A Class-Room Introduction to Logic

May 5, 2009

Unit-II: Nature of Implication

Filed under: Implication,Logic — Dr. Desh Raj Sirswal @ 6:24 am

Logical Reasoning:

Reasoning is an art as well as a science; it is something we do as well as understand. The mental recognition of cause –and –effect relationship is called ‘reasoning’. It may be prediction of an event from an observed cause or  the inference of a cause from an observed event. Logical Reasoning is a process of passing from the known to the unknown. It is the process of deriving a logical inference from a hypothesis through reasoning.

Logical Deduction: Another important factor in logical reasoning is logical deduction. Deriving an inference from units of arguments which are called proposition in logic or deducing an inference from statements is called logical deduction. For example:

All men are mortal.

Raveesh is a man.

Therefore, Raveesh is mortal.

From statement (a) and (b) we derive a logical conclusion that Raveesh is mortal.

Deduction & Induction:

In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.

Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a “top-down” approach. We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data — a confirmation (or not) of our original theories.

Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a “bottom up” approach In inductive reasoning, we begin with specific observations and measures, begin to detect patterns and regularities, formulate some tentative hypotheses that we can explore, and finally end up developing some general conclusions or theories.

The Idea of Form

The form or logical form of an argument is the representation of its sentences using the formal grammar and symbolism of a logical system to display its similarity with all other arguments of the same type. It consists of stripping out all spurious grammatical features from the sentence (such as gender, and passive forms), and replacing all the expressions specific to the subject matter of the argument by schematic variables. Thus, for example, the expression ‘all A’s are B’s’ shows the logical form which is common to the sentences ‘all men are mortals’, ‘all cats are carnivores’, ‘all Greeks are philosophers’ and so on.

In any discipline one seeks to establish facts and to draw conclusions based on observations and theories. One can do so deductively or inductively. In inductive reasoning, one starts with many observations and formulates an explanation that seems to fit. In deductive reasoning, one starts with premises and, using the rules of logical inference, draws conclusions from them. In disciplines such as mathematics, deductive reasoning is the predominant means of drawing conclusions. In fields such as psychology, inductive reasoning predominates, but once a theory has been formulated, it is both tested and applied through the processes of deductive thinking. It is in this that logic plays a role.

The other method of reasoning, the deductive method, begins with an accepted generalization–an already formulated or established general truth and applies it to discover a new logical relationship. That is, through deduction we can come to understand or establish the nature of something strange or uncertain by associating or grouping it with something known or understood.

Deductive arguments are formed in two ways:

1. General to Particular. This is the kind most people think of when they think of deduction. For example, the classic syllogism:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

2. General to General. Another kind of deduction arrives at new generalizations through the syllogism. For example:

All trees have root systems.
All root systems need nitrogen.
Therefore, All trees need nitrogen.

But before we get into syllogistic analysis, a little more needs to be said about deduction as a whole. We said earlier that deduction begins with an accepted generalization. Such a statement raises two questions: (1) Where do these generalizations come from and (2) Why are they accepted or assumed to be true?

The generalizations used in deductive thinking come from several sources:

  • Inductive thinking
  • Other deductive arguments (of the general to general type)
  • Revelation
  • Assumption (a priori givens that cannot be proved but that are assumed. All knowledge must begin with belief.)

In all four of these cases, the immediate source may be authority rather than personal experience. That is, the inductive conclusion, the deductive argument, the revelation, or the assumption may have been achieved by a third party who presents the generalization to us for acceptance on the basis of authority, in which case we take it on faith. You may not be able to do a large scale inductive experiment to find out whether a certain generalization is true, so you look in a book and accept the generalization of the authority.

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