Reasoning, Critical Thinking, and Changing Minds

 How arguments work:

  1. Arguments from Analogy

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Conceptual Analysis

Conceptual analysis is kind of like giving definitions: Conceptual Analysis : A description of constituent properties of a complex property or relation. Some complex property is usually built up of simpler properties. An example of a conceptual analysis is: X is a triangle = df. X is a shape with exactly three angles and straight lines in Euclidean space. This is more than a definition is picking out some properties of a property. Also, = df. means by definition. Another example: X is a bachelor = df. X is an unmarried man. Here a conceptual analysis is: Non-circular, the analysis refers to properties that aren’t the same thing as itself. It tries to include everything it intends to include and exclude what it intends to not exclude. It tries to pick out the properties that do this. (It’s not possible to have one condition without the other). Conceptual analysis helps you: Understand reality : reality contains things with properties, and conceptual analysis picks out properties...
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Discrete Math - Other Set Theory Basics

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The power set of set S is the set of all ways of selecting members from set S. This can be done in many ways. Example, say that S={0,1,2}, how do we determine p(S)? Table 18 One thing to note from the example above is that the empty set is always going to be an element of the power set . Instead of using a truth table (however), we can also use a tree. This is done by adding an extra element to each stage of the tree. For instance, if A={a,b}, then what is p(A)? Figure 36 One way to represent the sum of a set of numbers is to state it in predicate logic. This is the following: $ ∀xPx= ∑_(x∈P)x,I(P)=in set P $. An ordered pair is the following: (x,y)={{x},{x,y}}. An ordered tuple is the following: (x,y,z)={{x},{x,y},{x,y,z}}. A cartesian product is a set of ordered tuples founded by multiplying sets, it can be denoted: A×B={(a,b)|a∈A,b∈B}. Example: Say X={0,1,2},and Y={A,B} X×Y={(0,A),(0,B),(1,A),(1,B),(2,A),(2,B)} Y×X={(A,0),(A,1),(A,2),(B,0),(B,1),(B,2)} You can also find this in m...
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