Critical Thinking
Tip: See if you can specify more than one precise meaning in sentence, if you can it is not ambiguous or vague.
Lexical: Specific words.
Syntactic: Structure of the sentence. Different meanings of a sentence structure. Bad grammar can lead to miscommunication.
Induction: Likely to be true to some degree, not guaranteed.
Deduction: If the premises are true the conclusion must be true (guaranteed). You can have a deductive argument with all false premises. It the premises were true, than the conclusion reflects the premises.
Look for:
Look for vagueness
Look for standard forms of ambiguity (especially) bare plurals
Look for over / under expressions of confidence levels
Spot overconfidence: If certain concepts are repeated without strong backing, it might signal the person is relying on assertion instead of solid reasoning.
Identify under confidence: If there are few repeated themes or ideas, it might suggest a lack of conviction or evidence being presented to support an argument.
Recognize patterns and trends: By keeping an eye on what gets repeated and what stands alone, you can better understand the core message or spot weaknesses in the logic being presented.
Practice principle of interpretative charity (providing people with the benefit of the doubt in their argument).
Standardize Tips:
Find the premise indicators (since, because, therefore) that supports a conclusion.
Rewrite the argument in short form so that you focus on what matters.
What are the main concepts of the argument?
Keep an eye on pairs and singlets.
What words keep appearing in the sentence (pairs).
When adding premises and conclusions only add what is minimally necessary to make the argument work.
Adding and creating your own narrative alters the way of the original argument.
Factor in the Principle of Charity.
What causes what, what comes first.
What is greater than what:
X > Y
Y > X
X > Z
Deductive Arguments and Entailment
Modus Ponens (Valid Argument Form)
If P then Q.
P is true.
Therefore, Q is true.
Example:
If it is payday than I get paid
It is payday.
Therefore I get paid
Modus Tollens (Valid Argument Form)
Works by denying the second part (Q) to conclude the first part (P) is also false.
If P then Q.
Not Q.
Therefore, not P.
Example:
If Kaij goes not go to school, than she will be marked absent.
Kaij was not marked absent.
Therefore, Kaij went to school.
Disjunctive Syllogism (Valid Argument Form)
P or Q.
Not P (or not Q).
Therefore, Q must be true (or not Q).
Example:
It is either hot or cold outside.
It is not hot outside.
Therefore it is cold.
Hypothetical Syllogism (Valid Argument Form)
A logical statement that uses the words “if…then” statements. It connects two statements that lead to a conclusion.
The form is:
If P than Q
If Q than R
Therefore, if P than R
Example:
If it snows, then there will be snow on the steps
If there is snow on the steps than we will have to shovel.
Therefore, when it snows, we will need to shovel.
Affirming the consequence (Invalid argument, Logical Fallacy)
A logical fallacy. Assuming that something occurs because something else. Making something true that is not actually true. It is a fallacy because it assumes that if P occurs, that then Q will also occur, which makes P true.
If P than Q.
Q is true.
Therefore, P.
However, there are times when P does not lead to or cause Q. This results in P not being true because Q does not lead to it.
Example:
If Sage does not go to university, than Sage will not be successful.
Sage is not going to university.
So Sage will not be successful.
Through this fallacy, the assumption is being made (affirming the consequence) that Sage will not be successful because she is not going to university. This is untrue, as there are many successful people who have not attended university.
Denying the Antecedent (Invalid argument , Logical Fallacy)
A logical fallacy and mistake in reasoning. This is an assumption in reasoning that assumes that because something else did not occur that, the next thing did not occur. It comes from assuming that if the first condition is not met, that then the second condition is not possible.
If P than Q.
Not P.
Therefore, not Q.
Example:
If Onyx did not go to jail, than he must be innocent.
Onyx did not go to jail.
Therefore, Onyx is innocent.
Soundness: Means that your premises have to be valid, and they all have to be true. If all premises are true, than you should believe the conclusion. However, the more your confidence is reduced, you should be more cautious about the conclusion.
Flipping the Argument
This involves assuming the conclusion is false, instead of true. This method tests for entailment.
The process:
Assume the conclusion is false.
See if the premises can still be true without the conclusion being true.
If the premises can be true while the conclusion is false, the argument is not valid.
Example Argument:
Premise 1: If it rains, the ground will be wet.
Premise 2: It is raining.
Conclusion: The ground is wet.
Step 1: Assume the conclusion is false.
We assume the ground is not wet (this is the opposite of the conclusion).
Step 2: Check if the premises can still be true without the conclusion being true.
Premise 1: "If it rains, the ground will be wet." This can still be true, because it doesn’t mean the ground will always be wet every time it rains. Maybe there’s a shelter over the ground that keeps it dry.
Premise 2: "It is raining." This can also be true. It could be raining, but there might be something preventing the ground from getting wet (like the shelter).
So, both premises can still be true even though the conclusion (that the ground is wet) is false.
Step 3: Conclusion:
Since it’s possible for the premises to be true while the conclusion is false, the argument is not valid. This shows that the conclusion doesn’t logically follow from the premises because there’s a scenario where the premises could be true and the conclusion false.
Premises stay the same
Find negation of conclusion
Assess if P + negative C are consistent (if they can all be true, than invalid)
Common error: Do not go if consistent than valid, when working with negations.
Negations for Sentence Types
A: All S are P (universal affirmation)
E: No S are P (universal negative)
I: Some S are P (particular, not universal, affirmative)
At least one S in included in the class of P
O: Some S are not P (particular, negative)
AE
IO
Conditional Statement
This is when the antecedent (A), depends on the consequent (B).
The general structure is: If A, then B.
A is the antecedent (the condition or premise). It’s the part that must happen first.
B is the consequent (the result or conclusion that follows from the antecedent).
Example:
If it rains (A), then the ground will be wet (B).
A (it rains) is the antecedent (the condition).
B (the ground will be wet) is the consequent (the result).
In this case, the antecedent (it raining) is the condition for the consequent (the ground being wet).
Antecedent (Conditional Statement)
This is what comes before a consequence. This is part A in a conditional statement, and it has to occur for the consequence to happen.
A (it rains) is the antecedent (the condition).
Consequent (Conditional Statement)
This is a part of a conditional statement. This is part B, that occurs after part A happens. This is a result of the antecedent.
B (the ground will be wet) is the consequent (the result).
Logical Form
The structure or pattern of an argument that can be shared by different arguments. It focuses on how the argument is set up, not on the specific content.
In logical form, you replace parts of an argument with variables (like A, B, or X) so that you can see the overall pattern. This helps you understand how different arguments might follow the same logic, even if the content is different.
Example:
Argument 1:
If it rains (A), the ground will be wet (B).
It is raining (A).
Therefore, the ground will be wet (B).
Argument 2:
If I study hard (A), I will pass the exam (B).
I am studying hard (A).
Therefore, I will pass the exam (B).
Both arguments follow the same logical form, even though the content is different. In both cases, if A happens, then B will happen.
Counterexample
An example that shows a statement or claim is false. It’s like finding one situation where the rule or idea doesn’t work, proving that the claim isn’t always true.
How it works:
You have a general statement or claim.
You find one example where the statement doesn’t hold true.
That one example is a counterexample, and it shows that the statement isn’t true in all cases.
Example:
Statement: "All birds can fly."
Counterexample: A penguin is a bird that cannot fly.
Disjunction and Conjunction
Disjunction: A logical operation that connects two statements with "or." It means that at least one of the statements must be true for the whole disjunction to be true.
Example: "It is raining or it is snowing."
For this to be true, either "it is raining" or "it is snowing" (or both) must be true.
In critical thinking, disjunctions help evaluate situations where alternative possibilities exist, and only one needs to be true for the statement to hold.
Conjunction: A logical operation that connects two statements with "and." It means that both statements must be true for the whole conjunction to be true.
Example: "It is raining and it is cold."
For this to be true, both "it is raining" and "it is cold" must be true at the same time.
In critical thinking, conjunctions are used to identify when multiple conditions must be met together for a conclusion or statement to hold true.