Unit 4 Reason as a way of knowing
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Unit 4Reason as a way of knowing
Zendo
• The Master will present two Koans - one that follows the rule and one that does not.
• Teams will take turns presenting their own koans to the master to see if they follow the rule. With each new Koan, the presenting team with either say “master” or “mondo”
• If the team says “master” - the master will mark the koan with a white (follows the rule) or a black (does not follow the rule) stone. Play proceeds to the next team.
• If a team says “mondo” all teams must guess whether the new koan follows the rule by secretly revealing either their white (follows the rule) or black (does not follow the rule stones. Teams that are correct will receive guessing stones.
• Teams may turn in guessing stones on their turns to guess at the rule. Guesses should be clearly stated using the command terms presented on the next slide
• If the guess is incorrect, the master will present an example that follows the rule but violates the guess, or a counter example that follows the guess but violates the rule
• The winning team is the first to make a correct claim regarding the rule.
Zendo descriptors
• Color - yellow, blue, pink, black, green, red
• Number
• Size - small, medium, large
• Spacial relation - touching, not touching, nested, level in a nested stack
• Existence - is, is not
• Placement - flat, standing
• Grounded or not grounded
• At least or precisely
Rule 1
Rule 2
Rule 3
Rule 4
Rule 5
JournalDescribe, in as much detail as you can, the process by which the correct rule was determined.
What ways of knowing, that we have discussed did this activity demonstrate (explain)? What new way of knowing did this activity highlight? How does this new way of knowing differ from the WoKs we have discussed so far?
What real-world activities does this game model? Explain at least one and describe what makes them similar.
NIPINGor,
Non IP infringing mystery game• Get into your teams from yesterday
• Examine your cards and mark your detective’s notebook accordingly (your cards indicate suspects, weapons and location that you know were not involved in the crime.)
• On your turn you may either, 1) Make an suggestion that the crime was committed in a specific location, using a specific weapon, by a specific suspect. In clockwise order, each group must then try to disprove the suggestion. To do so they will silently show the suggesting group one of the matching cards involved in the suggestion, or 2) Make an accusation. To do this you accuse a specific suspect of the crime with a specific weapon in a specific location. I will tell you if you are correct or not.
• The winning team is the team that correctly identifies the correct suspect, weapon and location with the fewest false accusations.
Suspects Weapons LocationsMr. Alexandre
The Beast The IB office
Mrs. Sorgent A Graphing Calculator
Room A211
Mr. Kalis A Tamale The Principal’s Office
Mrs. Wallace A Referral The Parking Lot
Mrs. McKay The Common App
Los Potros
Mrs. Herman A knowledge question
The Gym
The Football FieldThe Biotech room
JournalDescribe, in as much detail as you can, the process by which the correct answer was determined.
How was this activity similar to the Zendo?
In what essential ways was the process used to determine truth in the clue activity different from the process used in the Zendo activity? Which process was more reliable?
What real-world activities does this game model? Explain at least one and describe what makes them similar.
Definition of reason and logic
Webster’s Dictionary defines reason as:
The power of the mind to think, understand, and form judgments by a process of logic
and logic as:
reasoning conducted or assessed according to strict principles of validity
For our purposes:
Reason is a way of knowing that uses existing knowledge (from our senses, language emotion etc.) to generate new knowledge.
The study of logic examines the rules, procedures and practices by that guide the creation of this new knowledge.
II. Basic terminology
• Arguments
• Premises and conclusions
• Induction v. deduction
• Fallacies
Deductive or inductive? Discuss each argument with your group and explain your rationale
1. All of the Giants are team players. Buster Posey is a Giant. Buster posey is a team player.
2. All stars contain plutonium. The sun is a star. The sun contains plutonium.
3. Most Democrats support gun control. Bernie Sanders is a Democrat. Bernie Sanders supports gun control.
4. The last time the dragons attacked, the town was destroyed. If they return we will have to rebuild again.
5. What goes up must come down.
6. If the first student to enter room a211 is Mr. Olmedo, it is Wednesday. Mr. Olmedo was the first student to enter room a211. It is Wednesday.
7. Mr. Hu eats apples and he is healthy. If I eat apples I will be healthy as well.
8. All diploma candidates have straight As. John is a diploma candidate. John has straight As.
Deductive or inductive? Discuss each argument with your group and explain your rationale
1. All of the Giants are team players. Buster Posey is a Giant. Buster Posey is a team player.
2. All stars contain plutonium. The sun is a star. The sun contains plutonium.
3. Most Democrats support gun control. Bernie Sanders is a Democrat. Bernie Sanders supports gun control.
4. The last time the dragons attacked, the town was destroyed. If they return, we will have to rebuild again.
5. What goes up must come down.
6. If the first student to enter room a211 is Mr. Olmedo, it is Wednesday. Mr. Olmedo was the first student to enter room a211. It is Wednesday.
7. Mr. Hu eats apples and he is healthy. If I eat apples I will be healthy as well.
8. All diploma candidates have straight As. John is a diploma candidate. John has straight As.
DeductiveDeductive
Deductive
Deductive
Inductive
InductiveInductive
Inductive
Induction
Definitions
• Inductive arguments are arguments where, if the premises are true and the argument strong, the conclusion is likely to follow
• A strong inductive argument with true premises is called cogent
Induction
Three types of inductive arguments
• Induction by generalization or enumeration
• Induction by analogy
• Causal inductionWith a partner discuss and record in your
journal one inductive argument in each category. The arguments can be informally written (ie -
not standard form)
Induction
3 examples:
• Small pox
• Education
• Public health
• 1936 election
C. Three basic types of inductive arguments •Induction by generalization or enumeration •Induction by analogy •Causal induction
Which type of inductive argument is each of the above examples?
Assessing inductive arguments
Three general principles
• Does the argument start with justified premises?
• Does the argument include all relevant information?
• Is the argument strong? (does acceptance of the premises justify confidence in the conclusion? Assessing strength uses criteria unique to each type of induction)
1. Carbon dioxide does not trap heat in the atmosphere
2. Global average temperatures have been shown to fluctuate widely over time
Therefore: The current increase in global temperatures results from natural rather than man-made factors
Example 1
Global average temperatures have been shown to increase the frequency of unusual weather events and this means the current drought in California is caused by global warming.
Example 2
All of the students currently here (in A211) care about their grades, therefore all Tracy High students care about their grades.
Example 3
Assessing enumerative arguments (3 questions)
1.On how many cases is the conclusion based?
2.Are the cases examined representative?
3.Could other conclusions be drawn?
Assessing analogical arguments
Assessing analogical arguments
• How many times does the analogy apply?
• In what number of respects are the things involved analogous?
• What is the strength of the conclusion relative to the strength of the premises?
• How many dissimilarities are there between the two things being compared?
• Is the analogy relevant?
Assessing Causal arguments
1. Is the causal claim a good explanation for the observed correlation? (Is the relationship serial rather than causal)
2. Is there any other reasonable explanation for the correlation?
Convert the ad to an argument in standard form. What type of argument is it? How strong is the argument?
Explain.
Republican: Fiorina, Trump. Carson, Kasich, Bush, Cruz, Paul, Christie, Rubio, Santorum, Huckabee, Gilmore
Democrats: Sanders, Clinton, O’Mally
Pick a Winner!
Fallacies
Categories of Informal Fallacies
•Fallacies of relevance
•Fallacies of weak induction
•Fallacies of presumption
•Fallacies of ambiguity(Materials on slides 29-39 were adapted from Dr. Craig Vasey Trinkle’s support pages his philosophy 151 class taught at the University of Mary Washington - accessed on 1.28.16 at http://logic.umwblogs.org)
Fallacies of relevance
•Appeal to the People
•Appeal to force
•Ad Hominum
•Straw person
•Red Herring
Fallacies of weak induction
•Hasty generalization
•Slippery Slope
•Appeal to Authority
•Confusion of Necessary with sufficient causes
•Two wrongs
Fallacies of Presumption
•Begging the question
•False dichotomy
Fallacies of Ambiguity
•Equivocation
Fallacies of Presumption
•Equivocation
Induction ProjectInduction is everywhere in the media. In this assignment you will identify, analyze and critique an argument found in an advertisement, a political cartoon or a political speech.
1.Find an advertisement, a political cartoon or a political statement that contains an inductive argument. Reproduce the original so that is is approximately 8.5 x 11 (so that it can be mounted on a single sheet of binder paper).
On a separate piece of paper which you will attach below the advertisement complete the following (please word process Times 12 point font):
• Identify the argument contained in the piece and put that argument into standard form. Your argument should have at least two premises and a conclusion.
• Identify whether the argument is enumerative, causal or analogical.
• Assess the argument based on the tools for assessing analogical arguments discussed in class. This should be done in 50 to 100 words.
• Identify and explain how the advertisement demonstrates at least one of the informal fallacies. You may use both those discussed in class and those on the IEP website. This section should also be 50-100 words
2. Create a one slide presentation that displays the original source and the standard form of your argument. Email your slide to your team captain,(drill sergeants, drum majors, top duck, etc.) team captains email group presentation to me by Friday Morning at 6:00 AM
3.Be prepared to present your analysis on Friday in class
Examples from slides 39 to 57 are adapted from Dr. Craig Vasey Trinkle’s Introduction
to Logic pageAccessed on 2.3.16 at http://logic.umwblogs.org
We must accept the traditions of the men of old time who affirm themselves to be the offspring of the gods –that is what they say–and they must surely have known their own ancestors. How can we doubt the word of the children of the gods? Plato, Timaeus
Begging the Question
Listen, as long as you’re going to live here at home and let your mother and me support you, you can rest assured that you’re going to cooperate. And that goes for your opinions as well as your behavior.
Appeal to Force
“The very fact that no sabotage has taken place to date is a disturbing and confirming indication that such action will be taken.” General J.L. DeWitt, Final Report on the Japanese Evacuation of the West Coast, 1943.
Appeal to Ignorance
“I would like to ask the learned gentleman, on which side he is descended from a monkey, his mother’s or his father’s?”
False Dichotomy
We must believe in God’s existence because it is taught in the Holy Scriptures, and we must believe the Holy Scriptures because they have come from God. Descartes, Meditations
Begging the Question
On the Senate floor in 1950, Joe McCarthy announced that he had penetrated “Truman’s iron curtain of secrecy.” He had 81 case histories of persons whom he considered to be Communists in the State Department. Of Case 40, he said, “I do not have much information on this except the general statement of the agency that there is nothing in the fiels to disprove his Communist connections.” Richard Rovere, Senator Joe McCarthy
Appeal to Ignorance
Socrates, I think you are too ready to speak evil of men, and, if you take my advice, I recommend you to be careful. Perhaps there is no city in which it is not easier to do men harm than to do them good, and this is certainly the case at Athens, as I believe that you know. Plato, Meno
Appeal to Force
“I see nobody on the road,” said Alice. ” I only wish I had such eyes,” the King remarked in a fretful tone. “To be able to see Nobody! And at that distance too! Why, it’s as much as I can do to see real people, by this light.” Alice in Wonderland
Equivocation
Paris Hilton says that “Scary Movie” is excellent, so it must be worth seeing.
False Authority
The secretaries have asked for lounge areas where they can take their coffee breaks. We’ll have to turn down this request. If we give them the lounge areas, next they’ll want a t.v., and then snack machines, a spa and a swiming pool. We can’t afford all that.
Slippery Slope
The Free-Lance Star carried a report about three teenagers arrested on drug charges. Teenagers these days are just a bunch of junkies.
Hasty Generalization
Animal rights activists say that animals are abused in biomedical research labs. But actually, pets are abused by their owners every day, and probably about 25% of pet owners neglect their pets. Some cases of abuse are enough to make you sick.
Red Herring
I know some of you oppose the appointment of Cole as the new sales manager. But I am sure you will see that he’s well-qualified for the job. If he’s not appointed, we may have to cut some personnel in your department.
Appeal to Force
Senator Barrow advocates increased Social Security benefits for the poor. It’s regrettable that he finds it necessary to embrace socialism. Socialism defeats initiative, takes away promised rewards and leads to inefficiency and big government. It was tried and failed in Europe. Clearly socialism is no good.
Straw Person
You should read An Inconvenient Truth. It’s been on the N Y Times Best Seller list for 29 weeks.
Appeal to the people/Begging the Question
There’s a lot of talk these days about getting the pesticides out of our fruits and vegetables. But many of these foods are essential to our health. Carrots are an excellent source of vitamin A, broccoli is rich in iron, and oranges and grapefruits have lots of vitamin C.
Red Herring
Smirnoff is the best vodka available: renowned violinist Pichas Zukerman says, “When it comes to vodka, Smirnof plays second fiddle to none.”
False Authority
The garment workers have signed a petition arguing for better ventilation on the premises. Unfortunately, air conditioning is expensive. Air ducts would have to be run through the factory, and a massive heat-exchange unit installed on the roof. The cost of operating it in the summer would be astronomical. In view of all this, the petition must be rejected.
Slippery Slope/Red Herring
Barbara Striesand, Paul Newman and Julia Roberts are Democrats. Therefore all Hollywood stars are Democrats.
Hasty Generalization
Deduction
Definitions
• Truth
• Validity
• Deductive arguments
• Syllogism
• Categorical propositions
• Deductive fallacy
Critical Note: Truth and validity are independent! True premises may lead to an invalid conclusion and false premises may lead to a valid conclusion!
Anatomy of a syllogism
All Wizards are clever
All Potters are a Wizards
Therefore:All Potters are clever
The predicate nominative of the conclusion is the major
term and is labeled p
The subject of the conclusion is the minor term
and is labeled s
The term which doesn’t appear in the conclusion is the middle term and is
labeled m
Anatomy of a syllogismCategorical propositions are assertions about classes of objects which affirm or deny that one class is included in another either in whole or in
part.
It is because syllogisms always contain categorical propositions that they are often called categorical
syllogisms
All Wizards are clever
All Potters are a wizards
Therefore: Potters are clever
4 types of categorical propositionsUniversal affirmative - A propositions
All caudillos are tyrants Universal negative - E propositions
No caudillos are democrats Particular affirmative - I propositions
Some caudillos are good for their country
Particular negative - O propositions
Some caudillos are not Mexican
AffIrmo
nEgO
All fish have wings
All dogs are fish
Therefore: All dogs have wings
A
A
APS
M
How can we evaluate the validity of the following syllogism? Discuss in your
group and describe your steps
All fish have wings
All dogs are fish
Therefore: All dogs have wings
A
A
APS
M
B. Assessing the validity of categorical syllogisms
First – Draw a triple Venn diagram, numbering the quadrants as shown. Second - Label the circles of a three circle Venn diagram with the syllogism’s three terms. It is customary to label the top left circle as the minor term (s), the top right circle as the major term (p) and the bottom circle as the middle term (m).Third – Diagram any universal premises by shading the areas excluded by those premises. Remember, the shaded areas are those excluded by the premise. Fourth – Diagram any particular premises by placing an “x” either
• Completely within a circle if it is clear from the premises that the particular term is wholly included in the circle
Or • On a line if the premises do not determine on
which side of the line it should go Finally – Inspect the diagram to see if the diagram of the premises is consistent with the conclusion.
Assessing syllogisms diagrams using Venn diagrams
1
7
6
5
4
32
Uruks Evil
Orcs
All Orcs are evil
All Uruks are Orcs
Therefore: All Uruks are evil
Assessing the validity of syllogisms using Venn diagrams
All Orcs are evil
All Uruks are Orcs
Therefore: All Uruks are evil Orcs
Uruks Evil
No
No
No No
1
7
6
5
4
3
2
Valid
Assessing the validity of syllogisms using Venn diagrams
All Disney movies are awful things
Some animated films are Disney movies
Therefore: All awful things are animated films Disney Movies
Animated filmsAwful things
NoSome
No
1
7
6
5
4
3
2True
premisses
- Invalid
argument
All syllogisms can be expressed symbolically, since each of the terms simply represents a variable
All B are A
Some C are B
Therefore: All A are C
B
CA
NoSome
No
1
7
6
5
4
3
2
Invalid
Nonsense words are fun, too
All Bangles are Bingles
Some Woot-Woots are Bangles
Therefore: All Bingles are Woot-Woots Bangles
Woot-WootsBingles
NoSome
No
1
7
6
5
4
3
2
Invalid
Assessing the validity of syllogisms using Venn diagrams
All soul eaters are shape shifters.
All Katamates are shape shifters.
Therefore:
All Katamates are soul eaters.
m
s p
No NoNo
1
7
6
5
4
3
2
Invalid
1.
No physical actions are chance occurrences.
All chance occurrences are random events.
Therefore: No random events are physical actions.
m - Chance occurrences
s - Random events p - Physical actions
No
1
7
6
5
4
3
2
No
Invalid
No
All events are things describable by science.
All mental decisions are events.
Therefore: All mental decisions are things
describable by science.
m -Events
s - Mental decisions p - Describable by science
No
1
7
6
5
4
3
2
ValidNo
No
No
2
3
All things describable by science are predictable events.
No free decisions are things describable by science.
Therefore: No free decisions are predictable events
m - Describable by science
s - Free Decisions p - Predictable events
No
1
7
6
5
4
3
2
NoNo
Invalid
4
No things describable by science are uncaused
happenings.
All mental decisions are things describable by science.
Therefore: No mental decisions are uncaused
happenings.
m - Describable by science
s - Mental decisions p - Uncaused happenings
No
1
7
6
5
4
3
2
No
No
No
Valid
No free choices are caused occurrences.
Some natural processes are not caused occurrences.
Therefore: Some natural processes are not free choices
m - Caused occurrences
s - Natural Processes p - Free Choices
X
1
7
6
5
4
3
2
No
Invalid
We don’t know for sure
what the x excludes
because it is ambiguous (on
the line). The conclusion
requires certain knowledge
that some natural
processes are not free
choicesNo
5
All free decisions are uncaused happenings.
No mental decisions are uncaused happenings.
No mental decisions are free decisions.
m - Uncaused happenings
s - Mental decisions p - Free decisions
1
7
6
5
4
3
2
NoNo
6
NoNo
Valid
Some decisions are careful reflections.
All uses of free will are decisions.
Therefore: Some uses of free will are careful reflections.
m - Decisions
s - Uses of free will p - Careful reflections
X
1
7
6
5
4
3
2
NoInvalid
We don’t know for sure
what the x includes
because it is ambiguous (on
the line). The conclusion
requires certain knowledge
that some uses of free will
are careful reflections
No
7
Some coerced decisions are not free choices.
Some desires are free choices.
Therefore: Some desires are coerced decisions. m - Free choices
s - Desires p - Coerced decisions
X
1
7
6
5
4
3
2
Invalid - To
be valid we need
an x in area 2!
9
X
Examples from class
The conclusion requires an x in 4 or 5. Since there is none,
it is invalid
IAI2Examples from class
Examples from class
Assessing the validity of syllogisms using Venn diagrams
Some cartons have wings
Some boxes are cartons
Therefore:
Some boxes have wings
m - Cartons
s - Boxes p - Wings
Some Some
1
7
6
5
4
3
2
Invalid
Assessing the validity of syllogisms using Venn diagrams
All ducks are birds
Some ducks can fly
Therefore:
Some birds can fly m - ducks
s - Birds p - fly
Some
No
1
7
6
5
4
3
2
Valid
No
Assessing the validity of syllogisms using Venn diagrams
All clarinets are instruments
No mayonnaise(s) is (are) an instrument
Therefore:
No mayonnaise(s) is (are) clarinets m
s p
No
No
No
No
1
7
6
5
4
3
2
Valid
An on-line venn diagram tool can be found at:
http://www.poweroflogic.com/cgi/Venn/venn.cgi?exercise=6.3A
http://www.poweroflogic.com/cgi/Venn/venn.cgi
Other means of assessing categorical syllogisms
Mood and figure
The Mood of a categorical syllogism is the series of three letters representing each proposition (AffIrmo, nEgO)
Thus
All A are B
No B are C
Therefore: All C are A
Would be in the Mood AEA
Mood and figure
The figure of a categorical syllogism has to do with the position of the middle term
3
Figure 1: The middle term is on the left in P1, and on the right in P2. Figure 2: The middle term is on the right in both premises. Figure 3: The middle term is on the left in both premises. Figure 4: The middle term is on the right in P1, and on the left in P2.
Let’s look at the other argument from earlier:
1. No states with coastlines are states that are landlocked. 2. Some U.S. states are states that are landlocked. 3. Therefore, some U.S. states are not states with coastlines.
Note that the middle term appears on the right in BOTH premises. So, this argument has “figure 2.” We can remember the four figures more easily with the following diagrams. If we call the subject of the conclusion “S” (﴾the minor term)﴿, and the predicate of the conclusion “P” (﴾the major term), and the middle term “M”, then the four figures look like this:
We can draw lines through the middle terms in each of these four diagrams to create a collar-like shape, like this:
In order to memorize the four kinds of figures, picture this “collar flap” image. From left to right, we see the layout of figures 1, 2, 3, and 4.
Accessed on 2.6.14 at http://rintintin.colorado.edu/~vancecd/phil1440/syllogisms.pdf)
Aristotle, you’re the man, but don’t fool with Boole!
4
3. Valid Argument Forms: Now that we know about the proper FORMS of categorical syllogisms, and also how to assess what MOOD and FIGURE each argument has, we can use some charts to assess when an argument is valid or invalid. Unconditionally Valid Forms: There are 15 combinations of mood and figure that are valid from the Boolean standpoint (﴾we call these “unconditionally valid” argument forms). This chart depicts ALL of 15 the unconditionally valid argument forms
Recall this argument from earlier:
1. All mammals are creatures that have hair. 2. All dogs are mammals. 3. Therefore, all dogs are creatures that have hair.
Its mood was “AAA” since all three propositions are “A” propositions (﴾i.e., they are all of the form “All S are P”)﴿. Its figure was “figure 1” since the middle term appears on the left and then on the right (﴾picture the leftmost diagonal line of the “collar flap” diagram)﴿. Now we can look up “figure 1 – AAA” in the chart above. If it DOES APPEAR on the chart, then the argument is valid from the Boolean standpoint. If it DOES NOT APPEAR on the chart, then it is invalid from the Boolean standpoint. Since “figure 1 – AAA” DOES appear on the chart, the argument is valid!! Let’s try the other one:
1. No states with coastlines are states that are landlocked. 2. Some U.S. states are states that are landlocked. 3. Therefore, some U.S. states are not states with coastlines.
This argument’s mood is “EIO”. Its figure is “figure 2”. Let’s look that up on the chart. Sure enough, under “figure 2 - EIO” appears on the list!! This argument is valid.
5
Conditionally Valid Forms: Now, recall that there were some inferences that were NOT valid from the Boolean standpoint which WERE valid from the Aristotelian standpoint—but only IF they were about existing things. The chart above listed argument forms that were valid from BOTH the Boolean AND the Aristotelian standpoint. The chart below lists argument forms that are ONLY valid: (1) from the Aristotelian standpoint, where universal propositions have existential import, and only IF (2) the term listed in the right-hand column actually exists. We call these “conditionally valid” argument forms. There are 9 conditionally valid argument forms for categorical syllogisms in addition to the 15 unconditionally valid argument forms:
Recall that the existential fallacy occurred when going from a universal premise to a particular conclusion. Similarly, all of the above “conditionally valid” argument forms have universal premises (﴾“A” or “E”)﴿ and a particular conclusion (﴾“I” or “O”)﴿. Consider the following argument:
1. All mammals are creatures that have hair. 2. All dogs are mammals. 3. Therefore, some dogs are creatures that have hair.
This argument is an “AAI” argument with “figure 1”. This argument does NOT appear on the “unconditionally valid” (﴾Boolean)﴿ chart, because it goes from universal premises (which do NOT have existential import) to a particular conclusion (which DOES have existential import), and this sort of inference commits the existential fallacy according to Boole. But, notice that this form (﴾“figure 1 – AAI”)﴿ DOES appear on the “conditionally valid” (Aristotelian) chart. So, it IS conditionally valid on the Aristotelian interpretation.
Aristotle, you’re the man, but don’t fool with Boole!
4
3. Valid Argument Forms: Now that we know about the proper FORMS of categorical syllogisms, and also how to assess what MOOD and FIGURE each argument has, we can use some charts to assess when an argument is valid or invalid. Unconditionally Valid Forms: There are 15 combinations of mood and figure that are valid from the Boolean standpoint (﴾we call these “unconditionally valid” argument forms). This chart depicts ALL of 15 the unconditionally valid argument forms
Recall this argument from earlier:
1. All mammals are creatures that have hair. 2. All dogs are mammals. 3. Therefore, all dogs are creatures that have hair.
Its mood was “AAA” since all three propositions are “A” propositions (﴾i.e., they are all of the form “All S are P”)﴿. Its figure was “figure 1” since the middle term appears on the left and then on the right (﴾picture the leftmost diagonal line of the “collar flap” diagram)﴿. Now we can look up “figure 1 – AAA” in the chart above. If it DOES APPEAR on the chart, then the argument is valid from the Boolean standpoint. If it DOES NOT APPEAR on the chart, then it is invalid from the Boolean standpoint. Since “figure 1 – AAA” DOES appear on the chart, the argument is valid!! Let’s try the other one:
1. No states with coastlines are states that are landlocked. 2. Some U.S. states are states that are landlocked. 3. Therefore, some U.S. states are not states with coastlines.
This argument’s mood is “EIO”. Its figure is “figure 2”. Let’s look that up on the chart. Sure enough, under “figure 2 - EIO” appears on the list!! This argument is valid.
5
Conditionally Valid Forms: Now, recall that there were some inferences that were NOT valid from the Boolean standpoint which WERE valid from the Aristotelian standpoint—but only IF they were about existing things. The chart above listed argument forms that were valid from BOTH the Boolean AND the Aristotelian standpoint. The chart below lists argument forms that are ONLY valid: (1) from the Aristotelian standpoint, where universal propositions have existential import, and only IF (2) the term listed in the right-hand column actually exists. We call these “conditionally valid” argument forms. There are 9 conditionally valid argument forms for categorical syllogisms in addition to the 15 unconditionally valid argument forms:
Recall that the existential fallacy occurred when going from a universal premise to a particular conclusion. Similarly, all of the above “conditionally valid” argument forms have universal premises (﴾“A” or “E”)﴿ and a particular conclusion (﴾“I” or “O”)﴿. Consider the following argument:
1. All mammals are creatures that have hair. 2. All dogs are mammals. 3. Therefore, some dogs are creatures that have hair.
This argument is an “AAI” argument with “figure 1”. This argument does NOT appear on the “unconditionally valid” (﴾Boolean)﴿ chart, because it goes from universal premises (which do NOT have existential import) to a particular conclusion (which DOES have existential import), and this sort of inference commits the existential fallacy according to Boole. But, notice that this form (﴾“figure 1 – AAI”)﴿ DOES appear on the “conditionally valid” (Aristotelian) chart. So, it IS conditionally valid on the Aristotelian interpretation.
Mood = AEA
All A are B
No B are C
Therefore: All C are A
Figure = 4
Invali
d!
Ooh! Ooh! It’s invalid when we do then Venn too!
All A are B
No B are C
Therefore: All C are A
B
AC
No No
No
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2
InvalidNo
Other means of assessing categorical syllogisms
Formal fallacies - No syllogism that commits one of the following formal fallacies is valid
• Fallacy of the undistributed middles - Any syllogism in which the middle term is undistributed (to be distributed means all members of a term’s class are affected by the proposition*) is invalid.
• Fallacy of Illicit Major/Illicit Minor - If a term is distributed in the conclusion, it must be distributed in one of the premises or the argument is invalid.
• Fallacy of Exclusive premises - Any categorical syllogism with two negative premises is invalid
• Fallacy of Affirmative Conclusion/Negative Premise and Negative Conclusion/Affirmative Premise - If an argument has a negative conclusion, one of the premises must be negative; if one of the premises is negative, the conclusion must be negative.
• Existential fallacy - If both of the premises are universal, the conclusion cannot be particular (Boole only)
*A term is said to be distributed if it is either the subject of a universal or the predicate of a negative.
An now we can name the reason why this argument is invalid
All A are B
No B are C
Therefore: All C are A
B
AC
No No
No
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2
No
Fallacy of
Affirmative Conclusion/Negativ
ePremise
No Mr. Haydock, not another way to test validity!
But wait, this one’s so much fun . . .
Remember that the conclusion of a valid syllogism must be true if the premises are true.
So . . . If we take any syllogism and substitute premises which we know to be true (taking care to make sure the form is the same), if the the conclusion is true, the syllogism is valid.
This is called assessing by substitution/counter example.
Let’s try it!
All A are B
No B are C
Therefore: All C are A
All ferns are plants
No plants are dogs
Therefore: All dogs are ferns
All Giggles are Googles
All Sniglets are Giggles
Therefore: All Sniglets are Googles
All sharks are fish
All Great Whites are sharks
Therefore: All Great Whites are fish
Two other types of syllogism
• Disjunctive syllogisms
• Hypothetical syllogisms
Disjunctive syllogisms
A disjunction is a statement that claims that at least one of two possibilities is true.
For example:
Either A or B
Not A
Therefore B
Inclusive or exclusiveIn common usage or is used exclusively:
Entrees come with fries or coleslaw
means you can get fries of coleslaw, but not both.
But in logic (and computer science) “or” is generally inclusive, meaning that at least one of a series must be true (but both could be).
Disjunctive syllogismsAssuming the inclusive or, determine whether the following are valid or invalid. Be prepared to explain why you believe each statement is valid or invalid. Remember, validity means the conclusion must follow
Either A or B
A
Therefore B
Either not A or B
A
Therefore B
Either A or not both B and C
A
Therefore both B and C
1. Invalid for either exclusive or inclusive
Either Fido ran away or he was hit by a car
Fido ran away
Therefore: Fido did not get hit by a car
ValidInvalid
Invalid
Invalid
Hypothetical syllogisms
Hypothetical syllogisms are two premise deductive arguments in which (at least) one premise is a conditional (if) statement.
There are two types of hypothetical syllogisms:
Pure hypotheticals
Mixed hypotheticals
Pure hypothetical syllogisms
In a pure hypothetical syllogism, both premises are hypothetical statements
If Gandalf fails then Godor Falls
If Godor falls then the Shadow will triumph
Therefore: If Gandalf fails then the Shadow will triumph
SymbolicallyIf p then qif q then r
Therefore: If p then r
The other valid form:
If Mary comes to the party then Dale will not come
If Dale does not come, then Ernie will not come
Therefore: If Mary comes to the party then Ernie will not come
SymbolicallyIf p then not r
If not r, then not qTherefore: If p then not q
Mixed hypothetical syllogisms
In a mixed hypothetical syllogism, there is a conditional premise followed by a premise which registers agreement or disagreement with either the antecedent or the consequent of the conditional.
The antecedent is the if part of the statement, while the consequent is the then part of the statement.
There are two valid and two invalid forms of mixed hypothetical syllogism:
Valid mixed hypothetical syllogisms
Modus Ponens (AA)
If Legolas is an elf, then he is immortal
Legolas is an elf
Therefore: Legolas is immortal
SymbolicallyIf p then q
not qTherefore: not p
Modus Tolens (DC)
If we are the only life in the universe, then the universe sucks
The universe does not suck
Therefore: We are not the only life in the universe
SymbolicallyIf p then q
pTherefore: q
Are the following valid or invalid? Why?Identify what type of argument is being made (PH/MH) and
why the argument is valid.
1.If Andy is here then I am not late
Andy is hereTherefore: I am not late
Valid - A
A 2.If Andy is here then I am not late
If I am not late then I will passTherefore: If Andy is not here then I
will not passInvalid
HS
3. If I am lying then Kant is right
Kant is rightTherefore: I am not not Lying
Invalid
- AC 4.
If A then BNot B
Therefore: Not A
Valid - D
C
5. If A then BIf B the C
Therefore: If A then C
Valid HS 6.
If there are monkeys then there will be trees
There are no monkeysTherefore: There are no treesInv
alid - D
A
Logic and computer science
• Logic is an essential component of how computers work
• We will be doing a small project to demonstrate the connection between computers and logic from codeacademy.org
JavaScript basics for our project
• Declare a variable:
var dogs
• Assign a value to a variable
var dogs = 1.5
var dogs = “rock”
var dogs = prompt(“What is your favorite animal?”)
Key concept - variables can change their value!
in JS = is used to assign variables, mathematical equivalency is indicated by ===
JavaScript basics for our project
• If statement syntax
if(some condition) {some action;}
else {some action;}
• if/else if/else syntax
if(some condition) {some action;}
else if (some condition) {some action;}
else {some action;}
Key concept - syntax matters!
JavaScript basics for our project
• console.log - prints something to the console
console.log(“some string”);
• return - returns a value and stops a function
return”you are right!”
Functions• Functions are special variables that, when called, carry out a
specific task.
• Function syntax
var functionName=function(argument1, argument2) {instructions to be carried out be the function}
The function we will write will contain some if/else statements which will return various strings.
• Calling a function - Functions do nothing until called. When a function is called, it will carry out its assigned task. Syntax for calling a function:
functionName(argument1, argument2)
The arguments in our case will be variables that we have previously defined and assigned values to.
Logic Unit QuizOn Monday we will have a culminating quiz on the logic unit. The quiz will count for 100 points in the minor assignments category. The quiz will be open notes
You will be asked to do the following on the quiz:
1.Explain the difference between inductive and deductive reason.
2.Examine three inductive arguments and identify the informal fallacy that they commit (I will be fairly obvious here).
3.Assess whether or not two arguments are valid categorical syllogisms using the venn diagram method and one other method (not substitution).
4.Identify whether three arguments are hypothetical or disjunctive syllogisms and assess the validity of each.
5.Briefly explain (one paragraph) why logic and coding are similar.
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Arguments
1.
2.
Therefore:
Arguments
1.
2.
Therefore:
Ad Hominem
(Attacking the person): This fallacy occurs when, instead of addressing someone's argument or position, you irrelevantly attack the person or some aspect of the person who is making the argument. The fallacious attack can also be direct to membership in a group or institution.
Appeal to ignorance
This fallacy occurs when you argue that your conclusion must be true, because there is no evidence against it. This fallacy wrongly shifts the burden of proof away from the one making the claim.
Begging the question
The fallacy of begging the question occurs when an argument's premises assume the truth of the conclusion, instead of supporting it. In other words, you assume without proof the stand/position, or a significant part of the stand, that is in question. Begging the question is also called arguing in a circle.
Confusion of Necessary with a Sufficient Condition
A causal fallacy you commit this fallacy when you assume that a necessary condition of an event is sufficient for the event to occur. A necessary condition is a condition that must be present for an event to occur. A sufficient condition is a condition or set of conditions that will produce the event. A necessary condition must be there, but it alone does not provide sufficient cause for the occurrence of the event. Only the sufficient grounds can do this. In other words, all of the necessary elements must be there.
Equivocation
The fallacy of equivocation occurs when a key term or phrase in an argument is used in an ambiguous way, with one meaning in one portion of the argument and then another meaning in another portion of the argument.
False dilemma
When you reason from an either-or position and you haven't considered all relevant possibilities you commit the fallacy of false dilemma.
Irrelevant AuthorityThe fallacy of irrelevant authority is committed when you accept without proper support for his or her alleged authority, a person's claim or proposition as true. Alleged authorities should only be used when the authority is reporting on his or her field of expertise, the authority is reporting on facts about which there is some agreement in his or her field, and you have reason to believe he or she can be trusted. Alleged authorities can be individuals or groups. The attempt to appeal to the majority or the masses is a form of irrelevant authority. The attempt to appeal to an elite or select group is a form of irrelevant authority.
Red Herring
This fallacy consists in diverting attention from the real issue by focusing instead on an issue having only a surface relevance to the first.
Slippery Slope
In a slippery slope argument, a course of action is rejected because, with little or no evidence, one insists that it will lead to a chain reaction resulting in an undesirable end or ends. The slippery slope involves an acceptance of a succession of events without direct evidence that this course of events will happen.
Straw man
This fallacy occurs when, in attempting to refute another person's argument, you address only a weak or distorted version of it. Straw person is the misrepresentation of an opponent's position or a competitor's product to tout one's own argument or product as superior. This fallacy occurs when the weakest version of an argument is attacked while stronger ones are ignored.
Two wrongs
If you try to justify an act/belief by pointing out in others a similar act/belief, you are committing the fallacy of "two wrongs make a right." This fallacy can occur by suggesting "if others are doing it, I can too" (common practice). Another form of the fallacy occurs when you dismiss a criticism of your action/belief, because your critic is acting/believing in a similar way (you do it, too).
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