Philosophy Basics

Table of Contents

  1. Critical Thinking & Formal Logic
  2. Arguments
  3. Which Arguments are Good?
  4. Two Common Good Forms
  5. Types of Argument
  6. Why Propositions and not Sentences?
  7. Relevant Links

1. Critical Thinking & Formal Logic

Critical thinking involves recognizing and forming good arguments. When we think critically, we don’t always question everything (at least not in the strong sense of that phrase). Rather, we are actively concerned with the reasons and justification one can have for making a certain claim. When someone, for example, claims that God exists, we can critically evaluate this claim. We ask, “What reasons do we have to believe that God exists?” instead of just accepting that claim because it would be hard work to figure out whether it’s true. So thinking critically requires that we use good reasoning and recognize when others aren’t reasoning well.

But how do we know when we’re reasoning well? Well, there’s actually a field of study called “logic” dedicated to finding a quite rigorous answer to that question. Logic is the formalization of arguments, which seeks to determine which arguments have a good sort of form. As it turns out, there are varies patterns or forms of reasoning or argument that are known to be good in form. This all requires studying the logical relations between truths and falsehoods.

2. Arguments

But what do we mean by “arguments” in this context? The sense of “argument” that we are primarily concerned with in philosophy is not merely disputes among people. Rather, philosophy is concerned with arguments in the following sense: sets of propositions (claims/statements) which contain premises that are offered to support the truth of a conclusion. A premise is a proposition one offers in support of a conclusion. That is, one offers a premise as evidence for the truth of the conclusion, as justification for or a reason to believe the conclusion. A conclusion is a proposition the truth of which one claims to be supported by the premises.

Example of an Argument

  1. All humans are mortal. [statement, premise]
  2. G.W. Bush is a human. [statement, premise]
  3. Therefore, G.W. Bush is mortal. [statement, conclusion]

Example of a Non-Argument

  1. Get us some milk, please. [imperative]
  2. Is anyone home? [question]
  3. Therefore, G.W. Bush is mortal. [statement, conclusion]

More Examples of Non-Arguments

  • “Why are you so angry?” is not an argument.
  • A couple’s fighting with one another about who should have put the dishes away is not an argument (in the sense we’re after).
  • A debate between two people about whether God exists is not an argument (in the sense we’re after)—it’s a debate—though it does involve each side putting forth arguments for their respective positions.

3. Which Arguments are Good?

Good arguments are ones that offer good support for the conclusion. There are two key features of a good argument:

  1. Good Form: the premises, if true, render the conclusion true or probable.
  2. Good Premises: every premise of the argument is true (or at least plausible or likely to be true).

Philosophers call arguments that have these two features logically sound (“sound” for short).

Good form has to do with the logical form of the argument, not whether the premises are in fact true or false. So the two features of a good argument can come apart. And if an argument fails to have either one of these features, it isn’t a good argument; it doesn’t give us any reason to believe the conclusion. Consider some examples:

Example of a Bad Argument (good form but bad premises)

  1. All women are Republican. (false)
  2. Hilary Clinton is a woman. (true)
  3. Therefore, Hilary Clinton is a Republican. (false)

Example of a Bad Argument (bad form but good premises)

  1. Some men are Democrats. (true)
  2. G.W. Bush is a man. (true)
  3. Therefore, G.W. Bush is a Republican. (true)

Example of a Good Argument (good form + good premises)

  1. If G.W. Bush won the 2004 presidential election, then a republican is currently president of U.S. (true)
  2. G.W. Bush won the 2004 presidential election. (true)
  3. Therefore, a republican is currently president. (true)

4. Two Common Good Forms

Modus Ponens (MP):

  1. If P, then Q.
  2. P.
  3. So, Q.

Example:

  1. If [Omar went to Disneyland], then [he will have brought a souvenir back].
  2. [Omar went to Disneyland].
  3. So, [Omar brought back a souvenir].

Modus Tollens(MT):

  1. If P, then Q.
  2. Not-Q.
  3. So, not-P.

Example:

  1. If [Omar went to Disneyland], then [he will have brought a souvenir back].
  2. [Omar didn’t bring back a souvenir].
  3. So, [Omar didn’t go to the Disneyland].

5. Types of Argument

A deductive argument is an argument the premises of which are intended to provide the strongest possible support for the conclusion (to prove with absolute certainty). (Note: When philosophers talk about good form for deductive arguments, they usually call it “deductive validity.”)

Example:

  1. All humans are mortal.[premise]
  2. Obama is a human.[premise]
  3. So, Obama is mortal.[conclusion]

A non-deductive argument is an argument the premises of which are meant to provide support for the conclusion, but this support is not supposed to establish the conclusion beyond doubt. (Note: Some of the most common forms of non-deductive argument are inductive and abductive arguments.)

Example:

  1. 90% of all cable users pay for cable.[premise]
  2. Omar is a cable user.[premise]
  3. So, Omar pays for cable.[conclusion]

6. Why Propositions and not Sentences?

We are concerned with propositions rather than sentences, because propositions are (roughly) the meanings of (declarative) sentences. For example, the English sentence “Snow is white” expresses the same thing that the French sentence “La neige est blanche” does, namely the proposition that snow is white. In logic, critical thinking, and philosophy more generally, we are concerned with truths, faslehoods, and the logical relations between them. And we cannot look to sentences for this, since sentences are merely the symbols that we use to express truths and falsehoods (that is, propositions).

For example, we are not concerned with the phrase “God exists,” but rather with whether God exists. The proposition that God exists can be expressed in many different languages. And we are not concerned with the languages, but rather what the languages are used to express. That is, we are concerned with what the English sentence “God exists” and the French sentence “Dieu existe” have in common, namely the proposition that God exists. (Notice that we use quotation marks to talk about or mention the bits of language, such as words or sentences, whereas we leave the quotation marks out to simply use the words to express the meanings they have.)

7. Relevant Links