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Argument logic

“One of the most important components of an argument is the logic used when arguing points. In order to properly analyze an argument, we must first determine the strength of each argument made.

Basic Terminology:

Definition: exact meaning of the word, defined through synonyms, examples, and stipulations

Assumptions: accepted as true or certain to happen. It is derived from examples, data, information, background, etc. In an argument, an assumption can be expressed or unexamined/unstated.

Premise: a stated assumption or definition used in an argument.

Deductive reasoning: This form takes a top-down approach. It takes proven premises and connects them to create a conclusion. A valid deductive argument is 100% supporting.

If      A → B

And B → C

Then A → C

Validity and Soundness: A deductive argument is evaluated based on its validity and soundness. Validity examines the link between the premises and conclusion. If the premises logically connect and lead to the conclusion, supporting it 100%, then the argument is valid. Soundness combines validity with fact checking. If all premises are true/acceptable AND the argument is valid, then the argument is sound.

Inductive reasoning: The inductive form uses a bottom-up approach. It takes premises that are observationally based to claim a conclusion that is less than 100% supporting. Although inductive arguments may not be as definitive as deductive arguments, they are useful in situations that do not have absolute certainty. Depending on the circumstances, a “beyond reasonable doubt” inductive argument may be the best, or only, choice.

Causal generalization: Establishes high probability of causation based on correlation.

Sampling: Extrapolates a finding taken from a small audience to a larger audience.

Analogy: Draws parallels between two situations. Analyze situation 1 to generate a particular conclusion. Use the similarities between situation 1 and situation 2 to argue a similar conclusion for situation 2.

Strength and reliability: These two concepts are similar to those of validity and soundness in deductive arguments. Strength examines the link between the premises and conclusions. If the premises support the argument more than 50%, it is strong. Reliability combines strength with fact checking. If all premises are true/acceptable, then the argument is strong.”

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Source: http://www.butte.edu/resources/interim/wmwu/iLogic/1.3/iLogic_1_3.html

Illogical Arguments/ Deductive Fallacies

“A deductive fallacy is a deductive argument that is invalid (it is such that it could have all true premises and still have a false conclusion). An inductive fallacy is less formal than a deductive fallacy. They are simply “arguments” which appear to be inductive arguments, but the premises do not provide enough support for the conclusion. In such cases, even if the premises were true, the conclusion would not be more likely to be true.”

Source: https://aphilosopher.files.wordpress.com/2010/09/42-fallacies.pdf

Examples: Slippery Slope, Strawman Fallacy, Red Herring, Equivocation Fallacy

Slippery Slope

Description: “The Slippery Slope is a fallacy in which a person asserts that some event must inevitably follow from another without any argument for the inevitability of the event in question. In most cases, there are a series of steps or gradations between one event and the one in question and no reason is given as to why the intervening steps or gradations will simply be bypassed. This “argument” has the following form:

  1. Event X has occurred (or will or might occur).
  2. Therefore event Y will inevitably happen.

Logical Form:

Person 1 makes claim X.‘K

Person 1 then escalates claim X to claim Y.

Person 1 then uses claim Y, an extreme version of claim X, to argue the point.”

Source: http://www.nizkor.org/features/fallacies/slippery-slope.html

Examples:

  1. “If we legalize gay marriage, then our children will learn about homosexuality. In that case, they will grow up to be gay!”
  2. “Our mayor wants to repave this road. Yet, if we repave this road, then everyone will ask to have their roads repaved. Then we will have to repave all roads!”
  3. The entire picture book – If You Give a Mouse Cookie by Laura Numeroff

Strawman Fallacy

Description: Arguing against an extreme, distorted, or misrepresented view of someone else’s argument or point.

Logical Form:

“Person 1 makes claim Y.

Person 2 restates person 1’s claim (in a distorted way).

Person 2 attacks the distorted version of the claim.

Therefore, claim Y is false.”

Source: https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/169/Strawman_Fallacy

Example:

Bryan: I believe that we should mildly reduce government financing in schools for appropriate reallocation of funds.

Chris: How can you possibly hate children so much that you do not want them to learn?!

Bryan: That is not at all what I am saying….

Explanation: Chris warped Bryan’s perspective of fund reallocation into Bryan hating children.

Red Herring

Description: “Attempting to redirect the argument to another issue that to which the person doing the redirecting can better respond. While it is similar to the avoiding the issue fallacy, the red herring is a deliberate diversion of attention with the intention of trying to abandon the original argument.

Logical Form:

Argument A is presented by person 1.

Person 2 introduces argument B.

Argument A is abandoned.”

Source: https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/150/Red_Herring

Example:

Laura: How could you have embezzled money from the company?

Claire: What even is appropriate distribution of money? 

Laura: Company revenue can be reinvested into the company, distributed to stock holders, or placed into the stock market.

Claire: It can also be used to cover expenses and pay back loans!

Explanation: Claire successfully diverted this conversation from her stealing to the concept of revenue usage through a misdirecting question.

Equivocation Fallacy

Description: “The fallacy of equivocation is committed when a term is used in two or more different senses within a single argument. For an argument to work, the words must have the same meaning each time they appear in its premises or conclusion. Arguments that switch between different meanings of words equivocate, and so don’t work. This is because the change in meaning introduces a change in subject. If the words in the premises and the conclusion mean different things, then the premises and the conclusion are about different things, and so the former cannot support the latter.

Logical form:

Person 1 defines WORD.

Person 1 defines WORD differently.

Person 1 uses the two definitions to construct a misleading argument.”

Source: http://www.logicalfallacies.info/ambiguity/equivocation/

Example:

  • An ambulance is a type of car.
  • An ambulance is a lifesaving device.
  • Therefore, cars are lifesaving devices.