Logic Homework Module 3 Part I Re

Logic Homework Module 3 45 Ptsname Part I Re

Logic Homework Module 3 (45 pts) Name __________________ PART I: Reconstruct the following syllogistic forms, draw the appropriate Venn diagram and use the five rules for syllogisms to determine if they are valid from Boolean standpoint, conditionally valid for Aristotle or invalid. If invalid, name the fallacy. (4) Example: IAO-1 Some M are P All S are M Therefore: Some S are not P Invalid, drawing a neg. conclusion from affirm premises/undistributed middle/illicit major Venn: Shade in 5/6, x on line between 3/. IAI-. EIO-. IAO-. EAE-. EAO-.

PART II: a. Translate the following into standard form categorical syllogisms(5). (Example: Putting it into standard form means making sure that it is All P are M Some M are S Therefore Some S are P So you know that it is in the correct order...the major term is in the major premise. etc Also remember that S, M and P are just placeholders for the Major term(P), Minor Term(S) and Middle term(M). In actual sentence, use any convenient uppercase letter.) b. Give the Mood and Figure (example: AII-4) c. Give the Venn diagram: Shade 6/7, x on line 2/3 d. Determine if the argument is valid or invalid (by Boolean or Aristotle) (example: Invalid both) e. Determine the fallacy the argument commits, if no fallacy, write no fallacy. (example: Undistributed middle) 6. All currently living dinosaurs are giant reptiles. All giant reptiles are ectothermic animals. Therefore, some ectothermic animals are currently living dinosaurs. 7. All survivalists are people who enjoy simulated war games. No people who enjoy simulated war games are soldiers who have tasted the agony of real war. Therefore, all soldiers who have tasted the agony of real war are survivalists. 8. No corporation that defrauds the government are organizations the government should deal with. Some defense contractors are not organizations the government should deal with. Therefore, some defense contractors are not corporations that defraud the government. 9. No concertos are symphonies. All symphonies are string quartets. Therefore, no string quartets are concertos. 10. Some people who are Republicans are people who voted for John McCain. No people who voted for Barack Obama are people who are Republicans. Therefore, some people who voted for Barack Obama are not people who voted for John McCain.

Paper For Above instruction

Introduction

The purpose of this paper is to analyze a series of categorical syllogisms from a logical standpoint, reconstruct their structures, evaluate their validity using Venn diagrams and Boolean logic, and identify any fallacies they may contain. The analysis divides into two parts: Part I focuses on reconstructing and evaluating syllogistic forms, while Part II involves translating natural language statements into standard form categorical syllogisms, determining their mood and figure, diagramming, and assessing their validity and fallacies.

Part I: Reconstruction and Evaluation of Syllogistic Forms

The first task involves providing accurate reconstructions of given syllogistic forms, drawing their Venn diagrams, and applying the five rules for syllogisms—namely, (1) only three terms, (2) the middle term must be distributed at least once, (3) the conclusion must not introduce a new term, (4) the conclusion must follow the form and mood of the premises, and (5) no fallacies like undistributed middle, illicit major/minor, or negative conclusion from affirmative premises should be present.

Let us consider some examples:

- Example: IAO-1 (Some M are P; All S are M; Therefore: Some S are not P). From a Boolean standpoint, this argument invalid because the conclusion is negative while premises are affirmative, violating the rule against drawing a negative conclusion solely from affirmative premises. The fallacy is the illicit negative conclusion, and the Venn diagram would show shading of regions corresponding to affirmative relations and an ‘x’ indicating the particular negative conclusion.

Moving to the other forms:

- EIO-: This form involves establishing whether the premises and conclusion uphold validity rules.

- IAI-: The mixture of affirmative and particular premises must be checked for validity, especially for undistributed middle.

- EAE- and EAO-1: These are classic forms that often violate the rules if the middle term isn't properly distributed or if the conclusion doesn't logically follow, respectively.

Applying the five rules systematically enables the classification of each as valid, conditionally valid, or invalid, and allows identification of specific fallacies like undistributed middle, illicit major or minor, or negative conclusion from affirmative premises.

Part II: Translation, Diagramming, and Evaluation of Arguments

In Part II, each natural language argument must be translated into standard form categorical syllogisms. This entails identifying the major term (P), the minor term (S), and the middle term (M), structuring the premises accordingly, and ensuring the placement aligns with the logical order—major premise first, then minor. For example:

- "All currently living dinosaurs are giant reptiles" translates to "All D are G."

- "All giant reptiles are ectothermic animals" translates to "All G are E."

- The conclusion "Therefore, some ectothermic animals are currently living dinosaurs" becomes "Some E are D."

Next, the mood and figure are identified based on the quality (A, E, I, O) of the categorical propositions and the position of the middle term. For the above example, the mood is AAA and figure 1, thus "AAA-1."

The Venn diagram then visualizes the relations: shading areas to indicate empty intersections and placing 'x' where particular affirmative relations are asserted. The complexity thresholds suggest shading 6/7 regions and placing 'x' on lines 2 or 3, depending on the specific form.

Assessing validity involves applying either Boolean algebra or Aristotle’s syllogistic rules:

- Boolean analysis involves checking the truth-values of the premises regarding set relations.

- Aristotle’s rules focus on the distribution of middle terms and fallacy prevention.

Using these criteria:

- For Example 6, the conclusion does follow from the premises, and the figures align, so the argument is valid from both perspectives.

- Example 7 involves a negative premise and a universal affirmative conclusion, thus invalid.

- Example 8, where some defense contractors are not organizations, violates the rule of distribution, rendering it invalid.

- Example 9's conclusion conflicts with the premises, making it invalid.

- Example 10 involves particular affirmative premises leading to a particular negative conclusion, which requires validation via diagramming and Boolean evaluation.

The identified fallacies include illicit process, undistributed middle, affirming the consequent, or no fallacy.

Analysis of Specific Arguments

1. Dinosaurs and Reptiles: Valid by syllogistic standards. Both premises are universal affirmatives with a proper middle term (giant reptiles), leading to a valid conclusion that some ectothermic animals are dinosaurs.

2. Survivalists and Soldiers: The structure involves a universal affirmative, but the negative second premise invalidates the deductive power, leading to invalidity owing to the fallacy of illicit process.

3. Corporations and Defense Contractors: The argument’s structure has an invalid conclusion due to improper distribution of terms, thus fallacious, likely committing the fallacy of illicit major.

4. Concertos and String Quartets: This is a valid syllogism with a universal affirmative structure, fitting the rule of distribution and proper categorical form, invalidity mainly from conclusion mismatch.

5. Voters for McCain and Obama: The particular affirmative premise and negative premise suggest potential invalidity, especially considering the fallacy of affirming the consequent if analyzed via Boolean algebra.

Conclusion

This comprehensive analysis demonstrates that logical validity hinges on strict adherence to syllogistic rules, proper structure, and accurate translation from natural language. Venn diagrams visually support the logical relations, while Boolean algebra provides a rigorous truth-functional perspective. Proper identification of fallacies strengthens the understanding of logical errors. Many of the provided arguments are invalid due to fallacies like illicit middle, affirming the consequent, or improper charting of relations, underscoring the importance of formal methods in logic reasoning.

References

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