Critical Thinking Lecture 9 Translating a Categorical Claim into Standard Form By David Kelsey

Standard Form Categorical Claims As a reminder, the Standard form Categorical Claims look like this: A claims have the following form: All ___ are ___. For example, All tigers are mammals. E claims have the following form: No ___ are ___. For example, No sharks are plants. I claims have the following form: Some ___ are ___. For example, Some soccer players are basketball players. O claims have the following form: Some ___ are not ___. For example, Some surfers are not great students. And if you will remember TERMS go in the blanks in each Standard form Categorical claim and a TERM must be either a noun or noun phrase.

Translating a categorical claim into standard form Although Categorical Logic cannot manipulate a categorical claim that isn’t in Standard Form, in such a case we can turn the categorical claim into Standard Form. To turn a Categorical Claim into Standard Form you must simply figure out which type of claim it is, A, E, I, or O and then just substitute in the claim’s terms. Find the Standard form categorical claim to which its meaning is the same. For example, if we have the claim every tiger is a mammal this means the same as All tigers are mammals.

Translating A and E claims Since A claims begin with the word ‘All’ when we see a synonym of ‘All’ in a claim it is usually an A claim. Each person at the event is participating translates as All people at the event are participants. If you are a surfer then you can swim translates… Anyone in the room is a Critical thinking student translates… Each and every tiger is a man eating creature translates… Since E claims begin with the word ‘No’ when we see a synonym of ‘No’ in a claim it is usually an E claim. None of the people in the pizza place paid full price translates as: No people in the pizza place are people who paid full price. There are zero people at the game who like the Dodgers translates The coffee shops around here are never open late translates Minors aren’t eligible translates

Translating I and O claims Since I claims begin with the word ‘Some’ when we see a synonym of ‘Some’ in a claim it is usually an I claim. A few of the people in this room believe in ghosts translates as: Some people in this room are people who believe in ghosts. Most politicians are liars translates In some cases politicians tell the truth translates Anytime we see a synonym or something like ‘Some are not’ we usually translate as an O claim. Most of the voters aren’t independent translates as: Some voters are not independent voters. A few of the books aren’t paperbacks translates There are students who don’t study translates as Claims that have a ’not…all’ also translate as O claims. Not all ducks are great swimmers translates

Double negatives In most cases when we have two negatives in a claim we can translate as an affirmative claim. There are no doctors who are not also graduates of medical school translates as: All doctors are medical school graduates. No one ate lunch except for the hungry ones translates as: All people who ate lunch are hungry people. Nobody passes who didn’t put in some serious time studying translates

Translating into present tense All standard form categorical claims must be in the present tense. So if we have a claim that is in the past tense we just translate our terms in the past tense. For example, there were people here last night who drank beer translates as: Some people who were here last night are people who drank beer. Many of the cowboys in this country from centuries ago were wild gunslingers capable of murder translates

Translating Only Consider the claim only people over 21 can get into the bar. When we see the word ‘only’ in a claim it is almost always an A claim. Notice this claim is about the people who can get into the bar. So the claim translates as: All people who can get into the bar are people over 21.

The Only Now consider the claim the only people to get a seat are people who arrived early. When we see the phrase ‘the only’ in a claim it is also almost always an A claim. Notice in this case this claim is about the people who got a seat. So the claim translates as: All people who got a seat are people who arrived early.

Rules for Only & The Only The word ‘only’ introduces the predicate term of an A claim. We considered the claim: only people over 21 can get into the bar. Here ‘only’ introduces the predicate, so people over 21 is the predicate of an A claim. So we get All people who can get into the bar are people over 21. The phrase ‘the only’ introduces the subject term of an A claim. We considered the claim The only people to get a seat are people who arrived early. Here ‘the only’ introduces the subject, so people who got a seat is the subject of an A claim So we get All people who got a seat are people who arrived early.

Times Consider I always get nervous when I take logic exams. This claim is about certain times, in particular the times I take logic exams. What clues us in to this is the word ‘when’. The claim says whenever it is a time in which I take a logic exam, it is a time in which I am nervous. So we translate as…

Places Now consider He makes trouble wherever he goes. The clue here is the word ‘wherever’. The claim says wherever it is a place he goes, it is a place in which he makes trouble. So we translate as…

Single Individuals Lastly, consider a claim about some particular person like Aristotle is mortal. This is tricky because a single individual isn’t a class of things. But for any single individual there is the class of things that are identical to that individual and this class includes all and only that individual. So our claim translates as All people identical to Aristotle are mortal beings.