From Informal Fallacies to Formal Logic

From Informal Fallacies to Formal Logic • Sign In! • Claims • Argument Diagrams (don't worry!) • Argument Structure • Categorical Arguments • Formal Logic • For Next Time: Read Chapter 8 pages 253-257

Claims • A claim is any sentence that can be true or false • We are now experts at identifying claims and separating out claims from non-claims • As we transition from informal logical thinking to formal logical analysis we will need to keep focused on the best ways of translating sentences into claims • We have also already learned a little about the uses of indicators in sentences to help us see how claims are related

Claims (more) • Words like: since, therefore, because, together, separately, implies, etc all have a function in an argument • Although these words are not parts of the claims themselves they do tell us how claims are logically related to one another • “Since we just put the medicine on him, the dog should be flea free in a couple of days” • What are the claims? What is the word 'since' telling us about those claims are related?

Claims (last slide) • Why are we reviewing the premise and conclusion indicators? • We are about to start adding several more indicators to our list that, while not part of the claims themselves, do help us understand how claims are structurally related • All, some, none, and, or, every, most, neither, is, is not, are • These words, when found before or between claims also help us see how claims function in an argument

Argument Diagrams • The most important skills you learned while diagramming arguments were the abilities to identify claims and determine their function within an argument • We will be relying on these skills for much of the rest of the course (though we will not be diagramming arguments in the same way) • Let's take a look at a sample argument

Sample Argument • Since the CLA building was built above a fault line, it will most likely have to be demolished. Also, there aren't any other good options to save the CLA building because it would be too expensive to retrofit it. Therefore the CLA building will most likely have to be demolished.

Sample Argument • Since[the CLA building was built above a fault line], [it will most likely have to be demolished]. Also, [There aren't any other good options to save the CLA building]because[it would be too expensive to retrofit it]. Therefore[the CLA building will most likely have to be demolished]. • How many different claims are there in this argument? • There are 4 claims. Why? Because when we identify claims we do not double count identical claims. We want to make sure to represent the repetition explicitly

Sample Argument (claim focus) • Since[1], [2]. Also, [3]because[4]. Therefore[2]. • The transition from informal to formal logic requires abstraction • We will focus almost entirely on argument structure and not care nearly as much on the content of each argument • If we abstract the content of the claims we get a very familiar looking schematic argument • Because of our argument diagramming experience we also understand what the indicators mean

Sample Argument (last slide) • The CLA argument is an inductive argument • For the next few weeks we will be focusing our attention on deductive arguments and analyzing their structure for validity • A deductive argument, recall, is an argument whose premises are intended to prove the conclusion • If a deductive argument is successful it is sound (valid + true premises) • We won't be as concerned with soundness because soundness is a property of the content of the claims and we will be abstracting away from content

Categorical Claims • When we were learning how to translate arguments into inductive or deductive forms we said that deductive arguments always have a universalizing premise • A categoricalclaim is a type of universalizing premise • Categorical claims relate two groups (categories) of objects with one another • “All monkeys eat bananas” • This claim relates one group (monkeys) with another (banana eaters)

Categorical Claims: Examples • For each categorical claim, tell me what groups are being related AND what the relationship is • All dogs go to heaven • Some textbooks are extremely expensive • Nobody was very late to class • All cars built since 1998 are required to have front and side passenger airbags

Categorical Indicators • Categorical claims have some standard indicators: • All, some, none, every, most, only • All = every single one (no exceptions) • Some = at least one • Every = All = every single one (no exceptions) • None = not a single one • Most = at least one • Only = there is nothing else that is included in the category • We may sometimes have to insert these indicators when we translate a categorical claim formally

Categorical Claims and Abstraction • Just as we did with the informal argument earlier, we can also abstract the content from a categorical claim to clarify the relationships between the two groups in the claim: • All dogs go to heaven (All As are Bs) • Some textbooks are extremely expensive (Some As are Bs) • Nobody was very late to class (...) • All cars built since 1998 are required to have front and side passenger airbags (….) • There was at least one student who forgot to bring their book to class (….)

Categorical Claims and Arguments • Categorical logic is a class of logic that is concerned with explaining the relationships between different groups or different members of groups • Categorical arguments will always contain at least one categorical claim [this sentence itself is a categorical claim] • Categorical arguments are deductive arguments (though they may not succeed, they can be invalid) • Let's take a look at categorical arguments

Familiar Argument Structures • We have seen categorical arguments many times this quarter: • 1. All humans are mortal • 2. Erick is human • 3. :. Erick is mortal • Although our conclusion in this argument is about a particular person (Erick) the first premise is categorical and the conclusion results from the relationships implied by the categorical claim and Erick's membership in a group (humans)

Example 2 • Everyone who gets a college degree is better off. All people who are better off as a result of getting a degree are good to have conversations with at parties. Therefore, everyone who gets a college degree is a good person to have a conversation with at parties. • First let's identify the claims then let's translate the claims into categorical claims

Example 2 • [Everyone who gets a college degree is better off]. [All people who are better off as a result of getting a degree are good to have conversations with at parties]. Therefore, [everyone who gets a college degree is good to have a conversation with at parties.] • Now let's put the argument into standard form

Example 2 • 1. Everyone who gets a college degree is better off • 2. All people who are better off as a result of getting a degree are people who are good to have conversations with at parties • 3. :. Everyone who gets a college degree is a good person to have a conversation with at parties • Notice that we had to modify claims to make the categories clearer • Now that we have the argument in standard form we can begin to translate the claims into categorical claims • What is the best way to translate “everyone”?

Example 2 (again) • 1. ALL [people who get a college degree] ARE [people who are better off] • 2. ALL [people who are better off as a result of getting a degree] ARE [people who are good to have conversations with at parties] • 3. :. ALL [people who get a college degree] ARE [people who are good to have conversations with parties] • Now that we have translated the claims into categorical claims we can abstract the content of the claims to look at the structure

Abstraction • 1. All As are Bs • 2. All Bs are Cs • 3. :. All As are Cs • Now we have the structure of this categorical argument represented clearly • This week we will be able to begin proving why any argument with this structure is valid • But it is important to be able to translate arguments into categorical claims and then abstract the claims in order to do this

For Wednesday • Read Chapter 8 pages 253-257

From Informal Fallacies to Formal Logic