Logic handout

Question 0

Argument

Answer 0

a set of statements consisting of a conclusion and one or more premises supporting that conclusion;
an argument has both factual and inferential claims –
the factual claims are the premises (the putative evidence) and the inferential claim is the assertion (either explicitly stated or just implied) that the premises are logically connected to (give reason to accept) the conclusion. An argument can be evaluated by its inferential connection (its validity or strength) or by the truth value of its premises or both (its soundness or cogency).

Question 1

Logic

Answer 1

reasoning, or the study of reasoning and arguments

Question 2

enthymeme

Answer 2

an argument in which one or more premises, or the conclusion, or both, is left unstated
For example, if someone were to say to you, “There’s a great party scheduled the night before your 8 a.m. exam.  Nobody who wants to do well in that class would go,” there is an implied argument with at least one unspoken premise (you want to do well) and an unspoken conclusion (you won’t go).  Enthymemes are often harmless, because they rely on widely shared background information and common processes of reasoning.  However, they can be problematic when the unstated premise or conclusion is something controversial or false.  It can also be difficult to evaluate the reasoning of the argument if all of the steps are not clearly stated.  For these reasons, recognizing and completing enthymematic arguments is an important skill in philosophy.

Question 3

premise

Answer 3

a statement that is meant to provide evidence for or reason to believe a conclusion
Some phrases or words that are often used to indicate that a statement is a premise are: because; since in light of; considering that; given; seeing as, etc.

Question 4

conclusion

Answer 4

the statement which is to be proved
Some phrases or words that are often used to indicate that a statement is a conclusion are: thus; therefore; so; we can infer; it must be, etc.

Question 5

inferential connection

Answer 5

the reasoning or logical link between a premise or premises and a conclusion
To make an inference is to reason or to make a logical move from some information to a new claim. If an argument has a good inferential connection then it is either valid or strong. An inferential connection is evaluated independently of the truth value of the premises; it is the relevance of the evidence, not its accuracy, that makes an argument valid or strong.

Question 6

deductive

Answer 6

This term is used to evaluate whether or not the inferential connection in an argument is the right type to provide a guarantee that the conclusion is logically implied by the premises.  That is, are the premises designed to make the conclusion unavoidable, logically speaking?
​Some types of argument that are best described as deductive:
arguments from mathematics
arguments from definitions (e.g. “All squares have four sides of equal length.  This shape has 3 sides of unequal length.  Therefore, it is not a square.”
categorical arguments (e.g. “All cats are felines; No felines are dogs; therefore, no cats are dogs.”)

Question 7

non-deductive

Answer 7

This term is used to evaluate whether or not the inferential connection in an argument is the type that just shows probability; That is, are the premises just meant to show that it is likely the case that the conclusion is true? (e.g. “Most U.S. dentists give out Oral-B toothbrushes; they must be the best toothbrushes.” The premise gives us pretty good reason to accept the conclusion, but we can still think of reasons why we might not agree that they’re the best even if we accept the premise.)
​Some types of argument that are best described as non-deductive:
arguments from analogy (e.g. “X is like Y in that they share these properties; Y also has property P; X probably also has P”) – these arguments have to be evaluated in terms of whether or not the shared properties are appropriately related to the new property.
predictions (e.g. “This is happened the past, so this is what will happen in the future.”)
arguments to the best explanation (e.g. “We have observed O. Theory T is the best explanation for O. Therefore, T is probably correct.”)

Question 8

valid

Answer 8

describes a deductive argument in which there is a relationship of logical necessity between the premises and conclusion such that if the premises are true, the conclusion must also be true; the sort of evidence that the premises give is exactly the sort that would guarantee the conclusion’s truth. (In evaluating validity, it doesn’t matter whether or not the premises are actually true; all that matters is whether they provide the right kind of information to support the conclusion in a logically necessary way.)
E.g. “If Angelina Jolie were a man, she would have XY chromosomes. Jolie is a man. Therefore she has XY chromosomes.” The second premise is false, but this is still a valid (but unsound) argument. There is no logical way to deny the conclusion on the basis of the claims made in the premises. If those claims were true, the conclusion would have to be true. Note that ‘valid’ in the logical sense describes arguments (not individual statements), and is much more rigorous than the everyday use of ‘valid.’

Question 9

invalid

Answer 9

describes an argument that does not meet deductive standards for a good inferential connection because the premises do not provide a logical guarantee for the conclusion (it is logically possible to accept the premises and deny the conclusion without any contradiction.)
E.g. “All happy people are smiling people. Joe is smiling. Therefore, Joe is happy.” Even if we accept the premises as true (and the first one is pretty questionable), we are not contradicting them if we deny the conclusion. It is possible Joe is smiling because he sees a camera, or someone threatened him to smile or he’d get hit, or maybe Joe has a facial defect that makes his smile muscles work whatever he is feeling. All of those possibilities mean that the premises could be true while Joe is actually pretty unhappy.

Question 10

soundness

Answer 10

A deductive argument that is valid and has all true premises is sound; if it is invalid, or has a false premise, or both, then it is unsound.

Question 11

strength

Answer 11

This describes the inferential connection of a non-deductive argument; strength comes in degrees and is judged by how probable the premises make the conclusion – if the conclusion is very probably true given the claims of the premises, then the argument is strong, but if the premises do not make the conclusion seem likely to be true, the argument is weak.
E.g. 1 - A very strong argument: “Drug X was given to 6 million victims suffering from a disease that has always been fatal in the past. Over 4 million survived after being given drug X. Drug X seems to be a promising treatment for this disease.” (In evaluating strength, it doesn’t matter whether or not the premises are actually true; all that matters is whether they provide the right kind of information to support the conclusion.)
E.g. 2 – A weak argument: “I took a vitamin once and did not feel healthier afterward, so vitamins don’t contribute to health.”

Question 12

Cogent

Answer 12

A non-deductive argument which is strong and has true premises is cogent; if it is weak, or has a false premise, or both, then it is uncogent.

Question 13

fallacy

Answer 13

A flaw in an argument other than the falsity of one or more of its premises