Ungenerated Being

 Conceptual Analysis: Introduction to 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...

Karl Marx was born in a middle income family in Trier Germany on May 5th, 1818. After the Napoleonic wars, Trier became a city under the jurisdiction of the Kingdom of Prussia. The laws at the time required Karl Marx's dad to convert to Christianity and change his name in order to be a  legal adviser at the Court of Appeal in Trier.  From  1830 to 1835, Marx went to  Frederick William High School. 

Over the course of a year, a quarter, or a month, we can look at the debits and credits that build up the entirety of an economy. National accounts looks at these debits and credits and record the transactions  While it can be the case we make more than we spend as individuals, this cannot be the case for entire economies. This is the old adage that every sale is something bought. In the context of macroeconomics we say that income over a period of time should be equal to expenditures over that period of time: Expenditures = Income For the case of this post, we will assume a hypothetical economy which only consists of domestic investment and consumption as transactions. We can define the two as follows: Consumption : Transactions that are associated with the destruction of asset values. Investment : Transactions that are associated with increasing assets values. To understand these definitions, we will look at two sets of debit and credit charts to show how these transactions are ...

A special kind of relation f ⊆ A×B is called a function from set A to set B if every element in set A has only 1 image in set B. This can be denoted as: f:A→B. A real valued function is a function which states f:R→ R. In this case we can use arithmetic operators between functions. An injective function has every image relating to distinct elements in x under f. Figure 42 A surjective function says every element in y is the image of some element x under f. Figure 43 There are non-surjective and non-injective functions. Figure 44 A composition of functions states that given 2 functions f:A→B  and g:B→C, we define a composition as g∘f:A→C. Invertible functions state that $ f^-1 :A→B $ can yield $ f^-1 :B→A $.

A relation from set S to set T is a subset of the cartesian product of S and T. R is a relation from S to T iff R⊆(S×T). It is also a subset of the cartesian plane. A binary relation is a relation between 2 sets, this is the most common relation in natural language. The most common example is the following: All coins have an associated value, (∀x)(∃y)Pxy⊆(Coins×Value),I(P)={(Penny,1),(Nickle,5),(Dime,10),(Quarter,25)}. Arity is an n-ary relation, i.e., it is a subset of S_1×S_2×S_3…×S_n. An n-ary relation is an n-placed relation. Given a relation R, when $ R=A_1×B_1 $, where R⊆A×B.: A is the domain of R, where $ A_1⊆A $ B is the codomain of R, where $ B_1⊆B, B_1 $ is the range of R. We can represent this where certain sets have elements which map onto each other. Figure 37 The image is the elements in the range. The pre-image is the elements in the domain used in the relation. Relations allow for more than 1 image per pre-image (unlike functions). If (x,y) are in relation R, we...

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...