Chapter 3: Basic Logical Concept §

(F) Day of the week: Tuesday Class: IS209 Created Time: April 7, 2020 4:39 PM Database: Class Notes Database Date: April 7, 2020 4:39 PM Days Till Date: Passed Last Edited Time: June 9, 2021 10:42 AM Type: Lecture

💡 How to figure out if the premise of a conclusion is true or not?

I. Deduction and Induction §

Deduction Arguments: try to prove their conclusions with rigorous, inescapable logic.

The conclusion must flow through all the premises to come to one objective conclusion

All humans are mortal. Socrates is human.Therefore,Socrates is mortal.

Inductive arguments: try to show that their conclusions are plausible or likely given the premise(s).

Ex: Polls show that 75 percent of Republicans favor a school prayer amendment. Joe is a Republican. Therefore, Joe likely favors a school prayer amendment.

Differences between the two §

Misconception:

Deductive Arguments moves from general premise to particular conclusion

Inductive Arguments move from particular premise to general conclusion

Difference in the Type of Premise

II. Telling the difference between Deductive Arguments and Inductive Arguments §

1. The Indicator Word Test §

Deductive Indicator Words §

Certainly

Absolutely

Conclusively

Definitely…

Inductive Indicator Words §

Probably

Likely

It is plausible to suppose that

It is a good bet that…

💡 Some arguments don’t contain Indicator Words to determine between the two using this test

Some arguments use indicator not corresponding to their conclusion

2. Strict Necessity Test §

• If the premise will strictly lead to only one outcome or conclusion and is impossible to be anything else, it should be treated as a Deductive Argument.
• If the conclusion shows any kind of physical or theoretical way it could be false, it should be treated as an Inductive Argument

Exceptions §

Arguments with conclusions that don’t follow from it’s premises counts as a deductive argument if:

1. The language and context of the argument is intended to be a deductive arguments (but the logic is not consistent)
2. The argument uses deductive pattern of reasoning without indication for inductive (chain arguments)

3. Common pattern Test §

Modus ponens: a conditional statement, a true statement, and a concluding statement from the 2 previous statements. Should always be treated as a deductive argument.

If A then B.

A. Therefore, B.

4. Principle of Charity §

💡 Principle of Charity: Unclear Passages should be interpreted as the stronger argument rather than the weaker. Bad arguments should be interpreted as a non-argument

If the 3 previous test still doesn’t conclusively determine what argument it is, use the Principle of Charity.

If it appears to be a bad Deductive Argument, interpret it as a good Inductive Argument instead

The Principle of Charity is only used to interpret an argument, it cannot be used to fix an argument

III. Distinguishing Inductive or Deductive §

Deductive

1. If the conclusion follow directly from the premise

Inductive

1. If the conclusion doesn’t follow directly from the premise unless a). it’s intended to be a deductive argument, or b). it uses a pattern of reasoning from a deductive argument

2. The pattern of reasoning that is characteristically one could be pointing to inductive or deductive.

3. The argument could contain indicator words that point to either deductive or inductive. (loosely used)

4. If there is doubt which one it is, we could interpret it as the best option in favor of the arguer.

IV. 5 Common Patterns of Deductive Reasoning §

1. Hypothetical Syllogism §

Syllogism is a three-line argument with 2 premises and 1 conclusion

Hypothetical Syllogism is an argument containing at least one hypothetical/conditional statement as the premise.

Consist of:

• Chain argument: 3 conditional statements linking together

  If A then B. If B then C. Therefore, if A then C.

• Modus tollens: denying the consequent to prove the condition is false

  a conditional + denying the consequent+ conclusion from denial

  If A then B. Not B. Therefore, not A.

• Denying the antecedent: saying condition is false and consequent is false in result

  Antecedent: what comes first (condition)

  If A then B. Not A. Therefore, not B.

  (not logically conclusive)

• Affirming the consequent: Proving consequent and saying condition is true as a result

  Consequent: what comes as a result

  If A then B. B. Therefore, A.

  (not logically conclusive)

2. Categorical Syllogism §

Using all, some or no to categorize and to make the conclusion

All oaks are trees. All trees are plants. So, all oaks are plants.

3. Argument by Elimination §

Eliminate other possibilities using logic or evidence until only one outcome remains

Either Joe walked to the library or he drove. But Joe didn’t drive to the library. Therefore, Joe walked to the library.

4. Argument Based on Mathematics §

Using math as premise for conclusion

Eight is greater than four. Four is greater than two. Therefore, eight is greater than two.

Mathematics can be used in inductive because of human errors

5. Argument from Definition §

Are premises that rely on general knowledge of accurately defined definition that helps prove the conclusion

Bertha is an aunt. It follows that she is a woman.

V. Common Patterns of Inductive Reasoning §

1. Inductive Generalization §

is generalization of a group based on the evidence of a sample from the group

Most college students work at least part-time.

All dinosaur bones so far discovered have been more than sixty-five million years old. Therefore, probably all dinosaur bones are more than sixty-five million years old.

Generalization states “Probably” or “Most likely” in their meaning even if it use Deductive keywords

All wild grizzly bears in the United States live west of the Mississippi River.

Men are so unromantic!

2. Predictive Argument §

is arguing whether something will or will not happen using evidence or patterns from the past. However, nothing is certain in the future and can change

It has rained in Vancouver every February since weather records have been kept. Therefore, it will probably rain in Vancouver next February.

Most U.S. presidents have been tall. Therefore, probably the next U.S. president will be tall.

Predictive Arguments can be deductive when the conclusion must be true if the premise is true

• Modus Ponens

3. Argument from Authority §

are claims that is supported by a presumed authority to be true, which might not be the expert in the field and may be unreliable

More Americans die of skin cancer each year than die in car accidents. How do I know? My doctor told me.

👮🏼 Authority: a reliable source of information from specific specialized fields

Authority Arguments could be deductive if it follows directly from the premise to be true.

4. Causal Argument §

to assume the cause by knowing the conclusion. We can’t be 100% sure that it’s definitely so.

I can’t log on. The network must be down.

Causal Arguments can be deductive.

5. Statistical Argument §

relies on a percentage of a group to argue something will probably happen.

Eighty-three percent of St. Stephen’s students are Episcopalian. Beatrice is a St. Stephen’s student. So, Beatrice is probably Episcopalian.

Statistical Argument can be deductive.

6. Argument from Analogy §

An analogy is a comparison of two or more things that are claimed to be alike in some relevant respect and concluding from the comparison

These things are similar in such-and-such ways. Therefore, they’re probably similar in some further way.

💡 Conclusion: Inductive generalizations, by definition, are always inductive. Predictive arguments, arguments from authority, causal arguments, statistical arguments, and arguments from analogy are generally, but not always, inductive.

VI. Deductive Argument Validity §

is a deductive argument that follows necessarily from its premises

Valid Argument: it must be logically consistent, follow necessarily from it’s premises

• premise and conclusion doesn’t have to both be true or false, can be any combination

  Exception: No valid deductive argument can have all true premises and a false conclusion

---

Valid Deductive Arguments must be either sound or unsound 100%

• Sound Arguments: all premises are true
  • Conclusion follow necessarily from its premises
  • All premises are factually true
• Unsound Argument:
  • Conclusion does not follow necessarily from the premise
  • One or more premises are factually false
  could be an Inductive argument if premises is probable instead of following necessarily

Invalid Argument: logically inconsistent, conclusion doesn’t necessarily follow from the premises

Always unsound

VII. Inductive Strength §

• Weak Inductive Argument: the conclusion does not follow probably from the premises

  the premises, even if they are assumed to be true, do not make the conclusion probable.

  • can have any combination of truth or falsity in the premises and conclusion.

  Always Uncogent

• Strong Inductive Argument: the conclusion follows probably from the premises

  • The premises provide probable, but not logically conclusive, grounds for the truth of the conclusion.

  • It doesn’t have to be factually true

  • can have any combination of truth or falsity in the premises and conclusion.

    Exception: no strong inductive argument can have true premises and a probably false conclusion.

  Cogent Argument: An Inductive Argument is stronger

  • The more likely for the premise to be true, the stronger it is
  • if the premises are true

  Uncogent Argument: the arguments are weak or has one more more false premise

  Second Conditional: if the premises were true

  • if the conclusion also true cogent
  • if the conclusion is false uncogent

💡 Fitting an argument into either Deductive and Inductive Common Patterns can help determine if the argument is logically conclusive or inconclusive therefore figuring out the validity