Applied Logic

Unit 2: Arguments and Inference

Learning Objectives

  • Recognise a logical argument and distinguish it from other text types
  • Identify premises and conclusions in short passages
  • Understand the role of inference in moving from premises to a conclusion
  • Apply the logical indicator test to locate conclusions
  • Evaluate the difference between an argument and a mere assertion
1

Types of Text

Not every piece of writing contains an argument. Before you can evaluate reasoning, you need to be able to identify whether reasoning is present at all. Consider the four short passages below. Only one is a logical argument. Read each one and decide which.

Text A

I broke the brand new monitor in my lab. My supervisor was furious. He shouted at me. I told him many times it was not my fault, but he continued to blame me. I still think he is wrong.

Text B

Create the content in HTML. Format the styles using CSS. Control the behaviour of the DOM with JavaScript. Server-side interactions can be managed using Python or PHP.

Text C

I was worried that I had a fever, so I took my temperature. The thermometer showed 36.8°C. My normal temperature is around 36.6°C. I do not have a fever.

Text D

Mathematics is the most important subject taught at school.

Which text is an argument? Which is a narrative? Which is a set of instructions? Which is an assertion?

Text A is a narrative — it tells a story. There is no attempt to give reasons for a conclusion.

Text B is a set of instructions (or a description of a process). No claim is being argued for.

Text C is an argument. The premises (thermometer reading, normal temperature) provide evidence for the conclusion (no fever). Even though the argument is short and informal, the structure — evidence leading to a reasoned conclusion — is present.

Text D is an assertion — a claim made without any supporting evidence. Assertions are common in everyday speech but should not be confused with arguments. Providing evidence turns an assertion into an argument.

2

What Makes an Argument?

A logical argument consists of two components:

  • Premises — one or more propositions offered as evidence or reasons
  • Conclusion — the proposition that the premises are intended to support

The movement from premises to conclusion is called inference. Logical language uses indicator words to signal whether a proposition is a premise or a conclusion.

Conclusion indicators

Words that often signal a conclusion:

therefore, thus, hence, so, consequently, it follows that, we can conclude that, this shows that, this proves that

Premise indicators

Words that often signal a premise:

because, since, given that, as, for, in view of the fact that, on the grounds that, assuming that, the reason is that

The "Therefore" test

A useful heuristic: place the word "therefore" before each sentence in a passage. The sentence that sounds most natural after "therefore" is likely the conclusion. Then ask: what evidence is offered for that sentence? Those are the premises.

All humans are mortal.  [premise]
Socrates is human.  [premise]
Therefore, Socrates is mortal.  [conclusion]
3

Identifying Arguments

For each passage below, decide whether it contains an argument. If it does, identify the conclusion and the premises. Note: arguments can be false, absurd, or even self-defeating — that does not prevent them from being arguments.

  1. Bananas are yellow. Strawberries are red. Apples are red or green.
  2. Bananas are fruit. Fruits are sweet. Therefore, bananas are sweet.
  3. This activity is too easy for me.
  4. The Earth is similar to the Moon of Jupiter called Io. There is life on Earth. Therefore, there is life on Io.
  5. The Earth is similar to a tennis ball. There is life on Earth. Therefore, there is life on a tennis ball.
  6. Each human has a heart. Professor X is human. Therefore, Professor X has a heart.
  7. Donald is a duck. The president's first name is Donald. Therefore, the president is a duck.
  8. Some members of the group attended class. Aiko attended the class. Therefore, Aiko is a member of the group.
  9. Professor X says there is a rabbit on the moon. You cannot prove that there is not. Therefore, there is a rabbit on the moon.
  10. A man was found in a classroom this morning. His face was cold and blue. He did not need hospital treatment. He had simply washed blue ink off his face.

  1. Not an argument — three independent descriptions with no conclusion.
  2. Argument — premises: bananas are fruit; fruits are sweet. Conclusion: bananas are sweet. (Note: "fruits are sweet" is a generalisation that is not universally true — the argument is contestable.)
  3. Not an argument — a bare assertion with no supporting evidence.
  4. Argument — analogical reasoning from Earth to Io. The analogy is weak (Io and Earth differ dramatically) but the structure is an argument.
  5. Argument — same structure as (4), but even weaker. Arguing from similarity when the cases are obviously dissimilar.
  6. Argument — a valid deductive argument (syllogism). True premises, valid form, sound conclusion.
  7. Argument — but the conclusion does not follow. The argument confuses a name (Donald) with a predicate (being a duck). This is a formal fallacy.
  8. Argument — but invalid. The conclusion does not follow: some members attended does not mean Aiko is one of them.
  9. Argument — but it commits the appeal to ignorance fallacy: the inability to disprove something does not prove it is true.
  10. Not an argument — a short narrative that resolves itself. There is no conclusion that is being argued for.
4

Inference and Indicator Words

The inference bar is a visual representation of the move from premises to conclusion used in formal logic notation:

P1: All humans are mortal.
P2: Socrates is human.
C:  Socrates is mortal.

The line separates premises (above) from conclusion (below). You will use this notation when mapping arguments in Unit 9.

Video: Argument structure

Watch this short video on how to identify the structure of an argument.

How to identify arguments

5

Critical Analysis: Professor X

Return to the Professor X passage from Unit 1 — this time with the tools of argument analysis. Read it again and answer the questions below.

Professor X

  1. Professor X is an efficient and effective teacher.
  2. All his students enjoy his classes according to the feedback given on the student feedback questionnaires.
  3. Every student who attended the course in full received a grade A, which is testimony of his expertise in teaching.
  4. The professor not only holds a doctorate in physics but is also a polyglot and a polymath.
  5. His course is always popular with students.
  6. Every course offered in the previous two years has seen enrolments meeting or exceeding the minimum number.
  7. To ensure he has enough energy, he always brings a cup of coffee to the classroom.
  8. This is yet more evidence of his dedication to his students.
  9. Finally, Professor X's Facebook page has received thousands of "likes", a clear indication of votes of confidence in his teaching.
  1. State the main conclusion in your own words.
  2. Identify which sentences are genuine premises — evidence that directly supports the conclusion.
  3. Identify which sentences are irrelevant to the conclusion (i.e., they do not support it even if true).
  4. Sentence 8 says the coffee is "evidence of dedication". Is this a valid inference? Explain.
  5. Sentence 9 uses Facebook "likes" as evidence of teaching quality. What assumptions does this require? Are those assumptions justified?
6

Check Your Understanding

Which of the following is a logical argument?

Correct! An argument requires at least one premise and a conclusion where the premise is offered as evidence for the conclusion. Option C provides a reason (the meeting has been cancelled) for the conclusion (Aileen will not attend). Options A and B are assertions; option D is a narrative.
Not quite — review the material and try again. An argument requires at least one premise and a conclusion where the premise is offered as evidence for the conclusion. Option C provides a reason (the meeting has been cancelled) for the conclusion (Aileen will not attend). Options A and B are assertions; option D is a narrative.

Which word is a premise indicator?

Correct! 'Because' signals that what follows is a reason or evidence — a premise. 'Therefore', 'consequently', and 'hence' are conclusion indicators: they signal that what follows is the conclusion being argued for.
Not quite — review the material and try again. 'Because' signals that what follows is a reason or evidence — a premise. 'Therefore', 'consequently', and 'hence' are conclusion indicators: they signal that what follows is the conclusion being argued for.

An assertion differs from an argument in that an assertion:

Correct! An assertion makes a claim but provides no evidence or reasoning to support it. An argument, by contrast, offers premises as reasons for a conclusion. Assertions may be true, false, or indeterminate — the absence of supporting evidence is what distinguishes them from arguments.
Not quite — review the material and try again. An assertion makes a claim but provides no evidence or reasoning to support it. An argument, by contrast, offers premises as reasons for a conclusion. Assertions may be true, false, or indeterminate — the absence of supporting evidence is what distinguishes them from arguments.

Review

Expand each concept to check your understanding before moving on.

A logical argument has two essential components: premises (propositions offered as evidence) and a conclusion (the proposition the premises are intended to support). The inference is the logical step connecting them. An argument can be short — even a single premise and a conclusion — and it can be false, absurd, or weak. Its defining feature is the presence of an evidential relationship between premises and conclusion.

An assertion is a claim made without supporting evidence. It states a conclusion but provides no premises. Assertions are extremely common in everyday discourse — advertising, political speech, and social media are full of them. The moment a speaker provides a reason for a claim, the statement becomes an argument (however weak).

Conclusion indicators (therefore, thus, hence, so, consequently, it follows that) signal the conclusion. Premise indicators (because, since, given that, as, for, on the grounds that) signal premises. These words are guides, not guarantees — they can appear in non-argumentative contexts — but they are highly reliable in academic and formal writing.

Place "therefore" before each sentence in a passage. The sentence that sounds most natural after "therefore" is likely the conclusion. This works because the word therefore signals that what follows is a claim being supported by what came before. Once you have identified the conclusion, the remaining propositions that provide evidence for it are the premises.

An argument is valid if the conclusion follows necessarily from the premises — regardless of whether the premises are true. An argument is sound if it is valid and the premises are actually true. You can have a valid argument with false premises, and an argument with true premises that is still invalid. These concepts are covered in depth in Unit 3.

Key concepts covered in this unit: argument, premise, conclusion, inference, assertion, narrative, instruction, logical indicator words (premise and conclusion indicators), the Therefore test, inference bar notation, validity (preview), soundness (preview).

Proceed to Unit 3: Deductive Reasoning when ready.

Applied Logic
Overview 01 Propositions and Truth 02 Arguments and Inference 03 Deductive Reasoning 04 Inductive Reasoning 05 Conditional Logic 06 Truth Tables 07 Informal Fallacies I 08 Informal Fallacies II 09 Argument Mapping 10 Applied Reasoning