "philosophy" you think of old guys in tweed jackets talking in long, confusing sentences about whether the table really exists. No, no, no. That's a caricature of philosophy. It's what Susan Pevensie is like at the beginning of The Lion, the Witch, and the Wardrobe. She wants to be realistic about everything and think things through, which are good things in and of themselves, but in trying to be grown up she's also become boring. Lucky for Susan, she realizes this and sees that she can be both realistic and jolly. As Aslan says in The Magician’s Nephew, "Jokes as well as justice come in with speech."
So a philosopher is not necessarily boring. But a philosopher is necessarily curious -- about the world and what it's really like.
Christians have always been interested in philosophy, not only for its own sake but for what it can help us understand about our faith. Many of the great philosophers have also been Christian, and many of these Christian philosophers have also been great Christians. In fact, in not a few cases, these Christians were great Christians -- real heroes of the faith -- not in spite of but because they were good philosophers: St. Augustine, St. Thomas Aquinas, Pascal, even C. S. Lewis.
Philosophy is known in the Christian tradition as the handmaiden to philosophy. What's a handmaiden? A handmaiden is a person who serves another, greater person. In the case of philosophy, philosophy is a servant to theology. Philosophy helps us to understand theology -- our Christian faith -- better. So for Christians, studying philosophy is a way of helping us increase our knowledge of God. And why is that important? Because knowledge and love go hand in hand. The more you know about God, the more you are able to love him. You can't increase in love without increasing in knowledge.
But why would you want to study Plato? After all, he wasn't a Christian, and doesn't the apostle Paul tell us to avoid vain philosophy?
We have to keep in mind that the same apostle who asked the Colossians to avoid vain philosophy is the same one who also eloquently and knowledgeably addressed the best philosophy of his time when he visited Athens. So Paul was no stranger to philosophy, and he most likely knew some Plato, too.
And as for Plato, a twentieth-century philosopher has said that all philosophy is a footnote to Plato. Plato is the real beginning of philosophy. There isn't much in philosophy that Plato didn't intelligently comment about. So if we want to follow in the footsteps of the great philosophers, we'll want to begin with Plato.
Thirty or forty years ago, a common attitude of Christians to philosophy was "Bah, philosophy." But then some Christians began to realize that the alternative to philosophy was not to not have a philosophy at all, the "alternative" to philosophy was to have a bad philosophy. And studying philosophy doesn't necessarily make you proud. As Christians we want to develop the virtue of humility, but the opposite of humility is pride, not ignorance. Lewis says in one of his most famous books that God requires us to love him with all that we are, and that includes our mind. The command to be good requires that we be as intelligent as we can.
In college, almost all of the criticisms you'll hear about Christianity will be philosophical ones. It might seem otherwise but it's not. Has science really shown that Christianity is false? Well, that's a philosophical question, not a scientific one. Can we really understand the text of the Bible because, after all, don't we have biases when reading the Bible? Again, that's a philosophical question, not a literary one. Is there such a thing as the soul, or can I be just reduced to my brain and nervous system? A philosophical question, not a psychological or neuroscientific one.
So can studying Plato help you in your Christian walk? Yes, most definitely. Will an understanding of good philosophy help you become a better disciple of Jesus Christ. Yes, most definitely. And that will be a very exciting thing; it won't be boring at all.
Friday, December 16, 2005
Martyrdom
Why is a martyr not guilty of suicide? The Christian church has approved of the former but not of the latter. Is it inconsistent?
No.
In the case of the suicide, the person committing suicide is violating directly the moral maxim to not harm oneself. Generally, the person committing suicide wishes to bring about something (peace, relief of burden to others, etc.) and so acts in such a way to attempt to bring those things to pass. But the suicide's justification is not sufficient, for in attempting to bring certain goods to be he is directly violating a moral maxim, or as some would say, a "basic value."
In the case of the martyr, the martyr does not directly violate the moral maxim to not harm oneself. The martyr does not directly bring about his or her own death. Rather, the martyr is responsible for, say, defying the wishes or commands of the tyrant to deny the Christian faith. It is the tyrant who brings about the death of the martyr.
No.
In the case of the suicide, the person committing suicide is violating directly the moral maxim to not harm oneself. Generally, the person committing suicide wishes to bring about something (peace, relief of burden to others, etc.) and so acts in such a way to attempt to bring those things to pass. But the suicide's justification is not sufficient, for in attempting to bring certain goods to be he is directly violating a moral maxim, or as some would say, a "basic value."
In the case of the martyr, the martyr does not directly violate the moral maxim to not harm oneself. The martyr does not directly bring about his or her own death. Rather, the martyr is responsible for, say, defying the wishes or commands of the tyrant to deny the Christian faith. It is the tyrant who brings about the death of the martyr.
Subscribe to:
Posts (Atom)