Symbolic Logic, Essay Example

Modus Ponens

If a contingent being exists, then a necessary being must exist as its cause.

A contingent being exists.

Therefore, a necessary being must exist as its cause.

In this argument, the major premise spells out the implication that any dependent being must have a necessary cause. The minor premise asserts the antecedent is real. So, the conclusion follows: there must be a necessary cause somewhere for existence.

d ? D

d

D

Modus Tollens

If anyone is born of God, then he loves his brothers.

Adolph does not love his brothers.

Therefore, Adolph is not born of God.

Here the antecedent (or conditional) premise is stated first and the consequent is denied.

B ? L

~ L

~ B

The symbols used here convey this. B (=X is born of God) and L (=X loves his brothers), as such, are not denied, but showing L to be false in the case of Adolph leads to the conclusion that B is not true in his case either.

Advantages and Disadvantages

The advantages of using symbols in logic are the same as in mathematics; symbols are easier to manipulate, they provide economical shorthand, and they allow us to see at a glance the overall structure of a sentence. By using symbols, we are able to deal with much more complicated arguments and thus take logic much further than we otherwise could (Virginia, 2008, p. 32). There are some limitations, however, to the use of symbols. Since English is an extremely subtle and complex language, something is bound to be lost in translation. This will mean, unfortunately, violating the full sense of the sentence on many occasions.

References

Virginia, Klenk. (2008). Understanding Symbolic Logic. Pearson Education India.