Outline
James Fieser, UT Martin
updated 6/1/2025
This chapter builds upon the basic concepts of argument structure that were presented in the Chapter 1 overview of logic. Additional concepts included here are (1) more premise and conclusion indicators, (2) a third type of inference used in argument diagrams, and (3) procedures for analyzing an argument in natural language.
A. PREMISE AND CONCLUSION INDICATORS
1. Inference indicators: words or phrases used to signal the presence of an argument
Two types: conclusion indicators and premise indicators
Inference indicators often have other functions in other contexts; no hard and fast rule
Example:
Since [premise indicator] all humans are mortal, and Socrates is human, it follows that [conclusion indicator] Socrates is mortal
2. Premise Indicators (asterisks indicate new ones not included in the logic overview)
Because
For
For the reason that
Given that
In view of the fact that
Since
*As shown by the fact that
*Assuming that
*Granted that
*Inasmuch as
3. Conclusion Indicators (asterisks indicate new ones not included in the logic overview)
Accordingly
Consequently
For this reason
Hence
So
Therefore
Thus
*As a result
*In conclusion
*It follows that
*The moral is
*This being so
*This proves that
*We can conclude that
*Which means that
*Which proves that
There are three types of argument inferences: (1) joint inference, (2) independent inference, and (3) inference chain. The symbols used for diagraming arguments and their respective inferences are as follows:
Plus sign (+): together with
Arrow (→): intended as evidence for
1. Joint Inference: premises must be taken together to produce the conclusion; each premise independently will not do that.
Example Argument: [1] The person is over 18 [2] and is a U.S. citizen. [3] Therefore, the person is eligible to vote in a federal election.
Diagram: 1 + 2 → 3
Explanation: This is a joint inference since the two premises must be taken together to lead to the conclusion. For, by itself the fact that the person is over 18 does not imply they are eligible to vote since non-citizens over 18 are not eligible. Similarly, the fact that the person is a U.S. citizen does not by itself imply eligibility since citizens under 18 cannot vote.
Example Argument: [1] Everyone at this retreat is a yoga instructor, and [2] all yoga instructors are flexible. Therefore, since [3] Kevin is at this retreat, [4] Kevin is flexible.
Diagram: 1 + 2 + 3 → 4
Explanation: This is a joint inference since all three premises must be taken together to lead to the conclusion. For, by itself the fact that Kevin is at the retreat does not imply he is flexible without knowing who else is there. Similarly, the claim that yoga instructors are flexible does not apply to Kevin unless we know he is one, and we only infer that by combining all the premises.
2. Independent inference: each premise by itself leads to the same conclusion. Essentially each premise is a distinct argument for the same conclusion, each of which stands independently of the other.
Example Argument: [1] The document has multiple spelling errors [2] and the arguments are poorly organized. [3] Therefore, it needs to be revised.
Diagram: (1 → 3) and (2 → 3)
Explanation: This is an independent inference since each premise separately supports the conclusion. The presence of multiple spelling errors alone is a good reason for revision, regardless of how the arguments are presented. Similarly, even if the spelling were perfect, the poor organization of arguments would still justify the need for revision. Each premise provides an independent path to the same conclusion.
Example Argument: [1] The milk is past its expiration date, [2] it smells sour, [3] and it tastes off. [4] Therefore, it should not be consumed.
Diagram: (1 → 4) and (2 → 4) and (3 → 4)
Explanation: This is an independent inference since each premise on its own is sufficient to support the conclusion. The fact that the milk is past its expiration date justifies discarding it, regardless of taste or smell. Likewise, sour smell or bad taste each independently provide reason not to consume the milk. Each premise offers a separate and sufficient justification for the same conclusion.
3. Inference chain: the conclusion of one argument becomes the premise of another.
Example Argument: [1] The machine is unplugged, [2] so it isn’t receiving power, [3] therefore it won’t turn on.
Diagram: 1 → 2 → 3
Explanation: This is an inference chain since the conclusion of the first inference (that the machine isn’t receiving power) becomes a premise for the second inference (that the machine won’t turn on). Each step follows logically from the previous one, and the chain of reasoning links the initial observation to the final conclusion through a sequence of dependent statements.
Example Argument: [1] The student didn’t attend class [2] which means she missed the lecture. Therefore, [3] she didn’t learn the material, and so [4] she did not do well on the exam.
Diagram: 1 → 2 → 3 → 4
Explanation: This is an inference chain since each step in the reasoning builds upon the previous one. The fact that the student didn’t attend class leads directly to the conclusion that she missed the lecture. From that, we infer that she didn’t learn the material, and this in turn supports the final conclusion that she did not do well on the exam. Each statement functions as a conclusion in one step and a premise in the next, forming a continuous chain of reasoning.
B. ANALYZING THE ORIGINAL ARGUMENT
1. Implicit Statements
Implicit statements are hidden statements in arguments that are incompletely expressed. For example, consider the sentence: "Her car is in the driveway, therefore she must be home". The missing statement is that she always drives her car when leaving home. Statements may be hidden for several reasons. Perhaps the author intends for the reader to draw the conclusion themselves. Perhaps the missing statement is considered too obvious to mention, or perhaps the author simply overlooks the need to make the reasoning fully explicit. Regardless of the reason, readers must supply the missing statements themselves to fully analyze the argument's structure. When doing so, the reader is expected to follow what logicians call the principle of charity. That is, the reader must give the arguer the benefit of the doubt and make the argument as strong as possible while remaining faithful to the arguer's thought. The goal of the principle of charity is to minimize misinterpretation. For example, consider this argument which has a hidden premise:
"You shouldn't trust him since he lied to me once."
The stated premise is that he lied once, and the conclusion is that he shouldn’t be trusted. The argument leaves out an important connecting statement. Now consider two possible ways of supplying the missing statement, one charitable and the other uncharitable. The uncharitable reconstruction would be: "Anyone who has ever lied even once can never be trusted again." This is too extreme and unlikely to reflect the speaker’s actual reasoning. A more charitable version would be: "If someone has lied in the past, then there is at least some reason to doubt their honesty." This supplies a more plausible connection between the premise and the conclusion, one that gives the arguer a fair reading without exaggerating the claim.
Example: "She must be wealthy; she drives a new Mercedes." This argument leaves out the implicit premise that anyone who drives a new Mercedes is likely to be wealthy. Without this connecting statement, the reasoning remains incomplete.
Example: "Don’t bother calling her; the lights are off at her house." The implicit statement is that if the lights are off, she is not home. This unstated assumption forms the bridge between the observation and the advice.
Example: "Of course she got the promotion, she’s the boss’s favorite." This suggests that favoritism led to the promotion, but the implicit premise is that the boss gives promotions based on favoritism rather than merit.
Example: "He’ll win the election; he’s ahead in the polls." The argument assumes that being ahead in the polls guarantees a win, leaving unstated the premise that poll results reliably predict elections.
2. Compound Sentences
Compound sentences are those that contain two or more statements, such as “The sky is cloudy, and the wind is strong.” Compound sentences can be of two types: breakable and unbreakable ones. It is only the breakable ones that concern us here. Breakable compound sentences are those that contain two separate thoughts that, even though expressed in the same sentence, must logically be considered as separate statements. For example, consider the sentence “The car is old, and it needs repairs.” This should be divided into two distinct statements: (1) The car is old, and (2) The car needs repairs. Each part can serve as an independent premise or conclusion in an argument and must be analyzed separately. Breakable compound sentences often contain the word “and” or a similar word such as “but,” which, in logical terms, functions the same way as “and.” For example, “He is tired but still working” implies both “He is tired” and “He is still working.” By contrast, unbreakable compound sentences should not be split into separate statements and treated as complete statements. For example, “If it rains, the picnic will be canceled” is a single conditional statement and should be treated as one unit. Unbreakable compound sentences often include terms such as “either-or” and “if-then,” which are complete logical structures in themselves and do not resolve into simpler independent statements.
Example: "The dog barked loudly, and the neighbors complained." This is a breakable compound sentence because it contains two distinct claims that can stand alone: (1) The dog barked loudly, and (2) The neighbors complained.
Example: "She was late for work, but she finished all her tasks." Although the sentence uses “but,” it still functions logically like “and” and contains two separable statements: (1) She was late for work, and (2) She finished all her tasks.
Example: "The engine was running, and the headlights were on." This sentence combines two observable facts that are logically independent: (1) The engine was running, and (2) The headlights were on.
Example: "The package arrived, but it was damaged." This is a compound statement in which the contrast word “but” still signifies two separate truths: (1) The package arrived, and (2) The package was damaged.
3. Steps for diagraming arguments
1. Bracket each statement in a way that best reveals the argument structure.
2. Circle clue words (and, but, therefore).
3. Number each statement sequentially.
4. Identify conclusion; if conclusion is implied, supply it and number it.
5. Work backwards from conclusion to premises.
6. Determine if any premise leads independently to a conclusion.
7. Determine if there are any intermediate conclusions.
8. Determine which premises need to be taken together.
4. Diagramming long arguments
Example: [1] All electronics must be packed securely for shipping. [2] This laptop is considered electronic equipment. [3] The box it was shipped in had no padding. [4] The laptop arrived with a cracked screen. [5] The damage could have been prevented with proper packing. [6] Therefore, the laptop was not packed securely.
Diagram: (1 + 2 + 3 → 6) and (4 + 5 → 6)
Example: [1] A valid experiment requires a control group. [2] It must also use random assignment. [3] The study in question had no control group. [4] It also used self-selection rather than random assignment. [5] Therefore, the study lacks two necessary conditions of a valid experiment. [6] So it is not a valid experiment.
Diagram: 1 + 2 + 3 + 4 → 5 → 6