principal: syllogisms part ii

Principal: SyllogismsPart IIWeek 1 ENG 1005: Writing about Social Justice

In answer to the question: why are the rules the rules… The “if you were an alien” explanation… Aristotle described the syllogism as ““a discourse in which certain (specific)

things, having been supposed something different from the things supposed, results of necessity because these things are so.”

Confusing, right? Essentially: syllogisms are like a common language. The rule were not so much invented as discovered, but they are universally true, meaning, the rules of logic—like physics or math—work anywhere in the universe. And, they are a way to mitigate uncertainty. They offer clarification and something as close to “proof” as human beings will ever get.

Further, syllogism are a way to see that a claim-with-reason (thesis) depends for logical completeness on an assumption–usually the major premise–which often needs to be supported in your argument.

Formulating the major premise of each claim-with-reason is a way of reminding yourself of the assumptions your audience must grant if your argument is to be persuasive.

In answer to “What are the rules of syllogisms, really” (1) If you have a negative conclusion, you must have at least

one negative premise. And, if you have a positive conclusion you must have two positive premises.

You can not have two negative premise in any one syllogism. If BOTH premises are universal, the conclusion cannot be

particular. If a term is distributed in the conclusion, it must be distributed

in the premise where it appears. The “middle term” must appear once in each premise, but not

in the conclusion. The subject term must appear once in one premise and once in

the conclusion. The predicate term must appear once in one premise and once

in the conclusion.

All A are B No B are C No A are C

Some A are not BNo A are X Some B are X

VALID

INVALID

All A are B No B are C No A are C

VALID

Some A are not BNo A are X Some B are X INVALID

RULE 1: Neg conclusion = at least 1 neg premise

All A are B All B are C All A are C

Some A are not B Some C are not B Some A are not C INVALIDVALID

RULE 2: Cannot have two neg premises

All R are S All C are R All C are S

No P are YNo P are W Some Y are not W INVALIDINVALID

RULE 3: Two universal = univ. conclusion All S are F

All L are F All S are L INVALID

RULE 4: If term is distributed in concl, must be distributed in the premise where it appears

How would you convert this thesis statement?

Women should be barred from combat units because the United States needs a strong army.

Student Thesis

An example of everyday use:Major Premise: Persons who lack the strength and endurance

for combat duty should be barred from combat units.Minor Premise: Women are persons who lack the strength

and endurance for combat duty.Therefore: Women should be barred from combat units.

A

BC

A

C B

Women should be barred from combat units because the United States needs a strong army.

Student Thesis

But we’re not there yet…And logic is imperfect… Formal logic helps you appreciate the structure but this kind of “formal

logic” only deals with the structure of an argument, not with the truth of its premises.

So, unless a properly structured argument also has true premises, we can conclude nothing about the truth of its claim.

That’s why Jon-Luke’s head was exploding in class Tuesday.Consider the following argument:

The blood of insects can be used to lubricate lawn-mower engines.Vampires are insects._____________________

Therefore, the blood of vampires can be used to lubricate lawn-mower engines.

Logic that’s Illogical? Because their premises are untrue, this argument is ludicrous but valid

structurally. Main concern of writers is to show the truth of the premises, so formal logic is of

limited value. And yet, you can’t argue any position if you start with an invalid claim. So

getting the syllogism or enthymeme right is kinda important! Incidentally, Sir Francis Bacon rejected the Aristotelian syllogism and deductive

reasoning, asserting it was fallible and illogical. System of argumentation dominated Western philosophical thought through the

17th Century; in the 19th Century, modifications to syllogism were incorporated. Rhetoric then—the appeals especially (logos, ethos, pathos, kairos)—works

alongside classic logic like style. Once you state your claim, how you arrange “the available means” results in persuasion. But you can’t build a persuasive argument on the back of a weak or invalid claim.

Using Venn Diagrams Since a categorical syllogism has three terms, you can use a Venn diagram of

three intersecting circles to solve for validity. Each circle represents one of the three premises/terms in a categorical syllogism.  So, take out paper/pen and drawn this:

Diagramming Syllogisms In order to use a Venn diagram to test a syllogism, the

diagram must be filled in to reflect the contents of the premises. 

Shading an area means that that area is empty.  First, diagram the premise sentences independently.Then see whether the conclusion has naturally been

diagramed.  If so, the argument is valid.  If not, then it is not.

Consider the following argument…All Greeks are mortal.  (All M are P)All Athenians are Greek.  (All S are M)So, all Athenians are mortal.  (All S are P)

Remember: it matters not which letters you use to represent the terms in a class.

So, draw an image that looks like this:

Diagram…Diagram each of the premises.  When doing this, act as if there are

only 2 relevant circles.  Begin with the first premise

(frequently the premise involving the major term, sometimes called the major premise). 

In our example you need to diagram the proposition "All M are P".  Ignoring for a moment the circle representing the minor term, your diagram sho8uld look like this:

Following the standard conventions we get:

Next, diagram the second premise:

"All S are M"--

Now, if we overlap the diagrams of the premises we get a diagram of the argument, and we are ready to determine whether the argument is valid or not.

Does this diagram express the informational content of the conclusion of the argument? 

Yes, all of the S's that remain are in region 5, and everything in region 5 is an S, an M, and a P.  Since all the S's are in region 5, all the S's are P's and the argument is VALID.

In-Class ExerciseBreak into groups of two and diagram the following

two syllogisms.SYLLOGISM 1:

All mathematicians are rational.  (All P are M)All philosophers are rational.  (All S are M)SO, all philosophers are mathematicians.  (All S are P)

SYLLOGISM 2:All philosophers are logical.Some physicists are logical.So, some philosophers are physicists.

AnswerAll mathematicians are

rational.  (All P are M)All philosophers are rational.  (All S are M)_____________SO, all philosophers are mathematicians.  (All S are P)

Beginning with the first premise we get:

Adding the second premise we get:

Does this diagram express the informational content of the conclusion "All S are P"?  NO. 

Region 4 of the diagram is not shaded (not empty) so it is possible that there is an S that is not a P. 

Accordingly, the argument is NOT VALID.

Answer:

Next example:All philosophers are logical.Some physicists are logical.__________________________So, some philosophers are physicists.

Answer: In the  following diagram, the

bar that crosses from region 5 into region 6 indicates that the argument is NOT VALID. 

All that we can be certain of is that there is either an SPM (region 5) or a PM non-S (region 6), but we don't know which.  Since we don't know which, the conclusion does not follow logically from the premises.

HomeworkComplete the assignment sheet found on the website, which

covers identifying arguments, premises, and conclusions.AND revise your argumentative essays based on your peer

feedback. As you’re doing so, start to rethink your thesis/arguments. Can

you convert your thesis statement into a syllogism? If so, what does this buy you argumentatively?