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Week 7, Friday
Friday in Logic we finished Chapter 7. Concepts to remember are:
Review:
Categorical syllogisms are based around three terms-the major, the minor and the middle, which connects the major and minor terms-and so their validity is dependent upon the relationship among the terms.
Hypothetical syllogisms don't have terms in the way that categorical syllogisms do. They are made up of propositions so their validity is dependent upon the relationship among the propositions.
New stuff:
Conditional syllogisms (which are a type of hypothetical syllogism) have two valid moods.
1) The Constructive Mood also called Modus Ponens. We have the constructive mood when the minor premise affirms the antecedent of the major premise. Its form is as follows:
If P then Q If all men are mortal then Socrates is mortal
P All men are mortal
Therefore, Q Therefore, Socrates is mortal
2) The Destructive Mood also called Modus Tollens. The destructive mood occurs when the minor premise denies the consequent of the major premise. Its form is as follows:
If P then Q If all men are mortal then Socrates is mortal
Not Q Socrates is not mortal
Therefore, Not P Therefore, Some men are not mortal
There are also two moods which are invalid.
1) Mood #3-Fallacy of Affirming the Consequent--this is an invalid mood--just because the consequent is true that does not necessarily mean that the antecedent is true. For example in the following statement the consequent is true but the antecedent is not: "If all men are Greek then Socrates is Greek"
2) Mood #4-Fallacy of Denying the Antecedent--this mood is invalid because even if you deny the antecedent there is nothing you can really say about the consequent. For example, we can deny the antecedent of the following statement, "If all men are short then Socrates is short", but that does not mean that Socrates is not short. It only means that not all men are short, but we are not sure which ones are or aren't short.
The forms of these invalid moods are as follows:
If P then Q If P then Q
Q Not P
Therefore, P Therefore, Not Q
Conditional syllogisms can be Mixed or Pure. So far we have been dealing with mixed conditional syllogisms. A Mixed Conditional syllogism has a conditional statement as its major premise, but it has categorical statements for its minor premise and conclusion.
A Pure Conditional syllogism uses conditional statements for both the premises and the conclusion. It is more complicated and we won't use it very often. The pure conditional syllogism has two valid moods just like the mixed conditional syllogism.
1) Constructive
If P then Q If all men are mortal then Socrates is mortal
If R then P If all men are created beings then all men are mortal
Therefore, If R then Q Therefore, If all men are created beings then Socrates is mortal
2) Destructive
If R then P If all men are created beings then all men are mortal
If P then Q If all men are mortal then Socrates is mortal
Therefore, If Not Q then Not R Therefore, If Socrates is not mortal then not all men are created beings
H.W. is to Read Chapter 8 and to complete Chapter 7 exercises 16, 19-24, 29, 31, and 32. Next class, we will have a quiz on Chapter 7.
God Bless,
Miss Russell
Week 7, Wednesday
Dear Families,
At the beginning of class on Friday I handed back the students' midterms. I am quite pleased with how well the students did.
After handing back the midterm we discussed the debate project that the students will be presenting at the end of the semester and I gave them the teams for the project. On the last day of class, the two teams will take part in an official debate which the US III girls will judge. Each team will be researching arguments and will present them at the start of the debate. After the presentation of arguments, the teams will have the opportunity to respond and object to each others arguments. The topic of the debate is whether the death penalty should be allowed in America. I will be leading the team arguing for the death penalty and Dr. Brown will be leading team arguing against the death penalty.
After discussing the debate we went through part of chapter 7. The concepts to remember from Chapter 7 are:
Categorical syllogisms vs. Hypothetical syllogisms
Categorical syllogisms: These are the syllogisms that we have been working with. The definition of a categorical syllogism is- a group of propositions in orderly sequence one of which (the consequent) is said to be necessarily inferred from the others(the antecedent). These syllogism have three terms which are connected through the middle term to form a conclusion. Because a categorical syllogism is united through a common term, the middle term, the validity of the syllogism is dependent on the relationship between the three terms.
Hypothetical syllogisms: the validity of these syllogisms depends upon the relationship among the propositions of the syllogism. These syllogisms are little more complex than the categorical syllogism. Rather than drawing a conclusion through a middle term, the hypothetical syllogism affirms or denies a judgement in the conclusion by affirming or denying one part of the major premise (a complex sequential proposition) in the minor premise.
In categorical syllogisms the major and minor premise are so named because they contain the major or minor term. In hypothetical syllogisms we don't have the terms in the same sense. In a hypothetical syllogisms the "terms" are really entire propositions. Thus the major premise is simply the 1st premise, which is the complex sequential proposition, and the minor premise is the second premise, which affirms or denies one part of the major premise.
There are three types of Hypothetical syllogisms: 1) Conditional, 2) Disjunctive and 3) Conjunctive. Chapter 7 deals with the conditional hypothetical syllogism.
Conditional syllogism: a hypothetical syllogism that contains a conditional statement as its major premise,.An example is:
If all men are mortal, then Socrates is mortal--Major Premise
If P then Q
All men are mortal--Minor Premise
P
Therefore, Socrates is mortal--Conclusion
Therefore, Q
Because we are dealing with a new kind of syllogism, we have a new notation to outline its form. Rather than using the S, P and M of the categorical syllogism which marked the different terms, we will use P and Q to mark the different propositions. (See above)
A Conditional proposition has two elements to it: 1) an antecedent and 2) a consequent. The antecedent is what comes after the "If", it provides the logical reason for the consequent. The consequent is what comes after the "then", it is what logically follows from the antecedent. In our notation, If P then Q, P is the antecedent and Q is the consequent.
Homework for Friday is to reread Chapter 7 and to do Chap. 7 exercises 1-15.
God Bless,
Miss Russell
Week 6, Friday
Many thanks to Miss Korkes and Mr. Sexton for subbing for me this week! Miss Korkes led the class in a quizbowl review on Wednesday and today the students took their midterm.
Homework for the next class is to read chapter 7.
Week 5, Friday
On Friday we started class off with a quiz on Chapter 5.
After the quiz I started going through Chapter 6 with the students. Concepts to remember from Chap. 6:
Most everyday arguments, like everyday sentences, are not nicely laid out in logical form. Chapter 6 deals with the most common form of everyday argument. It is called an Enthymeme.
Enthymeme: A syllogism which is missing either a premise or its conclusion. We use enthymemes a lot because we assume that the left out statement is obvious. For example:
All men are mortal Sam is an atheist Tall guys play basketball
Therefore, Socrates is mortal Therefore, Sam does not believe in God Sam is tall
Despite the missing step looking obvious you must always make sure to supply the missing premise or ask your opponent to. Sometimes the syllogism is invalid. Or your opponent is assuming a false premise. Remember you can get a true conclusion from false or invalid premises.
The following Enthymeme, for example, is invalid though it seems to make sense at first.
All men are mortal (the missing premise would be "Socrates is mortal" or "a mortal is Socrates"--in the first case the middle term is undistributed
Therefore Socrates is a man and in the second case we have fallacy of illicit process)
There are three types of Enthymemes based on what part of the syllogism is missing. First Order--Missing the major premise, Second Order--missing the minor premise and Third Order--missing the conclusion.
Homework for next class is to complete Chapter 6 exercises, 2-6, 8-10, 12, 14 and to review for the quizbowl we will be having on the Wednesday after break. The Friday following, the students will be taking their midterm in class. The summaries I have posted this semester will serve as a ready made study guide.
God Bless,
Miss Russell
Week 5, Wednesday
Dear Families,
Yesterday we went over the second half of Chapter 5. Concepts to remember are:
Review:
Rule C--add the missing complement--in logic you want to refer to the subject and predicate as classes of things you can do this by adding a complement.
Rule D--Add the missing copula
Rules C and D generally are steps best done together. All trips are things which rarely go as planned
(I will not require that you memorize the following rules but you will need to know how to use them. I might ask, for example, what sort of statement an exclusive sentence gets converted to but I won't ask you what Rule E is.)
Rule E--Change exclusive sentences to A statements. Do this by 1) Dropping "only", "none but" and 2) interchanging the subject and predicate. For example: Man is the only rational animal>>> All rational animals are men
Rule F--Change negative sentences to E/O statements. For example: Men are not irrational>>>>No men are irrational
Rule G--Change exceptive statements to E/A. These are tricky because you actually have two different statements that you can get from an exceptive sentence, however, you will only use one in a syllogism and either one will work. For example: No being but God is perfect>>>> a) The only perfect being is God or b) All beings other than God are imperfect
Rule H-- Change sentences which use "anyone, anything, if, whatever" etc to A. For example: If you are a man then you are rational>>>All beings which are men are rational
Rule I--Change sentences that use "Someone, something" etc to I. For example: There are people who have gone to the North Pole>>>Some people are people who have gone to the North Pole
Homework is to read Chapter 6 and do Chap. 5 exercises 8 and 17. There will be a quiz on the chapters we have covered so far on Friday.
God Bless,
Miss Russell
Week 4, Friday
Dear Families,
On Friday, I gave a quiz on Chapter 3. We then went through the first half of Chapter 5. The concepts the students are responsible for are:
Chap. 5---has to do with being able to put everyday statements into logical form. We have often commented on the fact that most arguments are not in nice syllogisms for us to analyze. Chap. 5 shows us to be able to put everyday arguments into their logical form.
Components of a logical proposition:
-Subject--what the statement is about
-Predicate--what is being said about the subject
-Quantifier--determines the quality and quantity of a syllogism--All, No etc
-Copula--To be verb which connects the subject and the predicate
There are nine rules that Chap. 5 gives for converting statements into their logical form. The first four and most important are:
Rule A--Clearly identify the subject and the predicate---Trips rarely go as planned
Rule B--Supply the missing quantifier--All trips rarely go as planned
Rule C--add the missing complement--in logic you want to refer to the subject and predicate as classes of things you can do this by adding a complement.
Rule D--Add the missing copula
Rules C and D generally are steps best done together. All trips are things which rarely go as planned
Homework for next class is to reread Chap. 5 and to do Chap. 5 exercises 1-4.
God Bless,
Miss Russell
Week 4, Wednesday (Reminder--Make Flash Cards of the concepts!)
Dear Families,
Over the last week, we have been going through Chapter 3 and putting its concepts into practice. The concepts that the students should remember from Chapter 3 are:
Review: There are four figures.
The most straightforward figure is the 1st figure, because of this Logicians like to reduce the other three figures to the first figure.
There are two types of Reduction: Direct and Indirect. Chap. 3 deals with direct reduction.
In the past we learnt that in our mnemonic verse, the vowels in the names stand for the mood of the figure. But many of the consonants also mean something for reduction. The beginning consonant tells you which syllogism in the first figure you want to reduce your syllogism too. There are 4 syllogisms in the 1st figure: Barbara, Celarent, Darii and Ferio. If you have a syllogism in the second figure and it starts with a C (Cesare for example) then it will reduce to the first figure syllogism Celarent. Similarly any syllogism which starts with a B will reduce to Barbara etc.
The consonants S, P, M, and C in the syllogism names tell you how to reduce the syllogism to the first figure.
S (simple conversion)-- convert the proposition indicated by the vowel before the s.
P (partial conversion)-- partially convert the proposition indicated by the vowel before the p.
M (mutatio)-- Switch the premises. Make the major premise the minor and the minor premise the major.
C (Reduction by contradiction--Indirect)--Only used on Bocardo and Baroco. We will not be covering this.
Review:
Conversion is when you switch the subject term and predicate term of a proposition.
Partial Conversion--used on the A statement--you 1) switch the subject and the predicate and 2) change the quantity. If you start with "All men are mortal" then you should end up with "Some mortal things are men".
Sometimes to reduce a syllogism to the first figure you must use more than one of the above operations, in this case you should perform the first operation that appears in the syllogism's name. For example to reduce Camenes you must perform simple conversion (S) and Mutatio (M). Since the M comes first in the name you start with that operation.
Reducing a Camenes syllogism to Celarent: 1)Mutatio 2) Conversion of conclusion----the syllogism is now in the 1st figure
All men are mortal No mortals are gods No mortals are gods
No mortals are gods All men are mortal All men are mortal
Therefore, No gods are men Therefore No gods are men Therefore, No men are gods
Homework is to read Chapter 5 (we are skipping chap. 4) and to do Chap. 3 exercises 27-34. There will be a quiz on Chap. 3 on Friday.
Until then,
Miss Russell
Week 3, Wednesday
Dear Families,
Today we finished up Chapter 2 and practiced using the list of names to identify whether a syllogism is valid. We also completed a "practical application" in class today, using figure and mood to determine the validity of some common arguments put forward regarding our late Pope, Francis. On Friday we will be having a quiz on Chapter 1 and 2. Students should remember the following concepts from today's class:
The vowels in the names of the syllogism give the mood and the line number gives you the figure of the syllogism.
Once you know the names it is much easier to see whether a syllogism is valid. Simply:
1) Identify the Figure---Second figure
2) Determine the Mood----EA
3) See if that Mood is included in the list of names for that figure.----Cesare
If it is in the mnemonic verse then it is valid, if not then invalid.
There are 19 valid syllogisms but some of them are more common than others. The more commonly used syllogisms are: 1) Barbara--1st figure, 2) Celarent--1st figure, 3) Cesare--2nd figure. 4) Camestres--2nd figure and 5) Camenes--4th figure.
Note all of the commonly used syllogism have a universal conclusion. The conclusion is either an A or an E statement.
Homework is to read Chapter 3, to complete Chapter 2 exercises 18-22, 26-34, and to study for the quiz.
God Bless,
Miss Russell
Week 2, Friday
Dear Families,
Friday, we covered much of Chapter 2. Below are the concepts the students are responsible for.
Mood is the disposition of the premises according to quality and quantity. So basically the mood of a syllogism is determined by which of the 4 categorical propositions its two premises use--A, E, I, or O. For example the mood of the following syllogism is AA. Both the major and minor premises are A statements.
All men are mortal
Socrates is a man
Therefore Socrates is mortal
There are 16 possible moods but 5 of them are entirely invalid because they break rules 5 and 4. Each of these moods can be used in the 4 different figures of logic making for a total of 64 possible syllogisms. Only 19 of these syllogisms, however, are valid as certain moods and figures do not work together. For example the second figure needs to have an affirmative and a negative premise in order to be valid and therefore the AA mood cannot be used in the second figure.
The 19 valid syllogisms have been named in a mnemonic device so that it is easy to identify what figures and moods together make a valid syllogism. Each of the lines in the following name device is for a different figure and the vowels in the names identify what the mood of the syllogism is.
Barbara, Celarent, Darii, Ferio-que prioris; ---1st figure
Cesare, Camestres, Festino, Baroco secundae; ---2nd figure
Tertia; Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison habet; ---3rd figure
quarta in super addit; Bramantip, Camenes, Dimaris, Fesapo, Fresison ---4th figure
Note because we identify the mood of a syllogism by EI or EA it is important that the major premise is always the first premise of the syllogism, as the first letter of the mood stands for the major premise.
Homework for next class is to reread Chapter 2, to memorize the above list of names and to do Chap. 2 exercises 3-10 and 13-17.
God Bless,
Miss Russell
Week 2, Wednesday
Nota Bene: To prepare for quizzes/the midterm, it would be very helpful to make flashcards of these concepts.
Dear Families,
Today, we went through Chapter 1 of Logic II. Below are the concepts for which the students are responsible:
Figure--The disposition or location of the terms in the premises. In other words the placement of the terms, particularly the middle term, determine a syllogisms figure. Figure helps us to determine the validity of an argument more easily.
First Figure-- Sub-Prae or Subjectum-Praedactum. The middle term is the subject of the major premise and the predicate of the minor premise. This is the most common and straightforward of the four figures.
All Men are Mortal
Socrates is a Man
Therefore, Socrates is Mortal
Second Figure--Prae-Prae. The middle term is the predicate of both the major and minor premises. In order for this figure to be valid one of the premises must be affirmative and the other negative otherwise you end up with the fallacy of the undistributed middle.
All bananas are yellow
No dogs are yellow
Therefore No dogs are bananas
Third Figure--Sub-Sub. The middle term is the subject of both the major and minor premises. In a valid syllogism of this figure the conclusion will always be particular.
All dogs are cats
All dogs are happy
Therefore some happy things are cats
Fourth Figure-- Prae-Sub. The middle term is the predicate of the major premise and the subject of the minor premise. This figure was considered by Aristotle to be a variation of the first figure (Indirect First) as he believed it is logically the same, that it only differs grammatically.
Socrates is a man
All men are mortal
Therefore some mortals are Socrates... or some mortal is Socrates
Homework for Friday is to read Chapter 2 and to do Chap. 1 exercises: 2,3, 6, 7, 9, 11, 12, 14, 16, 17, 19, 21, 22, 24, 29.
God Bless,
Miss Russell
Week 1
Dear Families,
This week, we reviewed concepts from Logic I by having quizbowls. Homework for next class is to read Chapter 1 of Formal Logic II and to be ready for the review quiz.
God Bless,
Miss Russell
P.S. The most important things to know for the quiz are being able to identify fallacies within syllogisms, important definitions such as the ones of the 3 Acts of the Mind, and knowing the charts for the square of Opposition and Distribution.
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