Logic & Reasoning

Logos The “logic” of an argument Go over other 3 elements- why focus on logos?

Facts Represent “truth” Credible Origins Use in non-debatable way Example: “In 2014, the official poverty rate was 14.8 percent. There were 46.7 million people in poverty. Neither the poverty rate nor the number of people in poverty were statistically different from the 2013 estimates” – US Census Bureau Want to use facts to support your point in a completely non-debatable way. Present them as the “truth” or verification via the credibility and placement -if doing an essay on poverty in the Usa and its exacerbation w/ new media then use fact from US census bureau-> Have to contextualize it

Facts Census, Official Government websites, Empirical Studies by Universities Secondary source information Locations include: (on slide)

Examples In real life observed In real life read about Events/things audience can relate to When visiting the library, there were a large number of homeless people there. Since the library is a public place, this emphasizes the amount of people living below the poverty in big cities. Examples give the reader a toe-hold. Always follow up a claim with facts or examples.

Precendents Use historical and personal from the past Want to make sure to contextualize these for reader (in case they have no knowledge of it) Ex: First amendment for the constitution has been used by individuals defending religious rights and freedom of practicing religion for over a century. This type of argument about lifestyle choices has similarly been used in the recent changes to marriage laws, which now allow the LGBTQ community an equal opportunity.

Authority Judged of quality timely Don’t use sources that are 60 years old unless for precedents

Propositional Logic Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements.  In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement.

Statements A statement can be defined as a declarative sentence, or part of a sentence, that is capable of having a truth-value, such as being true or false. So, for example, the following are statements: George W. Bush is the 43rd President of the United States. Paris is the capital of France. Everyone born on Monday has purple hair. Sometimes, a statement can contain one or more other statements as parts. Consider for example, the following statement: Either Ganymede is a moon of Jupiter or Ganymede is a moon of Saturn. In the second case there are 2 statements one of which is true- The term proposition is sometimes used synonymously with statement. However, it is sometimes used to name something abstract that two different statements with the same meaning are both said to "express". In this usage, the English sentence, "It is raining", and the French sentence "Il pleut", would be considered to express the same proposition; Paris capital of France or the Capital of France is Paris.

Example of PL Paris is the capital of France and Paris has a population of over two million. Therefore, Paris has a population of over two million. In English, words such as "and", "or", "not", "if ... then...", "because", and "necessarily", are all operators Propositional logic, also known as sentential logic, is that branch of logic that studies ways of combining or altering statements or propositions to form more complicated statements or propositions. Joining two simpler propositions with the word "and" is one common way of combining statements. When two statements are joined together with "and", the complex statement formed by them is true if and only if both the component statements are true. Because of this, an argument of the following form is logically valid -Propositional logic can be thought of as primarily the study of logical operators. A logical operatoris any word or phrase used either to modify one statement to make a different statement, or join multiple statements together to form a more complicated statement.

Deductive Pattern: P If P then Q So, Q Because deductive arguments are those in which the truth of the conclusion is thought to be completely guaranteed and not just made probable by the truth of the premises, if the argument is a sound one, then the truth of the conclusion is said to be "contained within" the truth of the premises; that is, the conclusion does not go beyond what the truth of the premises implicitly requires. A deductive argument is an argument that is intended by the arguer to be (deductively) valid, that is, to provide a guarantee of the truth of the conclusion provided that the argument's premises (assumptions) are true. This point can be expressed also by saying that, in a deductive argument, the premises are intended to provide such strong support for the conclusion that, if the premises are true, then it would be impossible for the conclusion to be false. An argument in which the premises do succeed in guaranteeing the conclusion is called a (deductively) valid argument. If a valid argument has true premises, then the argument is said to be sound The difference between the two kinds of arguments does not lie solely in the words used; it comes from the relationship the author or expositor of the argument takes there to be between the premises and the conclusion. If the author of the argument believes that the truth of the premisesdefinitely establishes the truth of the conclusion (due to definition, logical entailment, logical structure, or mathematical necessity), then the argument is deductive

Inductive Inductive arguments might conclude with some claim about a group based only on information from a sample of that group. Other inductive arguments draw conclusions by appeal to evidence or authority or causal relationships. EXAMPLE: Two independent witnesses claimed John committed the murder. John's fingerprints are the only ones on the murder weapon. John confessed to the crime. So, John committed the murder. An inductive argument is an argument that is intended by the arguer merely to establish or increase the probability of its conclusion. In an inductive argument, the premises are intended only to be so strong that, if they were true, then it would be unlikely that the conclusion is false. There is no standard term for a successful inductive argument. But its success or strength is a matter of degree, unlike with deductive arguments. A deductive argument is valid or else invalid.

Differences It is all in the evidence Because the difference between inductive and deductive arguments involves the strength of evidence which the author believes the premises to provide for the conclusion, inductive and deductive arguments differ with regard to the standards of evaluation that are applicable to them. The difference does not have to do with the content or subject matter of the argument. Indeed, the same utterance may be used to present either a deductive or an inductive argument, depening on the intentions of the person advancing it. 

In groups respond to the following writing prompt: New Media effects education, particularly at the college and highschool level. Use at least 1 form of each: facts, precedents, authority (2nd source), deductive statement and inductive reasoning.