Logic. What is logic? Logic (from the Ancient Greek: λογική, logike) is the use and study of...
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Transcript of Logic. What is logic? Logic (from the Ancient Greek: λογική, logike) is the use and study of...
Logic
What is logic?
• Logic (from the Ancient Greek: λογική, logike) is the use and study of valid reasoning. The study of logic features most prominently in the subjects of philosophy, mathematics, and computer science.
Informal logic is the study of arguments as presented in
ordinary language, as contrasted with formal logic, the
presentations of arguments in an artificial, formal, or technical
language.
A simple definition of inductive reasoning is using observation to
formulate an idea or theory. In this sense, inductive reasoning moves from the specific to the general.
Arguments based on experience or observation are best expressed
inductively.
Inductive reasoning involves finding the path that leads to a solution.
Inductive reasoning is the ability to combine pieces of information that
may seem unrelated to form general rules or relationships.
It is a primary attribute in scientific theory formulation. As an example of inductive reasoning, in a murder trial you have the evidence, and the goal is to use inductive reasoning to
determine the probability of the defendant’s guilt.
In contrast to deduction, inductive reasoning depends on working with cases, and developing a conjecture by examining instances and testing
an idea about these cases.
It is frequently used in mathematics and is a key aspect of
scientific reasoning, where collecting and analyzing data is the
norm.
A simple definition of deductive reasoning is taking a known idea or theory and applying it to a situation (often with the intention of testing
whether it is true).
In this sense, deductive reasoning moves from the general to the
specific.
Arguments based on laws, rules, or other widely accepted principles are best expressed deductively
(e.g. the Declaration of Independence).
Precis: In the “Declaration of Independence” (1776) Thomas Jefferson, et al., argue that the
American colonists have certain rights being denied by the British and therefore have the right to be
independent of British rule.
The authors of the document develop this thesis with careful
reasoning and compelling evidence: “grievances” that specify outrages carried out against the colonists by
the British.
The purpose of the document is to declare to the world the intentions
of the colonists and to provide a rational justification for them.
The audience is British authorities but also a “candid world” that has its eye on the rebellious colonists and might question their decision.
Formal logic, as its name states, is formal in the sense that it has a particular structure that is rigid,
unlike the casual flexibility of informal logic.
In logic and philosophy, an argument is an attempt to
persuade someone of something, by giving reasons for accepting a particular conclusion as evident
In formal logic, the argument is carefully structured or formed,
arriving at a conclusion that is self-evident (i.e. requires no
explanation).
A formal argument is based on premises, statements that define
what the argument is about.
A syllogism is a miniature deductive argument comprising three parts:
Major premiseMinor premise
Conclusion
Aristotle’s famous syllogism begins with a major premise, a general
statement on which his argument is based:
All homo sapiens are mortal.
Aristotle then applies that idea to a specific situation (Socrates) by
saying: Socrates is a homo sapien
This leads us to his conclusion:Therefore, Socrates is mortal.
Major premise: All people are mortal
Minor premise: Socrates is a person
Conclusion: Therefore, Socrates is mortal
Although it seems obvious, the conclusion “follows logically” from the premises because the premises are properly structured to make the
conclusion valid.
A valid logical argument is one in which the conclusions “follow”
logically from its premises, and its conclusions are consequences of its
premises.
There are six rules for determining the validity of a syllogism.
Because they’re technical and our study of syllogisms is cursory, we’ll not spend time learning the rules.
Suffice it to say, that in formal logic, when the form of an argument is
valid, the conclusion follows logically and is thereby valid.
Because of this, when challenging a formal logic argument, one
challenges the premises, not the conclusion.
Validity is a function of form. Just because an argument is valid in its
form does not mean it’s necessarily true.
If the premises are false, then the conclusion will be false, even if it is
properly arranged logically.
If an argument is both valid and true, it is said to be sound.