1
Q
what are the two basic notations in syllogistic logic
A
- standard form statements
- Venn diagrams
2
Q
what was aristotle’s goal? how did he acheive this?
A
- Standardize language so to reduce confusion and fallacy.
- all expressible statements reduced to “categorical statements”
So it’s exactly clear what you’re saying every time
3
Q
describe “categorical statements”
A
- they describe relationships between classes
- only allowable verb “to be” (is, are, were)
- quantities: all, some (at least one) or none
- statements can be affirmative or negative
- nothing else
4
Q
who invented Venn diagrams
A
John Venn circa 1880
5
Q
what do venn diagrams do
A
illustrate the logic of set relations
6
Q
any two sets can have only 3 possible relationships what are they?
A
- one set is a subset of another
- the sets have nothing in common
- there is partial overlap between sets
7
Q
how can we represent any of the set relationships expressible in aristotle’s syllogistic logic?
A
by shading or marking the venn diagram
8
Q
what are the four standard form statments?
A
A, E, I, O
(first 4 vowels)
9
Q
describe A form
A
- All subjects are predicates
- ex: all apples are healthy
- quantity: universal: refers to every thing in its subject class.
- quality: affirmative: it makes a positive claim that the subject class is a member of the predicate class.
10
Q
what does the scribble mean in venn diagram
A
that area is EMPTY, so you scribble out all things that aren’t true by the statement.
11
Q
describe E form
A
- No S’s are P’s (shows exclusion)
- No apples are poison
- quantity: universal: statement refers to every member of subject class
- quality: negative: statement denies that subject class is a subset of predicate class
12
Q
I form
A
- some S’s are P’s
- ex: some students are hardworking
- quantity: particular: refers to only some of the members of the subject class
- quality: affirmative: affirms that there is overlap between the subject class and predicate class
- interpretation of some = at least one.
13
Q
describe O form
A
- Some S are not P
- ex: some students are not coffee addicts
- quantity: particular, refers to some, but not all of the subject class
- quality: negative: denies overlap between subject and predicate classes
14
Q
what does X mean on venn diagram
A
X marks that at least one set member exists in this region, used when word some is used (means at least one)
15
Q
what is no one translated to for E form
A
No one > no people are people
16
Q
what is someone translated into in I form
A
Someone > some person is a person who
17
Q
what is ‘not every’ translated into in O form
A
not every > some are not
18
Q
what is everyone translated into in A form:
A
Everyone > All people are people who
19
Q
how should you translate a statement with direct reference to someone’s name to standard form?
A
make direct reference into a universal statement
* ex: from ted is going to the lecture to all people named Ted are going to the lecture
20
Q
how should you translate a statement with the word “only”
A
- translate it both ways, reverse subject and predicate
- then in your mind, test which one makes more sense
- ex: Only american citizens can buy land in Minnesota, could be all AC are minnesota land buyers (not true), or all minnesota land buyers are AC’s (now true)
21
Q
what’s direct inference
A
- logical relationships exist between any standard form statement and the other 3 possible statement forms using the same subject and predicate
- without any argument, you can make inferences about the true/falsity of related statements
22
Q
when does a contradiction occur
A
- In syllogistic logic: 2 statements are contradictory when their truth values are always opposite (if one is false and other must be true)
- they cannot both be true, and they cannot both be false
23
Q
the contradiction of an A form statement (all subjects are predicates) is
A
an O form statement (some S are not P)
24
Q
the contradiction of an E form statement is an I form statement (some S are P) is
A
an E form statement, No S are P
25
how can two statements be contrary?
* two statements are contrary if they **cannot both be true**, at the same time but they **can both be false**
* the contrary of an A form is E (and vice versa)
* ex: all leopard are spotted (A form) contrary is No leopards are spotted (E form)
26
how do you differentiate contradiction and contrary
think which is easier to prove:
* ex: E form statement: No rodents are vermin OR
* O form statement: some rodents are not vermin
* it's easier to prove O form: some rodents are not vermin, bc you just need to find at least one rodent that isn't vermin, so that's your contradiction
27
how can two statements be sub-contrary?
* two statements are sub-contraries if they **cannot both be false** at the same time, but **can both be true**
* opposite of contrary
* the sub-contrary of I form is O
28
how do you know if two statements are sub-contrary?
* avoid confusing what is "possible" with what is justified, if it's possible but not certain, the statement is false, and they must both be true to be subcontrary
29
what's the logical relationship of alternation between universal and particular statements of the same quality (A's and I's or E's and O's)
If the universal is true, the particular must also be true
ex: if it is true that "all fish are slimy" it must be true that "some fish are slimy"
30
sub-alternation
the opposite of alternation, if particular statement is false, the universal must also be false
31
how does aristotle handle empty sets in direct inference?
* no empty sets
* all statements that include something that's existence is not certainly known are false
* Ex: dragons are greedy
* this statement is interpreted as:
* all dragons, and there are at least one, are greedy (assumes there is one but there isn't, so it's false)
32
What's the modern or boolean way of handling empty sets?
* Empty sets are OK
* all statements that include something that's existence is not certainly known are true
* ex: all dragons are greedy is interpreted as: all dragons, if any, are greedy, so its true (ignores fact if they exist or not)
33
in ordinary language what do we rely on to indicate which interpretation we are using?
* context
* ex: all tresspassers are prosecuted is hopefully an empty set, but still true even if there's no tresspassers (boolean)
* ex: some students are going to pass the test
-false if there's no students, need at least one for this to be true
34
why does contrary disappear in modern/boolean interpretation?
bc it assumes all (A form) or no (E form) statements are true, bc it says if any exist, doesn't pay attention to existence:
ex: all sea monsters are dangerous
and no sea monsteres are dangerous
would normally be contrary bc they can both be false but bc they're assumed true
35
distribution of terms
* a term is distributed if the statement it is in refers to every member of the class denoted by the term
* otherwise it is not distributed
* they are marked with a flat line over distributed terms, and a U over undistributed terms
36
A form distributions
all subjects (distributed, talking about all) are predicates (undistributed not all are subjects)
## Footnote
tip: say to yourself does this refer to all or only some
37
E form distributions
No subjects (distributed refers to an entire class, subject is just not part of it), are predicates (still talking about whole class, just excluded from it)
38
I form distributions
Some subjects (undistributed, some is not every member of the class) are predicates (also undistributed still talking about some)
39
O form distributions
Some subjects (undistributed, some not all again), are not predicates (is distributed bc its reference is exclusionary, some are not in the entire class of predicates so it still refers to every member of the class)
40
what are the 3 guidelines for distributions
* subjects of universal statements > distributed
* predicates of negative statements (just excluded but still refers to all) distributed
* all other terms undistributed
41
what are the two formal features of a standard categorical syllogism (SCS)?
1. it has exactly two premises (and one conclusion). Each of the premises, and the conclusion, will be a proposition expressed in one of the four standard forms (A, E, I or O)
2. It contains exactly 3 terms, each of which occurs twice in the argument
42
where does the minor term occur in an argument?
It occurs as the *subject* term in the *conclusion*. It also occurs (as either subject or predicate term) in one of the premises.
-The premise containing the minor term is called the minor premise
43
where does the minor term occur in an argument?
The major term is the one which occurs as the *predicate* term in the conclusion. It likewise occurs once, as either the subject or predicate term, in one of the premises (but not in the minor premise).
-the premise containing the mjaor term is called the major premise
44
Where does the middle term occur in an argument?
Once in each premise, as either subject or predicate, but **not in the conclusion.**
45
# **important**
what are the 6 rules for validity of syllogisms?
1. avoid 4 terms. (The middle term must be exactly the same in each premise so there's only 3 different terms.)
2. the middle term must be distributed at least once
3. A term which is distributed in the conclusion must also be distributed in the premise in which it occurs
4. 4 -avoid 2 negative premises and 5-if either premise is negative the conclusion must be negative. These can be combined into one rule: number of negative premises (using no or not) must equal number of negative conclusions (impossible to have 2 negative conclusions, and requires 1 negative premise for a negative conclusion).
6. Particular conclusion requires at least one particular premise
46
what fallacy results from failure of rule 1 of validity: avoid 4 terms
four term fallacy
## Footnote
(similar to informal fallacy of equivocation where a word changes meaning in the course of an argument, bc if two terms mean different things it gives the illusion of four terms)
47
what fallacy results from failure of rule 3 of validity: a term which is distributed in the conclusion must also be distributed in the premise in which it occurs?
The fallacies of illicit major and illicit minor depending on if its the major (predicate) or minor (subject) term in the conclusion.
48
what fallacy results from failure of rule 4 of validity: avoid 2 negative premises
the fallacy of exclusive premises
49
what fallacy results from failure of rule 5 of validity: if either premise is negative the conclusion must be negative
fallacy of drawing an affirmative conclusion from a negative premise
50
what fallacy results from rule 6 of validity: particular conclusion requires at least one particular premise?
existential fallacy
51
what is the whole process you should go through to identify if an argument is valid?
* put the argument in standard categorical syllogism (SCS) form
* identify minor, major and middle terms
* identify distribution of terms
* apply the rules
