The Norton Introduction to Philosophy

Chapter 0: Getting Started

A Brief Guide to Logic and Argumentation

Philosophers don’t just answer questions, they provide arguments for their answers and reasoning. This chapter teaches about the tools that philosophers have developed to answer questions like “what is an argument” or “what is a good argument”.

What is an Argument? It’s a sequence of statements. The last claim is the conclusion, which the argument seeks to establish or support. Arguments usually include one or more premises. What is a Premise? It’s a statement asserted without proof, but may be supported by arguments from elsewhere. It’s an assumption that something is true. When reading, it’s important to understand what the premises are – what the author takes for granted.

Argument A:

• 1: The Bible says that God exists.
• 2: Whatever the Bible says is true.
• 3: Therefore, God exists.

1 and 2 are premises, 3 is conclusion. Premises can be “expanded” into other arguments.

Argument B:

• 4: The Bible has predicted many historical events that have come to pass.
• 5: Therefore, whatever the Bible says is true.

Arguments are valid if and only if it is absolutely impossible for its premises true and its conclusion false. Argument A is valid, assuming the premises are true. Argument B is invalid since it’s easy to imagine a circumstance where the bible is fallible on other matters besides historical events.

It is always possible to turn an invalid argument, or an argument whose validity is uncertain, into a valid argument by adding premises.

Just because an argument is valid doesn’t make it a sound argument.

Argument D:

• 1: All philosophers are criminals.
• 2: All criminals are short.
• 3: Therefore, all philosophers are short

Argument D is valid, but not sound and fails to establish its conclusion.

An argument is formally valid when it is an instance of a scheme where all of the scheme’s instances are valid (e.g. X == X).

Logical symbols and vocab:

• →: P→Q is “if P then Q”
• ~ or ¬: “It is not the case that”
• ∧: AND
• ∨: OR
• ⊻: XOR
• ↔: XNOR
• ↑: NAND
• ↓: NOR
• Modus Ponens: Latin for “mode that affirms by affirming” and is a rule of inference. Summarized as “P implies Q and P is asserted to be true, therefore Q must be true.” (
• Modus Tollens: Latin for “mode that denies by denying”. Summarized as “P implies Q, so the negation of Q implies the negation of P.”
• Disjunctive Syllogism (or MTP): Latin for “mode that affirms by denying.” If P is true OR Q is true and P is false, then Q is true. “I will be there or I will be here. If I am not here, I will be there.”
• Hypothetical syllogism: If P implies Q and Q implies R, then P implies R.
  • A Syllogism is a logical argument using deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.
• Contraposition: ~P implies ~Q. Thinking visually, if P is encompassed by Q, then anything not within Q cannot be within P.
• Sorites Paradox: 100,000 grains of sand is a heap. If 100,000 is a heap than 99,999 is a heap. If 99,999 is a heap then 99,998 is a heap. …so 2 grains of sand is a heap.

What makes an argument good?

• If it’s not circular. The premises must be credible independent of the conclusion.
• It must not “beg the question.” It must not attempt to pass (C → P) → C as the valid claim P → C. It cannot presuppose what it supposes to be true.

Vocab:

• Inductive Arguments: Take observations that exhibit a pattern as premises, then conclude the pattern holds a general rule. “In the past, events of type A have always been followed by events of type B. Therefore, in the future, events of type A will be followed by events of type B.”
• Abductive Argument: Or “inference to the best explanation.” Reasons backwards from a collection of settled facts to the hypothesis that would best explain them. “Certain facts are observed. The best explanation for these facts is H. H is a good explanation. Therefore, H is (probably) true.”

I’m skimming “Some Guidelines for Writing Philosophy Papers” and not taking notes since I’m not planning on writing any philosophy papers.

Things I’m Liking

• Fortnite Creative: Extremely popular games that feature “creative modes” typically are breeding grounds for new types of games. The beginnings of a first-person battle royale started its popularity with Minecraft, MOBAs came from a Warcraft 3 mod, and Counter-Strike came from Half-Life. So although I don’t play Fortnite, it’s a lot of fun to check out what’s being made in the space and guess what’s coming next.
• Keeping the Pirates at Bay: A technical blog post from 2001 about the copy/crack protection of Spyro: Year of the Dragon. It’s more interesting than it sounds.