critical thinking midterm 1

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Ad hominem abusive

"against the person" When a claim or argument is rejected based on alleged character flaws or a negative stereotype of the person making it.

Tu Quoque

"you, too" A type of ad hominem fallacy distinguished by the attempt of one person to avoid the issue at hand, or reject a claim or argument, by accusing the other person of being a hypocrite.

Because you started lifting weights without first getting a physical checkup, you will probably injure your back.

(argument)You will probably injure your back (conclusion; not already accepted as fact), because you started lifting weights without first getting a physical checkup (premise; supports conclusion).

A model

(for an invalid argument) is a description of a possible situation that makes the premises come out true and the conclusion come out false.

A counterexample

(for an invalid argument) is an argument of the same form, but whose premises are clearly true and whose conclusion is clearly false.

Begging the Question

Assumes as evidence in the premises the very thing that it attempts to prove in the conclusion; exhibits circular reasoning Not persuasive; only those who already accept the conclusion will be inclined to accept the premises Sometimes the conclusion is simply a rewording of one of the premises

False Dichotomy

A fallacy that occurs when it is assumed that only two choices are possible, when in fact others exist.

Cogency

is the inductive analog of soundness Sound: valid and all premises true Cogent: strong and all premises true

Strength

is the inductive analog of validity Valid: true premises make it impossible for the conclusion to be false Strong: true premises make it improbable for the conclusion to be false

Argument

A group of statements, some of which (the premises) are intended to support another (the conclusion) The conclusion is claimed to follow from the premise(s)

Enthymemes

Arguments with missing premises, missing conclusions, or both.

example of appeal to ignornace

Atheist: God doesn't exist. After all, every argument ever put forward for God's existence has been fallacious or downright silly. Theist: What are you talking about? Of course God exists. No one has ever proved otherwise. Both the atheist and theist are committing the fallacy of appeal to ignorance. The atheist claims the statement "God exists" is false because it hasn't been proven true, and the theist claims the statement is true because it hasn't been proven false.

Fallacy of diversion? If so, which one? Example Laws require a lawmaker. The universe behaves according to the laws of physics. Therefore, there's a lawmaker, God, who governs the universe.

Equivocation; in the first premise, the word 'law' means an enforceable prescription made by a legislative body (like a law against littering), whereas in the second premise, the word 'law' means a scientific law, which is a description of the behavior of some phenomena based on experimental observation (like Newton's Second Law "F=ma")

Invalid deductive argument

Even if the premises are true, it is still possible for the conclusion to be false Better: an argument is invalid iff it is (logically) POSSIBLE for all the premises to be true and the conclusion to be false.

Provide a counterexample to show the argument is invalid Example No atheists are Christian. All Christians believe in heaven. Therefore, no atheists believe in heaven.

Here is the argument form: No A are C. All C are B. No A are B. Here is a counterexample (it's possible to find true premises together with a false conclusion using this logical form): No cars are boats. (T) All boats are vehicles. (T) No cars are vehicles. (F)

Provide a counterexample to show the argument is invalid Example No Hillary supporters are libertarians. No Hillary supporters are Trump supporters. Therefore, no libertarians are Trump supporters.

Here is the argument form: No H are L. No H are T. No L are T. Here is a counterexample (it's possible to find true premises together with a false conclusion using this logical form): No dogs are humans. (T) No dogs are attorneys. (T) No humans are attorneys. (F)

Provide a counterexample to show the argument is invalid Example Some Bernie supporters oppose capitalism. Some people who oppose capitalism are violent. Therefore, some Bernie supporters are violent.

Here is the argument form: Some B are O. Some O are V. Some B are V. Here is a counterexample (it's possible to find true premises together with a false conclusion using this logical form): Some dogs are pets. (T) Some pets are cats. (T) Some dogs are cats. (F)

rigid application of a generalization example

Hey, officer. My supply of grenades and meth was stolen last week, but I heard you caught the thief. When can I pick up my stolen property? Normally, stolen property is returned to the original owner. But cases of illicit drugs, illegal weapons, and counterfeit money are (known) exceptions. The speaker assumes the generalization is universal (exception-less), which it obviously isn't.

Supply either the missing premise(s) or conclusion, applying the principle of charity Example You can prevent real human suffering (by donating that $50 to the Against Malaria Foundation), and to do so, you need not sacrifice anything of comparable moral significance (just forgo that new pair of shoes). Hence, you ought to donate that $50.

Missing premise. Once again, a moral principle has been suppressed. It is worth making explicit, since disagreement over this argument's conclusion may rest on disagreement over that moral principle, and that's where moral philosophy comes in. The argument is a valid deductive one. You can prevent real human suffering (by donating that $50 to the Against Malaria Foundation), and to do so, you need not sacrifice anything of comparable moral significance (just forgo that new pair of shoes). [If you can prevent real human suffering without sacrificing anything of comparable moral significance, then you ought to do it.] Hence, you ought to donate that $50.

Supply either the missing premise(s) or conclusion, applying the principle of charity Example If God does not exist, then everything is permissible. And if that's the case, then it's permissible to torture babies for fun. So, obviously God exists!

Missing premise. The moral claim that is left unstated here is presumed to be obvious. The argument is a valid deductive one. If God does not exist, then everything is permissible. If everything is permissible, then it's permissible to torture babies for fun. [It's not permissible to torture babies for fun!] So, obviously God exists!

Fallacy based on personal attack? If so, which one? Example Rob's a Democrat, and it turns out he's a liar. See, it's just like I told you: all Democrats are liars!

No fallacy based on personal attacks, but the argument is deductively invalid (from the fact that one Democrat is a liar, it doesn't follow that all Democrats are liars) or inductively weak (a single instance doesn't make the general claim probable)

Fallacy of unwarranted assumption? If so, which one? Example My roommate, who is a brilliant logician but has never studied biology or read anything other than (a few passages of) the bible, claims that there's no way humans could have evolved from another primate species. So, this just goes to show: people who are smart in one way can often be irrational in other ways.

No fallacy of unwarranted assumption; although the opinion of an unqualified authority on biology is mentioned, it is not used in support a claim in biology (but rather a claim about the person instead)

Generalization fallacy? If so, which one? Example We polled over 1000 UCSB students from over 50 different majors; 89% said they always get high or drunk when preparing for their exams, and they do just fine. So, most UCSB students agree that you can study buzzed.

No generalization fallacy; the sample is large and representative enough such that the inference is strong

Red Herring Fallacy

Occurs when someone completely ignores an opponent's position and changes the subject, diverting the discussion in a new direction.

Straw Man Fallacy

Occurs when someone's written or spoken words are misinterpreted or taken out of context, purposely distorting the original argument to create a new, weak argument that can be easily refuted (a straw man that is easily knocked down).

denying the antecedent

Occurs when the following (invalid) inference form is used: If P then Q Not P Not Q

affirming the consequent

Occurs when the following (invalid) inference form is used: If P then Q Q P

example of begging the question

Of course God exists! It says so in the Bible, which was written by God himself. And God is morally perfect so He would never lie. The argument intends to establish the conclusion that God exists, but it already assumes the truth of this conclusion in the premises (saying that God wrote the Bible and is morally perfect presupposes that God exists).

Deductive argument

One in which it is claimed that The conclusion follows necessarily from the premises True premises make it impossible for the conclusion to be false

Inductive argument

One in which it is claimed that The premises make the conclusion probable True premises make it improbable for the conclusion to be false

Generalization fallacy? If so, which one? Example I can't believe you just shoved that child (out of the way of that moving car)! Don't you know it's wrong to shove a child?

Rigid application of a generalization; clearly the moral principle "You shouldn't shove children" has (known) exceptions (like when it's the only way to save that child's life)

Valid deductive argument

True premises make it impossible for the conclusion to be false Better: an argument is valid iff it is (logically) IMPOSSIBLE for all the premises to be true and the conclusion to be false

Fallacy based on personal attack? If so, which one? Example Trump claims that we should support the troops, given the sacrifices they've made. But he avoided military service his whole life. So, who gives a shit?

Tu quoque; Trump's argument is being rejected/ignored based on his alleged hypocrisy

Explanation

Uses "because" to provide reasons for how an event occurred or why something is the case (an already accepted fact)

Biased Sample

Uses a nonrepresentative sample as support for a statistical claim about an entire population. Even if the sample is quite large (so it's not a hasty generalization), the inference will be weak if the sample doesn't accurately represent the wider population

example of appeal to unqualified authority

You really think anthropocentric climate change is real? Donald J. Trump, graduate of Wharton business school, creator of Trump Steaks, and star of the reality TV hit series The Apprentice, has one of the sharpest business minds of our time. And he claims it's a hoax created by the Chinese government in order to out compete us in manufacturing. So don't worry yourself; man-made climate change is absolute bullshit. This argument rejects a scientific claim based on the authority of someone who has no expertise in the relevant field (climate science). Such testimony is not likely to be reliable.

conditional statement

a compound statement of the form "If P then Q," where P (the antecedent) and Q (the consequent) are simpler statements

formal fallacy

a logical error that occurs in the form of an argument (making it invalid)

Argument or not? Example Abortion is immoral. Taxation is immoral. Wealth redistribution is immoral. These are all things that the opposing candidate supports. So, what does that tell you about her?

Argument. It contains statements that seem to be intended to support the claim that the opposing candidate is immoral (though this conclusion is not explicitly stated).

Sound argument

The argument is valid AND all the premises are, in fact, true

Proposition

The information content or meaning of a statement

Inference

The reasoning process expressed by an argument Arguments consist of premises, a conclusion, and the relation between them, which is "blank"

Logic

The study of reasoning In it, we can study how to evaluate one aspect of an argument: its inference

Cogent inductive argument

the argument is strong and the premises are true

Uncogent inductive argument

the argument is weak or has at least one false premise

Formal fallacy

A logical error that occurs in the form or structure of a deductive argument (making it invalid). If Bob is a Christian, then he's a theist. Bob is a theist. So, Bob is a Christian.

Informal fallacy

A mistake in reasoning that occurs in ordinary language, including mistakes due to relevance, assumption, ambiguity, or diversion. often involve invalid (or otherwise bad) inferences, but they are typically characterized by their content rather than their logical form

Fallacy based on personal attack? If so, which one? Example Rob argues that it's immoral to tax wealthy people to fund social programs like welfare, since it basically amounts to stealing from hard working people to pay for lazy moochers to sit on their asses. But Rob is clearly just a greedy, selfish sociopath, with no compassion for the plight of the less fortunate. So he and his argument can **** off!

Ad hominem abusive; Rob's argument is rejected based on his alleged character flaws

Fallacy based on personal attack? If so, which one? Example Sally claims that an omnipotent and benevolent god is required to explain why the universe contains intelligent life. But she lost her parents at a young age and so probably just wants to feel like she has a loving parent watching over her. Clearly theism is just wishful thinking, and Sally's wrong; God doesn't exist.

Ad hominem circumstantial; Sally's argument is rejected based on her life circumstances

Any substitutions in this exact form will also be VALID

All B are D. All D are M. All B are M.

Appeal to Ignorance

An argument built on a position of ignorance claiming either: a statement must be true because it has not been proven to be false, or a statement must be false because it has not been proven to be true.

Argument or not? Example You should buy an iPad instead of a Notebook. You should also buy an Xbox One instead of a PS4, and a Vizio television instead of a Sony.

Answer Not an argument. These statements do not offer support for the truth of any particular claim.

Fallacy of unwarranted assumption? If so, which one? Example If there's no God, then there's no such thing as right or wrong. After all, no atheistic philosopher has ever proven any secular theory of ethics to be true, or explained how moral value can exist in a godless world.

Appeal to ignorance; the speaker is arguing for something like the claim "moral value requires a God" based on the claim that no one has shown otherwise (i.e., shown that there can be moral value without God)

Fallacy of unwarranted assumption? If so, which one? Example Lawrence Krauss, a prominent theoretical physicist, cosmologist, and polemicist, says that morality is entirely subjective (dependent on human psychology) and relative to one's culture. Hence, clearly there is no such thing as absolute, objective moral truth.

Appeal to unqualified authority; Krauss has expertise in certain fields (physics and cosmology), but not in the field relevant to his claim (ethics, or, more specifically, metaethics, which is the study of the philosophical foundations of ethics)

Argument or explanation? Example Because we see a stunning variety of moral codes when we look at different societies and cultures, and since the best explanation of this fact is that there's no such thing as absolute morality, it follows that moral claims are only true or false relative to some moral framework or other.

Argument. Although this passage contains a (purported) explanation within it, it is used to argue for some version of moral relativism. This sort of argument is called 'abductive' or 'inference to the best explanation'.

Fallacy of unwarranted assumption? If so, which one? Example Monique is the smartest person in the class. After all, there's no one in the class who is as smart as she is.

Begging the question; the premise is just a rephrasing of the conclusion

Fallacy of unwarranted assumption? If so, which one? Example Every product of intelligent design was produced by an intelligent designer. Hence, the universe was produced by an intelligent designer.

Begging the question; this argument is an enthymeme, and can plausibly be reconstructed as follows: 1. Every product of intelligent design was produced by an intelligent designer. [2. The universe is a product of intelligent design.] 3. Hence, the universe was produced by an intelligent designer. Premise 2 is just another way of stating the conclusion (to be the product of intelligent design is just to have been produced by an intelligent designer; no one who rejects the latter will accept the former)

example of equivocation

Bernie is an attractive candidate. If a man is attractive, he can be a male model. So, Bernie can be a male model. Equivocation on 'attractive'; although this argument may appear valid, if we substitute the different meanings of 'attractive', it's clearly invalid: Bernie is a candidate who appeals to many voters. If a man is aesthetically pleasing, he can be a male model. So, Bernie can be a male model.

Generalization fallacy? If so, which one? Example I've done speaking gigs at over 50 colleges around the US, as arranged by the various chapters of the Young Republicans Club at those schools. Almost all of the students in my audience are very supportive of the president. So, clearly young people love Trump!

Biased sample; the sample of young Republicans (or other audience members) is not likely to accurately represent all young people

Deductive or inductive? Example If Trump gets re-elected, Democrats will riot. If Trump does not get re-elected, Republicans will riot. So, either way, we're gonna have a riot on our hands.

Deductive. Even though the premises cannot be known with certainty (they are predictions about what will happen), we know with certainty that IF the premises are true, THEN the conclusion is true.

example of false dichotomy

Either you support Trump or you hate America. or (1) Either you believe in God or you'll get punished for eternity. (2) You don't believe in God. (3) So, you'll get punished for eternity.

Fallacy of unwarranted assumption? If so, which one? Example Either God exists or humans are bags of chemicals with no inherent value. And if that's true, then there's nothing morally wrong with destroying them. So, if God does not exist, there's nothing morally wrong with destroying humans.

False dichotomy; the first premise does not exhaust all the logical possibilities (e.g., maybe God does not exist but humans still have immaterial souls; maybe God does not exist but some bags of chemicals, like humans or other living beings, still have inherent value; etc.).

Rigid application of a generalization

From the general to the specific When a generalization (i.e., statements of the form "Fs are G") is inappropriately applied to the case at hand. Many generalizations have (known) exceptions When a generalization with exceptions is applied to a particular case, the inference is not valid

Hasty Generalization

From the specific to the general An argument that relies on a small sample that is unlikely to represent the population. Typically, an inference from the claim that a few Fs are G to the claim that all or most Fs are G is weak

Generalization fallacy? If so, which one? Example Venezuela tried Socialism and it was a complete disaster! What other conclusion can I draw? Socialism never works!

Hasty generalization; the premises report only one (alleged) instance, while the conclusion generalizes to all instances, making a weak inference

Provide a model to show the argument is invalid Example Gail is dating Maria. Maria is not a philosophy grad student. Therefore, Gail is not dating a philosophy grad student.

Here are two models on which the premises are true and the conclusion is false: Gail is polyamorous, and she is also dating a philosophy grad student in addition to dating Maria. Gail is unfaithful, and she is cheating on Maria by secretly also dating a philosophy grad student.

Provide a model to show the argument is invalid Example All Christians believe in a god. Timmy believes in a god. Therefore, Timmy is a Christian.

Here are two models on which the premises are true and the conclusion is false: Timmy is a Muslim. Timmy is a New Age-y, non-religious theist.

Provide a model to show the argument is invalid Example Angela is over 5 feet tall. Itzel is over 6 feet tall. Therefore, Itzel is taller than Angela.

Here is a model on which the premises are true and the conclusion is false: Angela is 6'2'' and Itzel is 6'1''.

Provide a model to show the argument is invalid Example If it's raining, then the ground is wet. The ground is wet. Therefore, it's raining.

Here is a model on which the premises are true and the conclusion is false: It's not raining but someone turned on the sprinklers, which made the ground wet.

Provide a counterexample to show the argument is invalid Example All UCSB students like to get drunk. Some people who like to get drunk are a nuisance to society. Therefore, some UCSB students are a nuisance to society.

Here is the argument form: All U are L. Some L are N. Some U are N. Here is a counterexample (it's possible to find true premises together with a false conclusion using this logical form): All kittens are mammals. (T) Some mammals are doctors. (T) Some kittens are doctors. (F)

Deductive or inductive? Example Most women who live in Isla Vista drink beer. Jane is a woman who lives in Isla Vista. So, Jane drinks beer.

Inductive. If the premises are true, then it is probably true that Jane drinks beer. However, the conclusion could still be false, since we are told only that "most" women who live in Isla Vista drink beer. Jane could be in the (tiny) minority who don't. Compare (Deductive): All women who live in Isla Vista drink beer. Jane is a woman who lives in Isla Vista. So, Jane drinks beer. (If the premises are true, then it follows necessarily that Jane drinks beer.)

Is the following argument valid or invalid? Sound or unsound? Example Hillary is not the president. Neither Jill Stein nor Gary Johnson is the president. Hence, Trump is the president.

Invalid and unsound. Although all the premises and the conclusion are actually true, it is possible for the premises to be true and the conclusion false (suppose Bernie were president instead of Trump; then the premises would have been true and the conclusion false), hence it's invalid. And since it's invalid, it's also unsound.

Is the following argument valid or invalid? Sound or unsound? Example If Trump is president, then liberals are pissed. Liberals are pissed, therefore Trump is president.

Invalid and unsound. It's possible for the premises to be true and the conclusion to be false (suppose Ted Cruz had won instead; then the premises would have been true and the conclusion false), so it's invalid. And since it's invalid, it's also unsound.

example of hasty generalization

Lawyers are dishonest. My two brothers are lawyers, and they've been lying about everything their whole lives. The inference from two lawyers to all or most lawyers is weak. This is why anecdotes (stories about one's personal experience) typically do not provide good support for generalizations.

example of red herring fallacy

Opponent's position: There's no good evidence for God's existence. All of the arguments in favor rely on questionable metaphysical assumptions or highly speculative historical claims. The diversion: Not true! If people don't believe in God, there's nothing to stop them from cheating, stealing, and killing each other. Life without God is a pointless exercise in hedonistic pursuit, and before you know it, you're dead and gone forever.

example of straw man fallacy

Opponent's position: We should institute a small tax on companies that pollute, since that's the most effective way to disincentivize harming the environment. The distortion: She thinks the government should take all of our money and control every aspect of our lives, since we're too stupid to make decisions on our own.

Identify the premises and conclusion: Example Factory farming involves inflicting a shitload of suffering on sentient beings. We should abolish this harmful practice. After all, it is unnecessary for human survival.

Premises: (1) Factory farming involves inflicting a shitload of suffering on sentient beings. (2) Factory farming is unnecessary for human survival. Conclusion: (3) Hence, we should abolish the harmful practice of factory farming.

Identify the premises and conclusion: Example My grandfather wasn't a monkey, and I've never seen a monkey turn into a man. Hence, the theory of evolution is bullshit.

Premises: (1) My grandfather wasn't a monkey. (2) I've never seen a monkey turn into a man. Conclusion: (3) Hence, the theory of evolution is bullshit. (This way of structuring an argument is called 'standard form', with separate lines for each statement (premises/conclusion) and a line separating the last premise from the conclusion.)

example of biased sample

Recently, a sample of American Catholics revealed that 85% believe that abortion is morally wrong. So, evidence shows that most Americans believe that abortion is morally wrong. The sample surveyed only Catholic Americans, but the conclusion generalizes to all Americans.

Fallacy of diversion? If so, which one? Example You claim that Trump is incompetent and a liar, and does whatever he's told to enrich his billionaire friends? WRONG! Crooked Hillary is totally corrupt and pro-abortion! SAD!

Red Herring fallacy; the speaker diverts the discussion from a criticism of Trump to a criticism of Hillary Clinton

Appeal to Unqualified Authority

Relies on the opinions of people who have no expertise, training, or knowledge relevant to the issue at hand.

Generalization fallacy? If so, which one? Example We all know dogs have four legs. So that little furry, three-legged creature over there must be some sort of weird rodent. Get that ****ing thing away from me.

Rigid application of a generalization; clearly the generalization "dogs have four legs" is not universal (dogs typically have four legs, but there are obviously exceptions due to accidents, birth defects, etc.)

A sentence that is either true or false Every "blank" has a truth value (either true or false)

Statement

Fallacy of diversion? If so, which one? Example I can't believe you think the theory of evolution is a good explanation of the diversity of life. You actually think that a billion years ago, a fish mated with a monkey and had a mutant child who turned into a human? That's crazy.

Straw Man fallacy; the speaker is painting an inaccurate picture of the theory of evolution in order to make it sound implausible and easily refutable

Is the argument strong or weak? Example Only a tiny percentage of liberals like Trump. Stu is a liberal. So, Stu does not like Trump.

Strong. If the premises are true, the conclusion is made probable.

Does the added premise strengthen or weaken the argument? Example I took a poll of 30 college students. 27 of them said that they support Trump. Most college students support Trump. Added premise: I only polled members of the College Republicans Club.

The added premise weakens the argument. The added information tells us that the sample of college students polled may not be representative of the population of college students as a whole, which lowers the chances of the conclusion being true (given true premises).

Does the added premise strengthen or weaken the argument? Example That first apple you bought tasted terrible. That second apple you bought also tasted terrible. Most apples just taste terrible. Added premise: The apples you bought were rotten.

The added premise weakens the argument. The added premise lowers the chances (to some extent) of the conclusion being true (given true premises), since we've learned that the apples that tasted bad weren't representative of apples in general.

Unsound argument

The argument is invalid OR at least one premise is false

Is the following argument valid or invalid? Sound or unsound? Example If Bernie is president, then the president is a democratic socialist. The president is not a democratic socialist, therefore Bernie is not president.

Valid and sound. It's impossible for the premises to be true and the conclusion to be false (so it's valid). And all the premises are true (so it's sound).

Is the following argument valid or invalid? Sound or unsound? Example If it's snowing in Santa Barbara, then UCSB classes are cancelled. It's snowing in Santa Barbara. Therefore, UCSB classes are cancelled.

Valid, but unsound. It's impossible for the premises to be true and the conclusion to be false (so it's valid), but the premises aren't all true (so it's unsound).

Principle of charity

We should choose the reconstructed argument that gives the benefit of the doubt to the person presenting the argument.In other words, reconstruct the argument in a more reasonable way,

Generalization fallacies:

Weak (or invalid) inferences from particular cases to general principles or vice versa

Is the argument strong or weak? Example Most politicians are liars. Jones is a liar. Thus, he's a politician.

Weak. Even if both premises are true, they do not support the probable truth of the conclusion. Compare "Most politicians are liars. Jones is a politician. Thus, he's a liar." This is a strong inductive argument.

Is the argument strong or weak? Example Most (by which I mean two thirds) people in the class are conservatives, and most people in the class are religious. So, if you choose a person from the class at random, he or she will be a religious conservative.

Weak. Even if both premises are true, they do not support the probable truth of the conclusion. Let's simplify and suppose the class only has three people: A, B, and C. If A and B (but not C) are conservative, and B and C (but not A) are religious, then the premises are true but the conclusion is not probable (only 1/3 chance of picking a religious conservative at random). Good form: All Fs are G. Bad form: Most Fs are G. (deductive) All Gs are H. (inductive) Most Gs are H. So, this F is H. So, this F is H.

Is the argument strong or weak? Example I've rolled the die fifteen times, and so far, I haven't rolled an odd number once! So, the next roll is bound to be an odd number. After all, I'm due!

Weak. Even if the premises are true, they do not support the probable truth of the conclusion. No matter what you've rolled in the past, the chance of rolling an odd number remains at 3/6 = 1/2 (assuming the die is fair).

Ad hominem circumstantial

When a claim is rejected based on the life circumstances of the person making the claim.

Equivocation

When the inference in an argument relies on an intentional or unintentional shift in the meaning of a term or phrase. When a word appears multiple times in an argument, but it is used differently in different places, an argument that appears valid may not be

Truth value analysis

determines if the information in the premises is accurate, correct, or true (is it a true or false statement?)

Logical analysis

determines the strength with which the premises support the conclusion (is it a valid or invalid argument?).

Your back injury occurred because you lifted weights without first getting a physical checkup.

explanation)Your back injury occurred (explanandum; an already accepted fact that needs to be explained) because you lifted weights without first getting a physical checkup (explanans; does the explaining).


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