Taxonomy of Arguments
Arguments attempt to
provide good reasons why we should believe a particular claim. The claim one intends
to support is the conclusion of the argument, and the premises of the argument
are the reasons given to support it. ‘Inference’ and ‘reasoning’ are synonyms
for ‘argument’.
A. Categorical Logic – The basic unit of these arguments is the category, which takes the form of a noun with qualifiers (e.g., dogs, used books, overseas vacations). Categories are related to one another in categorical statements (e.g., ‘All dogs are mammals’, or ‘Some words are not verbs’). A categorical syllogism attempts to prove that a categorical statement is true by drawing on relationships between categories of inclusion and exclusion.
Uses: This type of logic is utilized to establish the relationship between two categories. It is especially useful when determining what properties things have, determining where they fall within a taxonomy, when applying general concepts or rules to particular cases, and when arguing for moral claims (e.g., “All violence is immoral”).
Tests for Validity: Venn Diagrams, Rules for Categorical Syllogisms
Examples: EIO-2 (Valid) (Argument Form)
1. No dogs are reptiles. 1. No P are M
2. Some animals are reptiles. 2. Some S are M
3. Therefore, some animals are not dogs. 3. Therefore, some S are not P
AII-4 (Invalid) (Argument Form)
1. All dogs are mammals. 1. All P are M
2. Some mammals are birds. 2. Some M are S
3. Therefore, some birds are dogs. 3. Therefore, some S are P
B. Propositional Logic – The basic unit of these arguments is the proposition or statement rather than the category; statements are modified or joined together with various logical operators, such as negation (‘no’, ‘not’), disjunction (‘or’), conditional (‘if … then …’), and conjunction (‘and’).
Uses: This type of logic has the widest range of application since it can be used to prove the truth of any type of statement. Propositional Logic is used extensively in the disciplines of mathematics, computer science, and electrical engineering. For example, it played a central role in establishing the foundations of mathematics and in the development of computers and digital electronics.
Tests for Validity: Truth Tables, Natural Deduction
Examples: Modus Tollens (Valid) (Argument Form)
1. If I drop the glass then it will break. 1. If A then B
2. The glass didn’t break. 2. Not B
3. Therefore, I must not have dropped it. 3. Therefore, not A
Denying the Antecedent (Invalid) (Argument Form)
1. If I graduated then I passed Composition. 1. If A then B
2. I didn’t graduate. 2. Not A
3. Therefore, I didn’t pass Composition. 3. Therefore, not B
II. Inductive – Arguments that intend to provide probable support for the conclusion – i.e., to demonstrate that the conclusion has a greater than 50% likelihood of being true. Inductive arguments never prove the truth of the conclusion with certainty because the inference depends on empirical knowledge which may be fallible or incomplete. As a result, doubt can never be completely eliminated. The degrees of possible support span the continuum from zero to 99.9% probability. In contrast to deductive arguments, inductive arguments are additive, i.e., it is always possible to further strengthen or weaken the argument through the discovery of additional evidence. If an inductive argument has the correct logical structure, it is strong. It is cogent or successful at proving that the conclusion has a greater than 50% likelihood of being true when it is (1) strong and (2) has all true premises.
A. Inductive Generalization – Argues from an observation about some members of a group (the sample) to a generalization about the entire group (the population).
Uses: This type of logic enables us to identify empirical patterns and formulate them as generalizations (e.g., “73% of Americans want the policy to be changed”). Polls and statistical arguments are forms of Inductive Generalization, and so is one version of the Scientific Method: Laws of nature (e.g., “The sun always moves from east to west in the sky”) are generalizations, and are often supported through the use of Inductive Generalization.
Criteria for Strength: How closely the sample represents the population, which is a matter of:
(1) Correlation – Whether there are one or more additional properties that are highly correlated with the property mentioned in the conclusion.
(2) Explanation – Whether there is a plausible explanation for the high correlation of these properties, which would confirm that the correlation isn’t merely a matter of chance.
(3) Representativeness – Whether the sample represents the population well in terms of these additional properties.
Examples: Strong Generalization
1. 73% of 1000
2. In the sample, views about issues of public spending are highly correlated with the demographic features political affiliation, age, and income. (Correlation)
3. This correlation isn’t surprising because the majority of the members of these demographic groups and their family members would directly benefit from increased spending on education. (Explanation)
4. The sample represents the population well in terms of political affiliation, age, and income. (Representativeness)
5. Therefore, it is probably the case
that 73% of all
Weak
Generalization (sample size too small)
1. Most salespeople I have met are not trustworthy.
2. Therefore, it is probably the case that the majority of salespeople are not trustworthy.
Weak Generalization (biased sample)
1. 99% of 1200 NRA members polled opposed laws banning the possession of handguns.
2. Therefore, it is probably the
case that 99% of all
Argument Form:
Complex Version
1. The Sample has the Relevant Property.
2. The Relevant Property is highly correlated with one or more Additional Properties.
3. A plausible explanation for this correlation.
4. The Additional Properties are well-represented by the Sample.
5. Therefore, the Population probably has Relevant Property.
Simple Version
1. The Sample has the Relevant Property.
2. Therefore, the Population probably has the Relevant Property.
B. Argument from Analogy – This argument compares two (or more) things, and infers that because the first thing shares one or more features in common with the second thing, it is probably similar in some further respect.
Uses: This form of argument is very versatile, since virtually any statement can be established on the basis of comparison. Arguments from Analogy are used especially to establish factual or normative claims when there is no general principle or precedent, and are used extensively in legal and moral reasoning.
Criteria for Strength: How strong the analogy is between these things, which is a matter of:
(1) Correlation – Whether there is a high correlation between the two properties mentioned in the first premise. The analogy can be strengthened by citing more things that share both properties, especially a diverse group of things, or by citing more relevant properties that the things share in common. It can be weakened by citing relevant differences, i.e., properties that are highly correlated with the property inferred in the conclusion that are found in the analogue but not the thing cited in the conclusion.
(2) Explanation – Whether there is a plausible explanation for the high correlation of these properties, which would confirm that the correlation isn’t merely a matter of chance.
Examples: Strong Analogy
1. I am a human being and aspirin is a safe and effective pain medication for me.
2. Jane is also a human being.
3. There is a high correlation between the effects of a medication like aspirin and the species a creature is a member of. (Correlation)
4. This correlation isn’t surprising since the effects of a medication depend on how it interacts with particular physiological features, and a creature’s physiological features are determined to a great extent by what type of species it is. (Explanation)
5. Therefore, aspirin is probably a safe and effective pain medication for Jane.
Weak Analogy
1. Me and Fido are both mammals.
2. Aspirin is a safe and effective pain medication for me.
3. Therefore, aspirin is probably a safe and effective pain medication for Fido.
Argument Form:
Complex Version
1. Thing A has Property 1 and Property 2.
2. Thing B has Property 1.
3. There is a high correlation between Property 1 and Property 2.
4. A plausible explanation for this correlation.
5. Therefore, Thing B probably has Property 2.
Simple Version
1. Thing A has Property 1 and Property 2.
2. Thing B has Property 1.
3. Therefore, Thing B probably has Property 2.
C. Causal Arguments – Any inductive argument whose conclusion consists in a causal claim (e.g., “The accident was caused by icy roads”). These can include any of the other types of inductive arguments. However, causal arguments normally use Mill’s methods and the process of elimination to identify the cause.
Use – This argument is used to prove that a particular thing or event is probably the cause of a particular effect, and applies only to causal explanations.
Criteria for Strength – (1) Correlation (Mill’s methods) – Whether there is a high correlation between the presence and absence of the cause and effect, or between the increase or decrease of certain properties. Each of Mill’s methods requires a different type of correlation.
(2) Explanation – Whether the cause is the sort of thing that could be the cause of this effect. This would confirm that the correlation isn’t merely a matter of chance and that one has avoided causal confusions such as being misled by coincidence or mixing up the cause and the effect.
Examples: Strong (Mill’s method of agreement)
1. My phone goes dead quite frequently, and it could be caused by a computer error at the phone company, a utility pole being knocked over, or a short in the cord.
2. It happens whenever I pull on the cord, and the other possible causes don’t occur as frequently as the effect. (Correlation)
3. A short in the cord is the sort of thing that could cause a phone to go dead. (Explanation)
4. Therefore, a short in the cord is probably the cause of my phone going dead.
Weak (misled by coincidence)
1. An hour after I changed the color of my socks, my headache went away.
2. Therefore, the color of my socks probably caused my headache.
Argument form:
1. A description of the effect and an exhaustive list of its possible causes.
2. (A) Only one of these causes satisfies Mill’s method of agreement, difference, or the joint method; or (B) One of the causes is highly correlated with the effect and is more highly correlated than the other causes.
3. A plausible explanation of the relationship between this cause and the effect.
4. Therefore, this cause is probably the cause of the effect.
D. Inference to the Best Explanation – This type of argument attempts to identify the best explanation of a particular phenomenon by comparing the virtues and vices of all the available explanations.
Uses – Unlike Causal Arguments, Inferences to the Best Explanation can be applied to all types of explanations, including causal explanations, teleological explanations, interpretive explanations, and procedural explanations. They are used to prove that a particular thing, event, act, or meaning is probably the best explanation of a particular phenomenon. The version Scientific Method involving the formation and testing of hypotheses is a form of this argument.
Criteria for Strength – The internal and external consistency of the explanation, the amount of confirming evidence, and the criteria of adequacy, i.e., the testability, fruitfulness, scope, simplicity, and conservatism of the explanation.
Examples: Causal Explanation
1. Crop circles are either caused by genetic defects in some of the plants, by extraterrestrials, or by pranksters.
2. The genetic defects explanation is externally inconsistent with laboratory tests of the plants.
3. The prankster explanation is easier to test and more conservative than the extraterrestrial explanation.
4. Therefore, the prankster explanation is probably the best explanation of crop circles.
Interpretive Explanation
1. When Mike said that he likes my new shoes, he was either being truthful, being sarcastic, or merely being polite.
2. The politeness interpretation is externally inconsistent because Mike has a reputation for speaking his mind and never restrains himself out of politeness.
3. Although the truthfulness interpretation would be a simpler explanation, the sneering tone of his voice provides substantial evidence that he was intending to be sarcastic.
4. Therefore, the sarcasm interpretation is probably the best explanation.
(A weak Inference to the Best Explanation is one that doesn’t properly consider all of the relevant explanations or all the relevant criteria for strength.)
Argument Form:
1. A description of what is being explained and an exhaustive list of the relevant explanations.
2. List any explanations with internal or external inconsistencies, and eliminate them from consideration.
3. List any advantages the remaining explanations have over one another in terms of the criteria of adequacy and the amount of evidence supporting them, and indicate which one has the greatest advantages.
4. Therefore, the explanation with the greatest advantages is probably the best explanation.
III. Informal Fallacies – Faulty arguments that provide no support (invalid) or insufficient support (weak) for the conclusion, due to the type of reason given rather than the form of the argument. Informal Fallacies are deceptive because they appear to be good arguments. They gain this appearance through sleight of hand, by exploiting our psychological insecurities, or by appealing to our emotions.
Use: To deceptively persuade someone to accept a conclusion when no logically relevant reasons can be found. Fallacies are used extensively in advertising and political discourse.
Examples: Appeal to Illegitimate Authority
1. Jane Doe, the Nobel prize winner in chemistry, claims that our economic policies will eventually bankrupt the country.
2. Therefore, our economic policies will eventually bankrupt the country.
Equivocation
1.
Really exciting
novels are rare.
2. But rare books are
expensive.
3. Therefore, really
exciting novels are expensive.