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Unit 4 Reason as a way of knowing Tuesday, March 4, 14

Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

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Page 1: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

Unit 4Reason as a way of knowing

Tuesday, March 4, 14

Page 2: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

I. Reasoning

• At its core, reasoning is using what is known as building blocks to create new knowledge

• I use the words logic and reasoning interchangeably. Technically, logic is reasoning conducted according to formal rules.

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II. Basic terminology

• Arguments

• Premises and conclusions

• Inductive v. deductive

• Fallacies

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Page 4: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

III. Induction

A. Definitions

• Inductive reasoning uses observed experience to make judgments about the unobserved

• Inductive reasoning uses the past to predict the future

• Inductive reasoning assumes that nature/reality follows predictable patterns

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Page 5: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

IV. Deduction

A. Definitions

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Page 6: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

III. Induction

B. Significance

• Inductive reasoning is the most common form of reasoning we use

List three examples of how you have reasoned inductively today

• Inductive reasoning is the basis for science

• Inductive reasoning works - it is pragmatic

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III. Induction

3 examples:

• Small pox

• Politics

• Education

• Public health

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?

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Assignment

• Read and annotate the two short articles

• Re-write each article as a standard form argument with 2-4 premises and 1 conclusion

• Review the paper assignment. How might these articles be relevant to the paper assignment?

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Page 9: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

III. Induction

3 examples:

• Small pox

• Politics

• Education

• Public health

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?

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Page 10: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

C. Assessing Inductive arguments

Three general principles

• Does the argument start with justified premises?

• Does the argument include all relevant information?

• Is the argument valid? (does acceptance of the premises justify acceptance of the conclusion?)

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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 is the results from natural rather than man-made factors

Example 1

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Page 12: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

1. Global warming causes unusual weather events

2. This week’s deep freeze in the central and eastern parts of the country was an unusual weather event

Therefore: This week’s deep freeze was caused by global warming

Example 2

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Page 13: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

1. Global warming leads to temperature increases

2. This week’s deep freeze in the central and eastern parts of the country saw temperatures plummet

Therefore: Global warming is not true

Example 3

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Page 14: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

C. Assessing Inductive arguments

Assessing enumerative arguments (3 questions)

• On how many cases is the conclusion based?

• Are the cases examined representative?

• Could other conclusions be drawn?

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C. Assessing Inductive 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?

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C. Assessing Inductive arguments

Assessing Causal arguments

• Is the causal claim a good explanation for the observed correlation? (Is the correlation serial rather than causal)

• Is there any other reasonable explanation for the correlation?

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Page 17: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

Informal fallacies

This section of the presentation is drawn from materials on the website of the Texas State University Department of Philosophy website.(Accessed on 1.16.14 at http://www.txstate.edu/philosophy/resources/fallacy-definitions.html)

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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.

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Page 19: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

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.

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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.

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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.

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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.

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Page 23: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

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.

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Page 24: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

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.

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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.

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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.

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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.

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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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IV. DeductionA. Definitions

• Deduction - Truth preserving!

• Truth - What is the case

• Validity - Whether a conclusion follows from its premises

• Syllogism - A deductive argument with exactly two premises and a conclusion which uses categorical propositions to express relationships between three terms

Critical Note: Truth and validity are independent! True premises may lead to an invalid conclusion and false premises may lead to a valid conclusion!

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Anatomy of a syllogism

All violists are clever

All virtuosos are a violists

Therefore: virtuosos are clever

The predicate nominative of the conclusion is the major

term

The subject of the conclusion is the minor term

The term which doesn’t appear in the conclusion is the middle term

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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 violists are clever

All virtuosos are a violists

Therefore: virtuosos are clever

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Page 32: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

4 types of categorical propositions

Universal affirmative - A propositions

All violinists are talentedUniversal negative - E propositions

No violinists are meanParticular affirmative - I propositions

Some violinists are left-handedParticular negative - O propositions

Some violinists are not Democrats

AffIrmo

nEgO

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Page 33: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

Using the definitions just provided, write three valid arguments that meet the

following conditions:

• Two true premises and a true conclusion

• Two true premises and a false conclusion

• One true and one false premise and a true conclusion

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Page 34: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

B. Assessing the validity of categorical syllogisms

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Page 35: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

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, the top right circle as the major term and the bottom circle as the middle term.

1

7

6

5

4

32

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 goFinally – Inspect the diagram to see if the diagram of the premises is consistent with the conclusion.

Assessing syllogisms diagrams using Venn diagrams

Virtuosos Clever

Violists

All violists are clever

All virtuosos are violists

Therefore: All virtuosos are clever

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Page 36: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

Assessing the validity of syllogisms using Venn diagrams

All violists are clever

All virtuosos are violists

Therefore: All virtuosos are clever Violists

Virtuosos Clever

No

No

No No

1

7

6

5

4

3

2

Valid

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Page 37: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

Assessing the validity of syllogisms using Venn diagrams

All crunchy things are apples

Some bland things are crunchy things

Therefore: All apples are bland things Crunchy

BlandApples

NoSome

No

1

7

6

5

4

3

2

Invalid

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Page 38: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

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

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Page 39: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

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

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Page 41: Unit 4 - dhaydock.org 4...Other means of assessing categorical syllogisms Mood and figure The Mood of a categorical syllogism is the series of three letters representing each proposition

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

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Other means of assessing categorical syllogisms

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)

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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.

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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!

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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

1

7

6

5

4

3

2

InvalidNo

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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.

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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

1

7

6

5

4

3

2

No

Fallacy of

Affirmative Conclusion/Negativ

ePremise

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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.

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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

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Two other types of syllogism

• Disjunctive syllogisms

• Hypothetical syllogisms

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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

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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).

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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 inclusive2. Valid for both

3. Not valid for inclusive, valid for exclusive

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

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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

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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

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Mixed hypothetical syllogismsIn 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 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:

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Valid mixed hypothetical syllogismsModus 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

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Are the following valid or invalid? Why?

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

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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

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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 ===

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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!

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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!”

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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.

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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 fallacies 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.Tuesday, March 4, 14

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1

7

6

5

4

32

1

7

6

5

4

32

Arguments

1.

2.

Therefore:

Arguments

1.

2.

Therefore:

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