Due Date:

2/9/2018
Subject:

English 10

## Valid propositional forms of logical syllogisms

**Modus ponens**

One valid argument form is known as modus ponens, not to be mistaken with modus tollens which is another valid argument form that has a like-sounding name and structure. Modus ponens (sometimes abbreviated as MP) says that if one thing is true, then another will be. It then states that the first is true. The conclusion is that the second thing is true. It is shown below in logical form.

If A, then B

A

Therefore B

Before being put into logical form the above statement could have been something like below.

If Kelly does not finish his homework, he will not go to class

Kelly did not finish his homework

Therefore, Kelly will not go to class

The first two statements are the premises while the third is the conclusion derived from them.

**Modus tollens**

Another form of argument is known as modus tollens (commonly abbreviated MT). In this form, you start with the same first premise as with modus ponens. However, the second part of the premise is denied, leading to the conclusion that the first part of the premise should be denied as well. It is shown below in logical form.

If A, then B

Not B

Therefore not A.

When modus tollens is used with actual content, it looks like below.

If the Patriots win the Super Bowl, there will be a party in Boston that night

There was no party in Boston that night

Therefore, the Patriots did not win the Super Bowl

**Hypothetical syllogism**

Much like modus ponens and modus tollens, hypothetical syllogism (sometimes abbreviated as HS) contains two premises and a conclusion. It is however, slightly more complicated than the first two. In short, it states that if one thing happens, another will as well. If that second thing happens, a third will follow it. Therefore, if the first thing happens, it is inevitable that the third will too.^{[3]} It is shown below in logical form.

If A, then B

If B, then C

Therefore if A, then C

When put into words it looks like below.

If it rains today, I will wear my rain jacket

If I wear my rain jacket, I will keep dry

Therefore if it rains today, I will keep dry

**Disjunctive syllogism**

Disjunctive syllogism (sometimes abbreviated DS) has one of the same characteristics as modus tollens in that it contains a premise, then in a second premise it denies a statement, leading to the conclusion. In Disjunctive Syllogism, the first premise establishes two options. The second takes one away, so the conclusion states that the remaining one must be true.It is shown below in logical form.

Either A or B

Not A

Therefore B

When used A and B are replaced with real life examples it looks like below.

Either you will see Joe in class today or he will oversleep

You did not see Joe in class today

Therefore Joe overslept

Disjunctive syllogism takes two options and narrows it down to one.

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**Constructive dilemma**

Another valid form of argument is known as constructive dilemma or sometimes just 'dilemma'. It does not leave the user with one statement alone at the end of the argument, instead, it gives an option of two different statements. The first premise gives an option of two different statements. Then it states that if the first one happens, there will be a particular outcome and if the second happens, there will be a separate outcome. The conclusion is that either the first outcome or the second outcome will happen. The criticism with this form is that it does not give a definitive conclusion; just a statement of possibilities. When it is written in argument form it looks like below.

Either A or B

If A then C

If B then D

Either A or B

Therefore either C or D

When content is inserted in place of the letters, it looks like below.

Bill will either take the stairs or the elevator to his room

If he takes the stairs, he will be tired when he gets to his room

If he takes the elevator, he will miss the start of the football game on TV

Bill either takes the stairs or the elevator to his room

Therefore Bill will either be tired when he gets to his room or he will miss the start of the football game

**Destructive Dilemma**

There is a slightly different version of dilemma that uses negation rather than affirming something known as destructive dilemma. When put in argument form it looks like below.

If A then C

If B then D

Not C or not D

Therefore not A or not B

When content is inserted in place of the letters, it looks like below.

Bill will either take the stairs or the elevator to his room

If he takes the stairs, he will be tired when he gets to his room

If he takes the elevator, he will miss the start of the football game on TV

Bill either does not take the stairs or does not take the elevator to his room

Therefore Bill will either not be tired when he gets to his room or he will not miss the start of the football game

**Fallacies and their Assumptions and Problems**

*A list of some logical fallacies*

All logical arguments draw conclusions from given evidence. A logical argument is an argument that makes a reasonable assumption to get to its conclusion. An illogical or *fallacious *argument draws a conclusion that is not supported by the stated evidence. **Most logical fallacies have a particular assumption associated with them. Any time you lay out an argument that commits that fallacy, the assumption will be the same.** These assumptions are listed below.

**BE WARNED!!! DO NOT JUST BLINDLY PLUG THESE PHRASES INTO YOUR REFUTATION WITHOUT ALTERING THEM TO FIT THE ARGUMENT! JUST LIKE ALL OTHER ASPECTS OF LOGIC, YOU NEED TO THINK CRITICALLY ABOUT WHETHER OR NOT YOUR REFUTATION MAKES SENSE AND WHETHER OR NOT YOUR REFUTATION ACTUALLY RESPONDS TO THE ARGUMENT.**

**Hasty Generalization**- The argument assumes that if (#) members of a group have a characteristic in common, then all members of that group also have that trait.

**Slippery Slope**- The argument assumes that if _____ happens then the only possible outcome is _____ (the nightmare scenario the argument describes), and that that is not a desirable outcome (i.e. We do not want that to happen).

**False Dichotomy**- The argument assumes that there are only two choices or possible outcomes, and that one outcome is very undesirable, so the only reasonable choice is the other one. **Whenever you cite a False Dichotomy you MUST give a counterexample, a third option or possible outcome, to prove that there are more than 2!**

**False Analogy**- The argument assumes that if 2 things are similar in one way, then they are exactly the same in every other way and should be treated the same way. **DO NOT WRITE: **The argument is wrong because _____ has nothing to do with ________. You need to be more specific and descriptive in your response to show why it matters that the two things are unrelated.

**Bandwagon**- The argument assumes that if everyone else is doing something then it must be right. **OR **The argument assumes that the majority is right, but this is not necessarily true because what is popular is not always right and what is right is not always popular.

**Non-Sequitur**- This fallacy does not have a particular assumption attached to it. The assumption depends on the argument itself. In a Non Sequitur the assumption is usually the major premise of the argument, and it is unstated because it is clearly absurd.

**Post Hoc**- This argument assumes that if one event occurred before another event, then the first event must have caused the second event to happen. The argument implies that _____________ happened *because* of _____________, when that is not necessarily the case.

**Arguing from Strength**- This argument assumes that if a person has the ability to enforce their will/take what they want by force, then they have the right to get what they want. The argument assumes that “might makes right,” which is not always true.

**Ipse Dixit**- This argument assumes that _________ is an expert on __________, which is not true.

**Arguing from Ignorance**- This argument assumes that if something has not yet been proven to be true then it must be false/that if something has not yet been proven to be false then it must be true. This argument suggests that if something is possible, then we should act as if it is definitely going to happen.

**Building a Strawman**- This argument assumes that the opponent is saying __________, when they are really saying _____________. The argument exaggerates/distorts the beliefs of the opposition to make the opponent seem irrational/evil/unpatriotic/unintelligent/out of touch/monstrous/etc. This tactic oversimplifies the issue.

**Tu Quoque**- This argument assumes that if one person is wrong but the other person is *more* wrong, then the first person must be right.

**Some fallacies try to distract the reader, to confuse the reader into making a decision based on emotions like fear or pity or scorn, rather than thinking about the argument’s merits and making a rational decision. When refuting these arguments you cannot use the normal refutation formula; you need to adapt to point out the flaw in the argument.**

**Ad Misericordiam- **This argument seeks to distract the reader by making them feel a powerful emotion such as anger, fear, pity or patriotism, so that they will not think too hard about the argument itself. The argument uses provocative, emotional words like _________, __________ and _________ to evoke strong feelings in the reader’s mind that overpower their reason.

**Ad Hominem**- This argument seeks to distract the reader from the argument by mocking or insulting the opponent, instead of pointing out flaws in the opponent’s argument. (This does NOT include an argument that attacks something the person did or said if it has to do with the argument. It’s only Ad Hominem if it is irrelevant to the argument.)

**Begging the Question**- This argument begs the question of whether or not __________. (This author seeks to win the argument by pretending that the question has already been resolved and then using the answer as a premise for a further argument.)

**A Few Other Things to Keep in Mind…**

· I know that you have had a long and passionate love affair with your favorite fallacy, Hasty Generalization, but you NEED to stop applying it to any argument that doesn’t have an obvious fallacy. If you don’t know the fallacy, KEEP THINKING! Don’t just fall back on your ‘safety fallacy.’

**The Real Definition of Hasty Generalization: **

A *generalization* is a statement about a whole group. (All Irish people have red hair; all of the Skittles in this bag are red; everyone in the room is wearing a hat; this class is going to suck)

“Hasty” means too fast, too soon

**Hasty Generalization means making a statement about a whole group based on only a small sample of that group. **(EXAMPLES: I know two Irish people and both of them have red hair, so all Irish people must have red hair; the first 4 Skittles I pulled from by bag were red, so this must be the best bag of Skittles ever, because they are all red; Adam and Courtney are in the room and wearing hats, so everyone in the room must be wearing a hat, too; the first 2 days of this class were awful, so this class is definitely going to be terrible, too.)

· Use a variety of synonyms for “states” and “assumes” in your refutations to avoid sounding repetitious and robotic. You can also vary the sequence of the parts of your refutation.

· End every refutation with a counterexample to show that what the author says is ALWAYS true can be false in some cases. The more specific and detailed your counterexample is the more persuasive your arguments will be.

· **REMEMBER THAT WHEN RESPONDING TO A PERSUASIVE ARTICLE POINT-BY-POINT, THE CONCLUSION OF **EVERY** ARGUMENT IN THEIR ESSAY IS GOING TO BE THE SAME, AND THAT CONCLUSION CAN BE FOUND IN THEIR THESIS SENTENCE IN THE INTRO PARAGRAPH. IT IS THE AUTHOR’S OVERALL POINT OR MAIN IDEA OR THESIS STATEMENT.**