Definitions

AXIOM:

A self-evident truth or proposition that is evident to all. It is an established principle that is universally accepted as true. It is the simplest truth, not derived from other principles.

BINARY:

A condition in one of two possible states. Binary comes from the Latin root "bi" meaning two. In a binary condition, the state is either true or false. In the base two system, the state is either one or zero, on or off. This condition of state is much like a light switch or a water faucet. In computer terminology this logic is called Boolean, named after George Boole, the English mathematician who proposed Boolean algebra in 1847. His ideas dealt with set theory, the area where two or more objects meet in common with shared attributes or physical occupation. The presentation model for this type of logic is known as a truth table. If there be only one switch or faucet (called a gate in computer logic), then if that gate be off, there is no further passing of events. However, what if we have a complex system of many gates, where if any one be on, there is flow? This gives rise to the logical concept of "and," "or," "not and," "not or," "exclusive and," "exclusive or", and the like.

AND GATE Input A Input B Output 0 0 0 0 1 0 1 0 0 1 1 1

To be true (output), both inputs must be true (equal to 1). The input in the truth table is the exact opposite for the NOT AND (NAND) table

OR GATE Input A Input B Output 0 0 0 0 1 1 1 0 1 1 1 1

To be true (output), either input can be true (equal to 1). The outputs are exactly opposite in the NOT OR (NOR) table

CAUSATION:

The events that produce a phenomenon.

CLAIM:

Another term for proposition

CLASS:

Aristotle first started classifying objects. Animals of the same kind or class are of the same species. A class is a group sharing the same attributes or properties. Classifications in biology consist of kingdom, phylum, class, order, family, genus, species. In language, the study of syntax involves classifying expressions, such as infinitive expressions, nominative subjective expressions (nouns), etc. Even object-oriented programming languages, such as Java and C++ use classes and objects. Unlike inline coding, these programs can involve instances of objects of classes. Since the class has the same properties, recoding of these properties in the object is unnecessary, which saves a lot of effort for the programmer.

CONCEPT:

Concepts form an important part in human cognition and learning, just as are constructs and percepts. Concepts involve organizing and discerning abstract thoughts, unlike percepts; however, concepts deal with the human ability to classify ideas which involves placing logically like-kind ideas into classes. Classifying could involve grouping state policemen, IRS agents, and immigration agents with the expectation of law enforcement. The three are distinct, but mentally they are grouped together abstractly. There is another lower level of conceptual classification called discrimination which involves objects. In this case, the classifying of the objects is on the basis of their percept properties. This lower level concept formation is based on size and shape. Compare a distinction of child (abstract thought distinctive) with an orange circle (more physical percept-based thought distinctive). The more variation in the exact percept of the concept is found in concepts such as beauty, love, kind, gentle, justice, fairness, patience, leadership, and happiness.

CONSTRUCT:

A construct differs from a concept in that concepts are logical, not mental. Constructs are usually hypothetical. They are mental pictures, totally abstract, of the essence of the reality of anything. Constructs are the bases of learning and cognition. For example, language formation is a symbolic representation of reality, yet to understand it has to be interpreted within a context. A context is the environment where the construct exits.

CORRELATION:

This is a measure of the degree that one object relates to another. An example is college marks and intelligence. There is definitely a relationship between intelligence and marks. The relationship is definite and not based on chance. Correlations tell if a certain conclusion or hypothesis be true. In statistics, correlation can be mathematically measured between two sets of data (events, characteristics, or properties). To calculate it, divide the covariance by the product of their standard deviations.

COVARIANCE:

A vector is an ordered pair of number (x and y) in two dimensional space (a graph). The values of x and y taken at various intervals are called elements and make up a table as follows. The mean of x is the average value of the x elements, and the mean of y is the average of the y elements. The two variables x and y must have the same number (N) of elements in the table. The covariance of vectors x and y is the sum of the products of the differences between the elements of x and the mean of x times the differences between the corresponding elements of y and the mean of y, all divided by N-1.

DEDUCTIVE REASONING:

Deductive reasoning is arguing from the general to the particular. Simply, this is arguing from a known principal or premise to an unknown conclusion. This is more considered more "conservative" in that it uses reliable, known (tried and true) theories. This type of reasoning process came into vogue and gained popularity after the Industrial Revolution (the late 1700s), with the rise of applied math in commercial industrialization. Fields using mathematical methodologies (engineering, computer science, and science), which are more exacting use deductive reasoning. Up until World War II and the Great Depression, economists used more conservative deductive reasoning. However, prior to World War II, economist John Keynes proposed theories using both deductive and inductive reasoning. The theories involving government deficit spending to "pump prime" the economy were not tried and true, until the outbreak of World War II. See inductive reasoning below.

DIALECTIC METHOD:

This is a method of logic. It is based on contradictions of opposites and their resolution. Simply stated, it is a means of question and answers designed to show the weaknesses in arguments or propositions put forward as true. Socrates first used this method primitively. Others following him developed it. Plato used it to determine the "real" essence of things, even in analyzing institutions such as government. Aristotle refined the process by building a form of reasoning using generally accepted premises. German philosopher Fichte developed the modern concept of thesis, antithesis, and synthesis. Hagel and Marx further developed this triad known as Marxism.

FORM:

Plato's theory that all physical reality was perfect in the conception of the mind. The relation between what is sensed in physical objects and the "form" is participation. In other words, a beautiful thing "participates" in the idea or concept of beauty. The concept is perceived in bits and pieces. As these experiences occur, a "construct" is developed of the reality form.

GROUNDS:

Information of fact or opinion used to provide verification for a claim; also known by the generic label evidence.

HYPOTHESIS:

A proposition (something presumed as true) or principal put forward so that an inductive reasoning process can be used to prove or disprove it. For sake of argument, sometime a person will play "devil's advocate" or take a position opposed to the hypothesis. This position is called a "null hypothesis." However, failure to reject the null hypothesis as true does not mean that the hypothesis is necessarily true (or that the hypothesis should be accepted). It is experimentally tested. In statistics, if the null hypothesis is rejected when actually true, this is a TYPE 1 error. When the null hypothesis is accepted when false, this is a TYPE 2 error.

INDUCTIVE REASONING:

Reasoning reaches conclusions based on correlations between data events observed. To reach that conclusion, a relation is inferred between the events and the concluded cause (called the conclusion). Conclusions are called hypotheses. The process of inductive differs from deductive reasoning, in that it involves reaching conclusions based on small samples of the causation population. As a result, sometimes there is not always agreement between the conclusion (consequences of the events) and the causes (the events or actions). This leads to a modification of the hypothesis. On the other hand, in deductive reasoning the initial hypothesis leads through the reasoning process to the necessary consequences. Economists, criminologists, politicians, behaviorists and others dealing with finding solutions to problems using new and untried approaches use inductive reasoning. When results are unknown, failures in the application of the untried solution hypothesis theory leads to modification of the hypothesis. This is a reasoning from the particular to the general.

INFERENCE:

A conclusion derived from reasoning. An inference is a deduction that follows from a reasoning process. This proposition flows to another reasoning process as a given, proven premise derived from the first (former) reasoning process.

LINK:

A logical connection. Sometimes this is called a copula: subject linking to a predicate complement.

METAPHYSICS:

See ontology

OBJECT:

Anything perceived by the mind. In language, an object is the recipient of action, directly or indirectly. However, in the context of this page (philosophy, logic, and science), the object can be like the sentence subject, too. Computer programming has been tending towards object models. Programming in languages like Java and C++ involve objects. Java has classes.

PARTICULAR:

In logic, designating a proposition which affirms or denied its predicate to a part of but not the whole of a subject limited in application to part of a class. The opposite of universal. An impression received by the mind from the senses, such as hearing, smell, feeling, taste, and seeing. It is in real time. See concept above for an explanation of the difference between percepts and concepts. Concepts are not in real time.

PERCEPT:

An impression received by the mind from the senses, such as hearing, smell, feeling, taste, and seeing. It is in real time. See concept above for an explanation of the difference between percepts and concepts. Concepts are not in real time.

POPULATION:

A population is the entire set of objects or observations that have some kind of common relationship.

PREDICATE:

In logic, a predicate is that which is affirmed or denied about the subject or proposition. In first-order logic the object can be quantified, but the relations or functions of that object cannot. In higher-order logic, relations and functions can be quantified as well. See subject below.



Language	Ontological commitment	Epistemological Commitment
Propositional Logic	facts	true/false/unknown
First-order logic	facts, objects, relations	true/false/unknown
Temporal logic	facts, objects, relations, times	true/false/unknown
Probability theory	facts	degree of belief
Fuzzy logic	degree of truth	degree of belief


Press here for a discussion of ontology and epistemology.

PREMISE:

This is the lowest reducible fact. It either comes from a proof or comes from general acceptance as a self-evident truth. It serves as the base for an argument. It is also called a proposition. Premises are used in drawing conclusions.

PROBABLE:

The likelihood of being true or real. Supported by evidence strong enough to establish presumption but not truth (absolute). It is measured as a percentage, where instances of the evidence coincide with the presumed phenomenon. A reasonable ground for assuming that a claim is supported.

PROPERTY:

Any characteristic of an object. This could be a quality, attribute, or state (an indicator of the attitude or disposition). Examples are hot, cold, on, off, true, false for state. Examples for attributes are color, shape, size, species, and what class it belongs to.

PROPOSITION:

In logic, this is an expression in which the predicate affirms or denies something about the subject. See premise above.

REASONING:

Offering explanation, evidence, proven facts, and generally accepted premises as a logical defense in supporting and proving a hypothesis or conclusion as true.

SUBJECT:

In logic, the subject is that term of a proposition concerning which anything is affirmed or denied. It is guilt by proof or, in probability, by association. One can say "loves Mary," the predicate, but there is no sentence without the subject. In as sense, axiom is a subject. We are defining or classifying the subject by the perceived relations and functions observed. See the types of commitments to ontology and epistemology following the predicate definition above.

SYLLOGISM:

Aristotle's form of reasoning which draws a logical conclusion from two premises. An example below uses the following truths based on the American Child Health Association studies:
• The desirable weight for a girl 14 years old that is 5 feet tall is 101 pounds. The desirable weight for a boy 14 years old that is 5 feet tall is 94 pounds.
• Fact 1: A 14 year old who is 5 feet tall weighs 101 pounds and is the overweight
• Conclusion 1: The 14 year old is a boy
• Fact 2: A 14 year old who is 5 feet tall weighs 94 pounds and is under the desirable weight
• Conclusion 2: The 14 year old is a girl
• Fact 3: A girl weighs 101 pounds and is over the desired weight
• Conclusion 3: The girl is not 14 years old

UNIVERSAL:

In logic, a general term or concept. A broad class such as species, property, genus, or any other domain. Opposed to particular or individual or instance of a class. The generic aspect of universal is that many individual or classes of individuals are grouped together by a similarity of some description.

WARRANT:

A reasoning process that causes one to mentally leap from grounds to certifying the truth or probability a claim. It is the process of assurance about a claim.