Logic: The Science of Arguments

1. Logic: The Science of Arguments Critical Thinking: critiquing one’s own thinking

2. Two Main Types of Arguments • The two types are: Deductive & Inductive. • Deductive reasoning claims that the connection between the truth of the premises and the truth of the conclusion is such that whenever all of the premises are true, the conclusion must necessarily already be true. • Inductive reasoning only has a probabilistic connection between the truth of the premises and the truth of the conclusion. Hence, if the premises are all true, then probably the conclusion is true.

3. Deductive Reasoning and Validity • Definition of a valid argument: An argument where whenever the premises are all true, then necessarily the conclusion of the argument is true and can never be false. In other words: • IF all of the premises were true, then necessarily the conclusion is true and cannot be false.

4. Examples of Valid Logical Forms Modus Ponens (mode of affirming) (1) If P, then Q. (2) P. _____________ Therefore, (3) Q. Example of Modus Ponens (1) If it rains, then the streets are wet. (2) It rains. ________ Therefore, (3) The streets are wet.

5. Properties of Valid Arguments Arguments that satisfy the definition of validity do so by virtue of the arguments logical form and not its semantic content. Form concerns structural relationships and not meaning or what is said or meant. A valid logical form can have a substitution instance (an example) with all false premises and a false conclusion. • All wines are whiskeys. • All whiskeys are soft drinks. • Therefore, All wines are soft drinks.

6. Properties of Invalid Arguments Just because all of the premises are true does not mean that the truth of the premises supplies one with a reason to believe that the conclusion is necessarily or probably true. Invalid arguments CAN have all true premises with a true conclusion and still be invalid. • All triangles have three sides. (2) This is a triangle. _____________________ Therefore, (3) Obama is President of the US.

7. How to argue for your claims • Proving that your premises are true is insufficient to establish the correctness of your argument since invalid arguments can have all true premises. • Proving that your argument has a valid logical form is also insufficient. Just because one uses a valid argument form does not make the premises have to be true, so therefore the conclusion need not be true either. Since valid arguments can have false premises this does not prove the conclusion in this case must be true.

8. Proving your argument is Sound • A Sound argument is a deductive argument that actually has all true premises and is valid. One must prove that one has all true premises and that one has either a valid argument or an inductively strong one (making the inductive conclusion highly probably true). • A Cogent argument is an inductively strong argument with all true premises. An inductively strong argument is one where were all of the premises to be true, then the conclusion would be highly probably true.

9. Proving your argument is Relevant with a Warrant • One must prove that one has all all true premises and that one has either a valid argument or an inductively strong one (making the inductive conclusion highly probably true). • A warrant justifies ones reasoning as relevant. If a general principle and its consequences are true, then specific instances of it must also be true. • Turabian discusses claims, reasons, and warrants. • A claim is a declarative statement that holds that a sentence is either true or false. A reason is evidence or reasoning which supports that a claim is true. A warrantis a justification given for believing the reasoning is relevant to the claim.

10. Acknowleding and Responding to the Reader’s Point of View • Because you are writing an argumentative paper you are trying to convince the reader that what you are claiming should be accepted as true. • To convince the reader one must anticipate any problems that the reader may have with your claims and the reasoning used to support them. • This requires asking and answering questions and objections and problems that are hostile to your thesis. • Turabian (p. 53) mentions two types of objections: Internal and external.

11. Internal and External Objections • Internal Objections deal with the reasons and evidence offered to support your claims. • Is your reasoning consistent? Is it too weak to support your claim? Are you reasons relevant to the truth of your claim? What is the status of your evidence: inaccurate, insufficient, not representative, etc. • External Objections consist of alternative viewpoints regarding fundamental issues. • Turabian suggests asking what could cast doubt on my claims, reasoning and evidence? And then trying to address these issues so an opposing reader’s viewpoint is acknowledged and considered in relation to one’s own thesis.