Logic is, most broadly, the study of arguments. Logic is the analysis of whether conclusions follow, logically, from premises or initial statements that are assumed.
For example, if we assume the premise that "All drugs are deadly" then it will necessarily be true that the conclusion "Aspirin is deadly" is true. This is regardless of whether or not the premise "All drugs are deadly" is actually true in the world we can observe because it was stated as assumed in the beginning of the argument. Only investigations of the empirical world, through observation, can show that it is not actually true that "All drugs are deadly" because we can clearly see that many drugs can be life saving.
Again, logic does not exist to verify the assumed premises but rather to determine whether or not conclusions follow from such premises.
Much of modern logic is concerned with the formalized study of deductive reasoning as opposed to inductive reasoning (induction is not really reasoning but assumption based on consistency). Never take anything as true unless it makes sense to you.
Whether it comes from a novice such as myself or an "expert", make sure it is correct to you and not simply assumed to be correct because of the source. All too often experts are not happy to be wrong and would rather go to their graves arguing something that has been shown to be wrong.
A definition of truth and how muddy truth actually is, shows how sometimes the biggest egos or loudest voices come out ahead because truth can be beaten into people even when it's false.
There can be no true logic of induction because induction, fundamentally, is not reason but faith in consistency which is, at base, an assumption.
There can be no true logic of ethics but only logic of ethical assumptions based on emotional reactions to belief.
Logic is the way in which we work with assumptions not a way in which we find reasons to make assumptions.
Deductive reasoning is the process of reasoning from general principles to specific instances. Deductive reasoning with logic is the process of assessing whether a conclusion follows from, or is entailed by, one or more given premises.
A premise is a statement that may or may not be true but can be assumed to be true for the sake analalysis of the whole argument. An argument is said to be valid if and only if the truth its premises result in the turth of its conclusion.
An argument is said to be sound if and only if its premises are true and if and only if it is valid. In other words, a valid argument may not be a sound argument because one or more of the premises may not be true.
Consider the following argument. The first premise, P1, is "All cats are black". The second premise, P2, is "Pandora is a cat". The conclusion, C, is "Pandora is black". While this argument is valid, it is not sound, because P1 is not true because at least one cat is not black.
Logic is a way of studying whether conclusions, which are propositions, can be found to logically follow from other propositions.
So, logic can tell us if it is true or false that one proposition follows from another but it can not tell us anything about the content of such propositions or, in other words, logic can teach us nothing about the facts of the world as it is but only teach us about how we can manipulate the relations between atomic linguistic or symbolic objects.
Logic can tell us that if "All humans have hair" and "Harold is a human" then it follows that "Harold has hair". Logic can not tell us whether or not "All humans have hair" and it can not tell us whether or not "Harold is a human". The soundness of a proposition is a scientific statement based on observation whereas logic itself requires no observation of specific cases of the actual world.
The study of logic is vast and can be divided in a number of ways.
Informal Reasoning studies logic in linguistic arguments and includes the study of logical fallacies. For example, consider the following argument. "John believes that there are twenty-two marbles in the jar, but he is a complete idiot, so there can't be twenty-two marbles in the jar".
This is an example of an ad hominem logical fallacy. In an ad hominem fallacy, a personal attack is used that has nothing to do with the argument but is used to make the ridiculed person's conclusion appear false.
Computer Logic examines the logical processes that are used to make calculations in computers for both hardware and software applications.
All computers use a series of 1's and 0's, or True and False, or On or Off, at their most basic level. The basic logical structure used in most computers and many systems is Boolean Logic, created by George Boole in the mid 19th century. Boolean logic is logic in which each element has only two possible values, a concept used to create the idea of the computer bit as having either a value of 1 or 0.
Syllogistic Logic or Traditional Logic or Aristotelian Logic studies the use of arguments that take the form of two premises and a conclusion, where the premises take the form "All X are Y", "No X is Y", "Some X are Y", and "Some X are not Y".
Epistemic Logic examines the logic of knowledge and belief.
Deontic Logic studies the logic of ethical reasoning. Deontic logic attempts to analyse statments such as "Everyone ought to fight for human rights" and "It is important to always consider the greater good".
Mathematical Logic is a field of mathematics and studies the theories of sets, models, recursion, and proofs.
Fuzzy Logic is the attempt to develop a logical system that is based on degrees of truth.
Philosophical Logic attempts to formalize language in order to evaluate linguistic expressions.
Symbolic Logic is the study of logic that uses symbols for linguistic expressions.
Propositional Logic, Propositional Calculus or Sentential Logic examines propositions, sentences, or statements.
Predicate Logic or Quantifier Logic studies the interior structure of atomic and compound sentences.
Modal Logic studies the logic of necessity and possibility using modal operators.
I have begun a tutorial in symbolic logic that will expand as time allows and as my understanding increases.
I hope to get into much more detail and complexity as time allows.
1. Logical Symbols - a list of the relational symbols in symbolic logic.
2. Logical Rules - a list of valid implecational argument fords
