Notes of Classical Logic | What is An Argument?


Critical Thinking: the careful application of reason in the determination of whether a claim is true.

Premise (on Wiki): a premise is an assumption that something is true. (note that we can assume sth. to be false too)

$$Premise \subset Assumption$$

Assumption: presupposition, axioms, taking for granted.

Difference between hypothesis and assumption:

  • A hypothesis is a theory that seeks to explain a phenomenon or a set of phenomena. Scientists or researchers make up hypothesis to see if they hold true. They conduct a number of experiments and test this hypothesis, and if the hypothesis indeed proves correct, it is deemed to have become a theory.
  • A hypothesis is an assumption that has been made working. It is a theory in waiting as it can be called theory only after verification.
  • An assumption is any statement that is believed to be true. Thinking about the feelings of others is merely assumption as there is no way to tell what a person is thinking or feeling. (It does not have the purpose as a hypothesis does)
  • Anything taken for granted is an assumption, and a hypothesis is at best a working assumption. (能不能理解为, hypothesis的可信度更高)


An argument is:

  1. a set of claims, or statements, or propositions
    • a claim is whether true or false, not both
  2. one of the claims is called the conclusion, the remaining are called the premises
  3. the premises are intended as offering reasons to believe or accept the conclusion

A simple argument: (in standard form)

Why a claim should either be true or false is important?

  1. Not all sentences can function as claims for argumentative purposes.
    • Questions don’t count as claims
    • Commands are not claims
    • Premises can be beliefs, support, other conclusions, data, ideas, studies, statistics, opinions
  2. In saying that a sentence can function is a claim, we’re saying that all parties have a shared understanding of the meaning of the sentence. ❓

Three hidden pieces to arguments:

  1. Implied Conclusions
  2. Unstated Premises
  3. Missing Connections

An unstated premise is going to provide some kind of link between the stated premises and the conclusion, and there could be more than one unstated premise.


A CEO of a major company noted a serious decline in worker productivity during the previous five years. According to a report done by an outside consultant, productivity dropped by 35% by the end of that period. The CEO has therefore initiated a plan to boost productivity by giving employees shares of the company as part of their pay package.

Premise: “A CEO of a major company noted a serious decline in worker productivity during the previous five years.”

  • Premises are the facts or evidence that support or lead to the conclusion. Unlike assumptions, they are explicit in the text.

Assumption: “Owning something or part of something obliges you work harder to make it succeed.”

  • Assumptions are the facts that support the conclusion, like the premises does, but unlike the conclusion and premises they are not stated in the text: they are implicit.

Supporting Information: “According to a report done by an outside consultant, productivity dropped by 35% by the end of that period.”

  • Supporting information does not support the conclusion or main idea, rather, it supports information that is already in the text. Like a premise, this is stated and explicit information embedded in the text, but unlike a premise, it does not support the conclusion.

This sentence supports the first sentence, the premise that notes that productivity has dropped.


Identifying premises and conclusions is a very important critical thinking skill in general, also required for LSAT (a law exam).

For example: (「because」is an 「indicator word」)

Why is it easy to know?

Because we read for the argument: what claims are we being asked to believe or accept, what other claims are being offered as reasons to accept that claim.

Keywords that indicate a conclusion:

  • therefore
  • so
  • hence
  • thus
  • it follows that = 由此得出结论
  • as a result
  • consequently
  • clearly

Keywords that indicate a premise:

  • since
  • if
  • because
  • from which it follows
  • for these reasons

However, sometimes there is no indicator:

Way to identify: ask yourself, is the main point that the arguer is trying to convey, or is it to put forward to believe another claim?

A Good Argument

An argument that gives us good reasons to believe the conclusion.

Two types of bad arguments:

Necessary conditions for an argument to be good:

  1. All the premises must be true. (Truth Condition)
  2. The conclusion must follow from the premises. (Logic Condition)

Notice that they are not sufficient conditions. Arguments may fail to be good still.

The Truth (Plausibility) Condition

All premises must be true.

The statement may be problematic, instead we should use plausible rather than true.

Eg: “The Earth rotates on its axis once every 24 hours.”

It does not allow us to acknowledge that the medievals had good arguments.

All premises must be plausible. ⇔ X is regarded by a given audience as true (They have good reasons to think it true).

Therefore, an arguer is trying to make premises plausible to the intended audience. It’s them who decide whether those premises are true.

Objection: subjectivism vs. relativism

We can still use 「true」 or 「false」, but they don’t play a role in a real world argument.

The Logic Condition

The conclusion follows from the premises. ⇔ The premises support the conclusion.

Notice: Two conditions are focusing two different properties of an argument. When evaluating the logic of an argument, we’re not interested in whether the premises are actually true or false. We have a hypothetical. 👉 “if premises are assumedly true”

Two forms that satisfy the Logic Condition:

Argument analysis is a two-stage process. The actual truth or falsity of the premises is irrelevant to the logic of the argument. They are independently considered.

Validity & Strength

Two different ways an argument can satisfy the logic condition:

  • Valid (Validity)
  • Strong (Strength)


An argument is valid if it has the following property:

  • If all the premises are true, the conclusion cannot be false.
  • It is logically impossible for the premises to be true and the conclusion false.
  • The truth of the premises guarantees the truth of the conclusion.

An argument is invalid if it has the following property:

  • If all the premises are true, the conclusion can be false.
  • It is logically possible for the premises to be true and the conclusion false.
  • The truth of the premises does not guarantees the truth of the conclusion.

But, an invalid argument doesn’t imply that the argument is bad. Invalid arguments can still be good arguments, because they can still give us good reasons to believe the conclusion. (Still satisfy the Logic Condition)

An important point to remember about the terminology:

Eg, The premise is invalid.


Premises make it very likely that satisfy the Logic Condition: (Strong)

Remember that Satisfy the Logic Condition is Premises offer good (not perfect) reasons.

Not satisfy the Logic Condition: (Weak)

Note that, Valid vs. Invalid is a sharp one. Strong vs. Weak has no cut-off.

Validity is like pregnancy 「cool」

The threshold is determined by conventional choice, not by logic.

So, what is a Good Argument?

First Pass. If an argument is good then:

  1. it has all true premises
  2. the conclusion follows from the premises (satisfy the Logic Condition)

Second Pass. if an argument is good then:

  1. it has all plausible premises
  2. it is either valid or strong

Deductive & Inductive

Reference: What is an argument?

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