Deductive Logic

Inductive Logic rests on likelihood or the probability of an event, not certainty.

ex. Gravity. How do you know when you drop this object that it's going to go down and not up ? "Because of gravity." How do you know gravity would always obtain? "Because it always has." That's inductive logic.

Deductive Logic aim at certainty. The conclusion is true not just beyond a reasonable doubt, but beyond a possible doubt.

ex. What is your name? "Ivy" But are you sure? "Of course I am sure. That's what I had been going by all my life." But what if your parents hid all your identification documents and they were playing a practical joke on you and your name is actually Bert?

Argument: a pair of things, the premises and the conclusion

• Premises: a set of sentences
• Conclusion: a sentence
• All arguments have conclusions but not all arguments have premises

ex. "I don't think I'll be going out this weekend if there's a chance of snow. And this morning the weather forecast called for snow. So it looks like I'll be staying in this weekend."

Formal Restatement:
P1 If there is a chance of snow this weekend, then I will not go out.
P2 There is a chance of snow this weekend.
C I will not go out.

Identifing words of the conclusion of an argument:

• Thus
• So
• Therefore
• Hence
• Ergo, if you're a pompous ass

Validity: an argument is valid if the truth of its premises guarantees the truth of its conclusion

• If it is possible for the conclusion of an argument to be false when its premises are all true, then the argument is invalid
• If it is not possible for the premises of an argument to be true together, then it is valid
• Validity and Soundness only obtains to Deductive Logic

Valid:

P1 George will say hello to every person who will come into the store today.
P2 Bill is a person will come into the store today.
C George will say hello to Bill.

P1 Every good ballerina is an elegant dancer.

P2 Arnold Schwarzenegger is a good ballerina.

C Arnold Schwarzenegger is an elegant dancer.

Invalid:

P1 Every U.S. President lives in the White House.

P2 Michelle Obama lives in the White House.

C Michelle Obama is a U.S. President.

P1 Every U.S. President lives in the White House.

P2 Trump lives in the White House.

C Trump is a U.S. President.

P1 All men are mortal.
P2 Socrates is mortal.
C Socrates is a man.

P1 + P2 does not necessary --> C

Entailment: when an argument is valid we say that its premises entail its conclusions
Soundness: valid argument with true premises

• No sound arguments have a false conclusion
• Soundness is the goal of an argument and in determining whether it is persuasive or not. It is more practical in the real world than validity.

Unsound:

P1 All good cars are reliable
P2 All Yugos are reliable
C All good cars are Yugos

Yugo could be a battleship or type of horse cart.

P1 All good cars are reliable
P2 All Yugos are reliable
C All good cars are Yugos

This argument is valid, but P2 is (presumably) false.

P1 Abortion involves the killing of an innocent person
P2 It is never morally permissible to kill an innocent person
C  Abortion is never morally permissible

Uncertain: To determine the soundness of this argument, we'd need to hear further arguments in favor of the individual premises.  That's why arguments end up being so important in philosophy!