Logic II

Week 10, Friday

Dear Families, 

We continued Chapter 10. Below are the concepts the students are responsible for: 

Review: A Polysyllogism is a syllogism that links together several categorical syllogisms, in such a way that the conclusion of the one syllogism serves as the premise of the next syllogism. 

A Sorite is a chain argument which, through a a chain of premises, connects the subject of the first premise with the predicate of the conclusion. In this form of argument the conclusions are left out except for the final one. They are, however, still implied. 

There are two types of Sorites: 1) Aristotelian also know as Classic and 2) Goclenian. 

An Aristotelian Sorite is a series of 4th figure syllogisms with all of the conclusions unexpressed except the last one. Note the predicate of one premise will always be the subject of the next premise in this sort of sorite. This provides a series of middle terms to connect the syllogism. 

        Aristotelian Sorite                               vs.                                                   Polysyllogism

            All A is B                                                                                            All A is B                                                                
            All B is C                                                                                                   All C is A
            All C is D                                                                                 Therefore, All C is B
            All D is E                                                                                                   All D is C
Therefore, All A is E                                                                                   Therefore, All D is B

There are, however, two rules that a particular to Sorites:
Rule 1--Only the premise that contains the minor term, that is A, can be particular, that is a "some" statement.
Rule 2--Only the premise that contains the major term can be negative.

Extrapolation is when you provide the missing conclusions of the sorite. You do this by turning the the sorite into a series of first figure syllogisms. To make it a first figure syllogism you: 1) Switch the first two premises, 2) Provide the missing conclusion and 3) Use the conclusion of each new syllogism formed as the minor premise of the next part.

Just as with polysyllogisms the validity of sorites is dependent upon all of their parts being valid. In the above sorite there are three parts. Each part is first figure, AAA, so they are Barbara syllogisms and therefore valid and so the whole sorite is valid. 

Homework for Tuesday is to do reread Chapter 10 and do exercises 11-17. After extrapolating the sorites in 17, test them for validity.

Have a lovely Thanksgiving Break!

Miss Russell

Week 10, Wednesday

Nota Bene: yesterday, I returned the quiz from last week on Chapter 8. Grades were unusually poor on it so I will curve it by 10 points. If you received under a 70 percent to have those ten points added on, you need to hand in corrections on the quiz. If there is no grade at the top of the quiz, then it needs to be corrected.

Dear Families,

Yesterday, after taking a quiz, we started into Chapter 10. We will finish Chapter 10 on Friday. The concepts to know from the first part of the chapter are:

Simple vs Complex arguments--Simple arguments have relatively fewer parts whereas Complex ones have more. Up to this point we have been dealing with simple arguments. Chapter 10 introduces us to complex ones.

Simple arguments:

Categorical syllogisms

Hypothetical syllogisms

Complex arguments:

Polysyllogisms

Sorites

Epicheirema

Dilemmas

A Polysyllogism is a syllogism that links together several categorical syllogisms, in such a way that the conclusion of the one syllogism serves as the premise of the next syllogism.

One example of the outline of a polysyllogism:               Actual polysyllogism:

All A is B                                                                     All Men are Mortal

All C is A                                                                     All Greeks are Men

Therefore, All C is B                                                   Therefore, All Greeks are Mortal    

All D is C                                                                     All Athenians are Greek

Therefore, All D is B                                                  Therefore, All Athenians are Mortal      

Note, Polysyllogisms may contain as many syllogisms as the user desires. So the outline started could keep going onto E, F, etc.

Since polysyllogisms are made up of categorical syllogisms they follow the same rules. You simply have to make sure that each syllogism within the polysyllogism is a valid categorical argument to determine the validity of the whole syllogism. So in the argument above since the two syllogisms are first figure, AAA we know that they are Barbara syllogisms and the whole polysyllogism is consequently valid.

For Friday please reread Chapter 10 and do Chap. 10 exercises 1-9. 

God Bless,

Miss Russell

Week 9, Friday

Dear Families,

Friday, we had a fun class. As a practical application of logic we watched a video and noted strategies for debating well. We then went through the progression of argument in the video. The class ended with a great discussion on "stealing" when you are starving.

Homework for our next class is to read Chapter 10 and to prepare for a quiz on the 3 types of hypothetical syllogisms--chap 9 will have more questions since we covered it most recently.

God Bless,

Miss Russell

Five strategies for debating well:

1) Using questions to help people reconsider the foundation of their ideas

      --Can be done by using common ground

2) Using concrete examples

3) Defining terms

4) Showing the logical progression of a particular idea--where you end up by assuming an idea

5) Addressing the person and not talking past them

Week 9--Note a couple exercises have been dropped from what was assigned on the syllabus.

Dear Families,

We started today off by taking a quiz on Chapter 8. Afterwards we went through Chapter 9. Concepts to know are:

A Conjunctive Syllogism is a hypothetical syllogism whose major premise is a negative conjunctive statement(Not both P and Q) . That is a conjunctive statement which denies that both of its parts can be true at the same time. 

Note a conjunctive statement does not have to use the word both. For example this is a perfectly acceptable conjunctive statement: "Socrates cannot be man and god".

The parts of the major premise are called the first and second conjunct.

There are two forms of Conjunctive syllogisms. The forms are called by the same names as the two forms of the disjunctive syllogism, but unlike the disjunctive the Ponendo Tollens is valid and the Tollendo Ponens is invalid.

1) Tollendo Ponens--affirmation by denial. This form is invalid. Below are the two moods that it can take. This form is invalid because there is nothing to prevent both options from being false, so just because P is not true that does not necessarily mean that Q is. For example both of the options in the following statement are false: "Socrates is not both Chinese and Roman"

Not both P or Q                        Not both P or Q

 Not P                                      Not Q

Therefore, Q                           Therefore, P

2) Ponendo Tollens--denial by affirmation. This form is valid. Below are the two moods it can take.

Not Both P or Q                                                                                 Not Both P or Q

P                                                                                                         Q                

Therefore, Not Q                                                                               Therefore Not P         

Just as the disjunctive syllogism can be reduced to a conditional syllogism so can the conjunctive syllogism. The students don't need to memorize the particulars of how this is done.

Homework for Friday is to complete chapter 9 exercises 1-8, 16-23, 25                        

God Bless,

Miss Russell

Week 8, Friday

Dear Families,

In class we finished up Chapter 8 and then went through the Chapter 8 case study which deals with C.S. Lewis' Trilemma about the divinity of Christ. Concepts to remember are: 

Review:

A Conditional syllogism is a hypothetical syllogism which has a conditional statement (an If..then" statement) as its Major Premise. The parts of a conditional statement are called the antecedent and the consequent. The constructive mood is valid when you affirm the antecedent and invalid when you deny the consequent. The destructive mood is valid when you deny the consequent and invalid when you deny the antecedent.

A Disjunctive syllogism is a hypothetical syllogism which has a Disjunctive statement (an Either...or" statement) as its Major Premise. The two parts of a conditional statement are called first and second alternate. They are the two "alternatives". The two forms of this syllogism are Ponendo Tollens (affrimation by denial--Valid and Tolendo Ponens (denial by affirmation)--Invalid. Note--If the two alternates of the major premise are exclusive (contradictory) then Tollendo Ponens is valid.

New Material:

When the alternates are contradictory then it is called an Exclusive Disjunctive. When the major premise is an exclusive disjunctive then Ponendo Tollens form is valid. The form would look like this:

Either P or Not P                              Either Socrates is mortal or immortal

P                                                        Socrates is mortal

Therefore, Not Not P                       Therefore Socrates is not immortal

Just as you reduce categorical syllogisms to the first figure so you reduce disjunctive syllogisms to the conditional syllogism. There are two rules for doing this.

Rule 1--The minor premise and the conclusion remain the same.

Rule 2--The major premise is changed from a disjunctive to a conditional statement by:

            Step 1--Placing the alternate denied in the minor premise in the consequent

            Step 2--Placing the denial of the other alternate in the antecedent

The transformation looks like this:

Before:                                                                             After:

Either P or Q                                                                     If not Q then P

Not P                                                                                Not P

Therefore, Q                                                                     Therefore, Q

Either P or Q                                                                     If not P then Q

Not Q                                                                                  Not Q

Therefore, P                                                                     Therefore, P    

Homework is to read Chapter 9 and do Chapter 8 exercises 25 (just steps 2 and 3) and 27-32. There will be a quiz on Chapter 8 on Wednesday.

God Bless,

Miss Russell

Week 8, Wednesday

Dear Families,

Yesterday, we had a quiz on Chapter 7 and then went through part of Chapter 8. Concepts to remember:

Disjunctive syllogisms are the second type of hypothetical syllogism. The major premise is a disjunctive statement. That is an "either...or" statement. The two parts of the statement are called the 1st and 2nd alternate.

There are two forms of disjunctive syllogisms.

1) Tollendo Ponens--affirmation by denial. This form is valid. Below are the two moods that it can take.

Either P or Q                           Either P or Q

 Not P                                      Not Q

Therefore, Q                           Therefore, P

2) Ponendo Tollens--denial by affirmation. This form is invalid. Below are the two moods it can take.

Either P or Q                                                                                Either P or Q

P                        >>Fallacy of affirming the 1st alternate             Q     >>Fallacy of affirming the second alternate

Therefore, Not Q                                                                        Therefore Not P             

This mood is invalid because the two alternates are not necessarily mutually exclusive. It is possible for both of them to be true. So when you affirm one that does not have to mean that the other is false. For instance both options in the following statement could be affirmed, "Either Socrates is a soldier or Socrates is a philosopher." This is called an Inclusive Disjunctive when both of the alternates are potentially true.

When the alternates are contradictory then it is called an Exclusive Disjunctive. When the major premise is an exclusive disjunctive then Ponendo Tollens form is valid. The form would look like this:

Either P or Not P                              Either Socrates is mortal or immortal

P                                                        Socrates is mortal

Therefore, Not Not P                       Therefore Socrates is not immortal

Homework for Friday is to reread Chapter 8 and to complete Chapter 8 exercises 3-5, 8-11,and 14-24. 

God Bless,

Miss Russell

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.