jeremy_liberius

Logic 2

jeremy.liberius@gmail.com — Tue, 30 Sep 2008 21:15:00 GMT

I met with the professor after class today, and I was able to demonstrate to him that the Caesar and the TV Star syllogisms were invalid. Following a tip (Thanks, Virum) I investigated into the <url=http://en.wikipedia.org/wiki/illicit_major>Illicit Major Fallacy</url>, and discovered that the error was due to distribution (meaning, in syllogisms, whether every member of the class is referred to). Browsing around a bit, I found the best way to demonstrate distribution was the Venn Diagram, and so I prepared another argument using the proper terminology and Venn Diagrams to back up my point. After I drew a few on the board for him, he understood where the error was.

He was very understanding and courteous through the entire process. Apparently, he saw the conditional statements in the my email, and assumed that my questions would be answered by today's lecture. He also noted that it had been a couple years since he had used Venn Diagrams to help teach syllogisms, as they apparently confuse people.

I want to thank Virum again for pointing me in the right direction, and for the vote of the confidence. When I posted last night, I was at ends over this; I didn't know whether I displaying some massive logical error, or whether I was completely incoherent.

Logic

jeremy.liberius@gmail.com — Tue, 30 Sep 2008 02:39:23 GMT

Any of you who have studied logic, can you look over the following and tell me whether I have lost my mind?

I am taking a class called "Introduction to Logic", and last Tuesday we started Categorical Syllogisms. During the class activities the professor represented "He would not take the crown: therefore 'tis certain he was not ambitious." (Julius Caesar, act 3, sc 2) as

"One who would take the crown is ambitious.
He would not take the crown.
Therefore, He was not ambitious."

, supplying the major premise.

This struck me as wrong, but I had to continue on with other work, so I decided to come back to it. Eventually I came to this later example:

All certified public accountants are people of good business sense.
No television stars are certified public accountants.
Therefore, No television stars are people of good business sense.

I thought this was a fairly good example of why the previous Caesar syllogism was invalid, and called the teacher over to ask him about it. He thought I was getting held up over whether the syllogisms were true (as it is distinct in syllogisms), and he stated that this (TV Star syllogism) was valid.

Still confused after class, I came up with the following syllogism, hoping to prove by analogy that both the preceding were invalid.

All fish are mortal.
Socrates is not a fish.
Therefore, Socrates is not a mortal.

Both of the premises are ostensibly true, yet the conclusion is ostensibly false. Thus, the syllogism must be invalid, and so must the Caesar and TV Star syllogisms, as they share the same form (AEE-1).

The professor had encouraged us to contact him by email should we have any questions, and since I had to contact him for an unrelated purpose anyway, I decided to send him the following:

...

I have some questions about syllogisms that I don't feel we resolved in class. This is due most likely to my underdeveloped abilities to express myself verbally, and my tendency not to speak clearly. Hopefully, by asking in writing, it will be easier to discern where I am in error.

In class, you implied that the following categorical syllogisms were valid, though not necessarily true.

One who would take the crown is ambitious.
He did not take the crown.
Therefore, he is not ambitious.

All certified public accountants are people of good business sense.
No television stars are certified public accountants.
Therefore, No television stats are people of good business sense.

I had a great deal of trouble expressing why I felt these syllogisms were invalid in addition to being untrue. Hopefully, it will help to assemble a syllogism of the same pattern, but with ostensibly true premises, and an ostensibly false conclusion, proving that the flaw is one of validity.

All fish are mortal.
Socrates is not a fish.
Therefore, Socrates is not mortal.

The error in this syllogism (and the previous) is not in the premises, but how the major premise is interpreted. In order to come to the conclusion "Socrates is not mortal", the major premise would have to be "Only fish are mortal," in which case the syllogism would cease to be true. Otherwise, one cannot make any conclusion about the mortality of not-fish.

It is similar to the difference between if and iff (if and only if), in that

If P, then Q.
Not P.
Therefore, not Q.

is invalid, while

Iff P, then Q
Not P.
Therefore, not Q.

is valid.

Thus, my question is: where is my analysis mistaken? Is it a rule for categorical syllogisms that all Major Premises must be taken as exclusive definitions, in which the major term cannot be true in any other case except the middle term? If this has all been a misunderstanding, which of the six rules of categorical syllogisms do these break?

To which he responded:
As far as your inquiry on categorical syllogism I want to make clear that for a deductive syllogism to be sound it must have both a valid form and true premises. What we are doing is analyzing the validity of the argument form and not analyzing the truth of the premises at this time. It is important that you be able to put the argument into a standard form and then insure that the form is indeed valid. Validity is completely separate from the truth or falsity of the argument. Please refer to the explanation in my distributed notes and also the section in chapter 3 on sound arguments. You are getting the validity (correct form) analysis mixed with the truth/falsity analysis of the premises...these are two separate components of our analysis of this categorical argument form.

Feeling as though he had misunderstood me entirely, I sent him the following:

I believe I understand the distinction between truth and validity. However, the two are related in so much as the syllogism can be sound, and the conclusion true, only if the syllogism is both valid and the premises true. The only reason I brought up truth at all was to demonstrate that the error in the Fish-Socrates syllogism must have been one of validity, as both the premises were true.

All fish are mortal.
Socrates is not a fish.
Therefore, Socrates is not mortal.

This syllogism must be invalid, as the premises are true, yet the conclusion is false. If the premises are true, yet the syllogism unsound, validity must be the cause of error.
This syllogism is categorized as AEE-1, identical to both the Ambition and the TV Star syllogisms. As such, both of these syllogisms are invalid in the form you gave us.

To put my argument into standard form:

Fish-Socrates syllogism:

All fish are mortal.
Socrates is not a fish.
Therefore, Socrates is not mortal.

Ambition syllogism:

One who would take the crown is ambitious.
He did not take the crown.
Therefore, he is not ambitious.

TV Star syllogism:

All certified public accountants are people of good business sense.
No television stars are certified public accountants.
Therefore, No television stars are people of good business sense.

Issue (1): Is the conclusion of the Fish-Socrates syllogism true?
Premise 1: The conclusion is "Socrates is not mortal"
Premise 2: Socrates is mortal.
Conclusion (1): The conclusion of the Fish-Socrates syllogism is false.

Issue (2): Is the Fish-Socrates syllogism sound?
Premise 1: A syllogism is sound if and only if the conclusion is true.
Premise 2: The conclusion of the Fish-Socrates syllogism is false. (Conclusion 1)
Conclusion (2): The Fish-Socrates syllogism is not sound.

Issue (3): Is the Fish-Socrates syllogism true?
Premise 1: A syllogism is true if and only if all the premises are true.
Premise 2: The statement "All fish are mortal" is true.
Premise 3: The statement "Socrates is not a fish" is true.
Conclusion (3): The Fish-Socrates syllogism is true.

Issue (4): Is the Fish-Socrates syllogism valid?
Premise 1: A syllogism is sound if and only if it is both valid and true.
Premise 2: The Fish-Socrates syllogism is not sound.(Conclusion 2)
Premise 3: The Fish-Socrates syllogism is true. (Conclusion 3)
Conclusion (4): The Fish-Socrates syllogism is not valid.

Issue (5): Is AEE-1 a valid syllogistic form?
Premise 1: The validity of a syllogism is determined only by its form.
Premise 2: The Fish-Socrates syllogism is not valid. (Conclusion 4)
Premise 3: The Fish-Socrates syllogism has the form AEE-1.
Conclusion (5): AEE-1 is not a valid syllogistic form.

Issue (final): Are the Ambition and TV Star syllogisms valid?
Premise 1: The validity of a syllogism is determined only by its form.
Premise 2: The form of both the Ambition and TV Star syllogisms is AEE-1.
Premise 3: AEE-1 is an invalid form. (Conclusion 5)
Conclusion (final): The Ambition and TV Star syllogisms are not valid.

Respectfully,
Jeremy C. Sanders

To which he responded only with:

I cannot follow your logical progression. We need to discuss this after the class on Tuesday (I will only have about 10 minutes...but I think that will be sufficient).

Is my logic severely flawed in some way I can't notice? I feel like I must not make any sense at all, and it is really bothering me.

jeremy.liberius@gmail.com — Sat, 27 Sep 2008 13:58:26 GMT

Looking over my journal, I have found it overly self-referential.

Darn it.

jeremy.liberius@gmail.com — Wed, 28 Nov 2007 15:11:49 GMT

Stomach flu sucks, as does missing one's first final,and the review period for all the others.

jeremy.liberius@gmail.com — Sat, 03 Nov 2007 17:42:30 GMT

An astute literary observation:
15th century morality play "Everyman" is comparable to Dr. Seuss.

Everyman, trying to convince his friend, Fellowship, to come with him to reckoning.

"Everyman: Yet I pray thee, take the labour, and do so much for me
To bring me forward, for saint charity,
And comfort me till I come without the town.
Fellowship: Nay, and thou would give me a new gown,
I will not a foot with thee go;
But and you had tarried I would not have left thee so."

Emphasis mine.

jeremy.liberius@gmail.com — Tue, 04 Sep 2007 00:06:29 GMT

Hey, it is another going back to school entry. Looking over my accumulated school documents, I found my favorite piece from last year was not a masterful essay, but a whimsical list of tips for the English portion of the ACT/MME test. The assignment was simply an exercise intended to make us review our notes on how to take the dreaded test, and then whimsy struck. They start to get more interesting around number four.

Top Ten- In no particular order
1. Read quickly, but entirely, searching for the main ideas and themes rather than details. This enables you to finish the essays with enough time to answer the questions, which do not focus on details, but rather on the general theme of the piece. Most important is to understand the position of the author, and the ability to extrapolate this knowledge to answer the questions.
2. Learn to eliminate infeasible answers, in order to narrow down the possible answers. Search for outliers, such as extremes and absolutes, which tend to exaggerate the authors position, in order to tempt one away from the correct answer. The “bait and switch” tactic lures you in by mirroring the wording in the text, but it either changes a crucial portion, or it is not relevant to this question. Finally, do not assume the author’s position on a point not mentioned.
3. Annotate the piece, in order to facilitate easy answering. Mark important sentences that define the passage, while ignoring erroneous details. Take special note of so-called “shifters”, as they tend to signal a shift in the passage. Finally, annotate the tone of passage using the easily recognizable + and – symbols, for easy reference.
4. In the essay section, take a position and hold fast. This is a test of your ability to write persuasively, not generally outline the issue. You are not an unbiased journalist reporting the facts, but a vehement editorialist. Even if you have no opinion, make something up; without a position you can’t win.
5. Discard all your high-falutin’ ideas of style and format, and just write a five-paragraph essay. They want to see that you can tie together your opinion and supporting arguments into a tight package, tying it off with a conclusive bow. Do everything by the elementary book of composition, and try not to let your literary tears stain the page.
6. While things such as eloquence and diction are but secondary on the ACT/MME, at least passable grammar is necessary to convey your ideas. As such, you might be best off avoiding overly complicated sentences, as the benefits are negligible, while the risk of confusion increases.
7. Be prepared to read various boring documents, and to then ascertain their meanings. You are forewarned, however, that some such pieces may be brick walls of legalistic text, requiring the most close of reading to interpret. In such cases, it may behoove you to read the questions prior, so as to pinpoint the section document relevant.
8. Whilst attempting to “beef-up” your essay, avoid merely restating what you have already said in different words. Though such filler tactics may be effective against lesser English teachers, the ACT board selects only the most cold-hearted and ruthless of instructors to assess the papers. Their steel eyes, magnified most likely by overlarge opticals, will see through such diversions, and then proceed to (metaphorically) tear your essay to pieces.
9. In order to ensure your favorable grade on the essay section, be certain to pepper your essay with interesting transitions at suitable junctions. Such segues serve to coherently tie your essay together, as well as showing off your undeniably lucid stream of thought. Strive to avoid such hackneyed transitions as “firstly”, “lastly”, and the absolutely abominable “In conclusion”.
10. In the multiple choice rhetorical skills section, show preference to the short and simple, rather than the wordy and circumlocutious. A simple method would be to count the number of resultant words, however, one must still be vigilant for grammatical mistakes. Curb your love of subordinate phrases and extraneous modifiers so as to meet their prole-ish requirements.

Simon Pegg

jeremy.liberius@gmail.com — Wed, 07 Mar 2007 23:37:22 GMT

Simon Pegg

After watching Spaced, Shaun of the Dead, the new Doctor Who series, and Mission Impossible 3, I simply figured that loads of British blokes look like that. Now that I know it is a single man, I must say I am a bit of a fan.

In Honor of a Great Man

jeremy.liberius@gmail.com — Fri, 17 Nov 2006 20:10:15 GMT

Milton Friedman, economist of the Chicago school, died yesterday on the 16th of November. He was 94 years old at the time of his death.

http://video.google.com/videoplay?docid=6813529239937418232&q=milton+friedman&hl=en

jeremy.liberius@gmail.com — Wed, 30 Aug 2006 01:04:27 GMT

If you would like to see boring world of my thoughts, leave a comment.

EDIT: If you are already on my friends list, you don't need to bother.