Syllogism

The emergence of syllogism and its part in reasoning ability dates back to the Aristotelian era. Aristotle had described syllogism to be an important aspect of reasoning in which he stated syllogism reasoning to be a discourse in which certain arguments or elements are differentiated to be dissimilar to normal considerations as these syllogism aspects are supposed to be.  Even though Aristotle’s theory of syllogism gave a new phase to the doctrine of prior analytics and allowed thinkers to possibly debate on ideas and structures, it had some contradictions too. The concept of vaguely used terms by Aristotle such as ‘possibly’, ‘necessarily’, etc., might even often contraindicate some of his statements on syllogism reasoning as to some extent might even have been not so efficient in answering syllogism questions. This brings us to the fact of understanding what is syllogism and the aspects of syllogism reasoning.

What is a syllogism?

A syllogism is a type of logical statement or premise intended on finding out the degree of truth while focusing on the mental element of figuring out deductive inferences based on two declarative sentences that are considered or supposed to be true. Syllogism reasoning based arguments is mainly based on a three-lined structure to derive the conclusion. George Boole modified and accepted Aristotle’s theory of syllogism by enhancing the model of syllogism by:

• providing the syllogism reasoning with mathematical logics and agreements
• Increasing the range of applications for the use of syllogism and expanding prepositions or arguments
• Boole’s model of syllogism could handle multi-term statements in comparison to Aristotle’s two models of preposition based subject and predicate.

Structure of a syllogism

An ideal syllogism consists of three main parts:

• Major premise
• Minor premise
• Conclusion

The working of a syllogism or the concept of syllogism reasoning can be better understood by providing an example like:

• Major premise: All humans die.
• Minor premise: All Romans are humans.
• Conclusion: All Romans die.

Each of these vivid categories represents a different argument to derive to proceed into the conclusion. Here die is the major term, Romans are the inferior term and humans is the adjoining term. Both of the logical arguments are universal as well as the conclusion is inconclusive too. This speciality of syllogism reasoning makes it a unique ability of reasoning that has played an intricate part in a modern-day model of logic and reasoning along with the use of syllogism questions.

Syllogism Reasoning and Syllogism questions

Syllogism Reasoning is a form of logical apprehension in which a conclusion is figured out from a set of prepositions based premises or phrases that further allows us to come out to a condition of deductive inference. Syllogism Reasoning may require the user to consider the statements to be relevant even if they are different from facts. 

Various methods are available for understanding the procedure of solving syllogism questions with a proper explanation of syllogism logic and reasoning behind them.

The types of methods for apprehending syllogism reasoning and understanding syllogism through syllogism questions.

Type-1: Analytical Method

All these types of statements used in the above table are fictitious statements that are just used for explanation. These statements may also be quite varied away from facts.

Deriving conclusions:

• With two particular phrases, no universal inference is possible
• With two positive sentences, no negative deriving is possible
• With two negative expressions, no positive result is possible
• With two particular phrases, no absolute result can be obtained, except when an ‘I’ type of sentence is given and then by reversing it, an ‘I’ type of result is obtained.

Important facts to remember:

• A phrase of type ‘E’ when reversed, gives a result of type ‘E & O’.
• A sentence of category ‘A’ when reversed, provides a conclusion of type ‘I’.
• A sentence of type ‘I’ when changed opposite, gives a result of the category ‘I’.

Type-2: Venn Diagram

Syllogism questions can also be solved based on Venn diagrams that might be helpful to some extent for obtaining answers. These diagrams, although may not always be possible for drawing for solving every syllogism question but syllogism reasoning can be well understood.

1. Q) To find out the possible conclusion among the two conclusions?

Example:

• Some bats are dwellers.
• Some dwellers are not rats.

Conclusion:

• Some dwellers are bats.
• Some rats are bats.

These sentences may be variant from normal facts but that’s exactly the approach for solving syllogism questions. The syllogism reasoning behind the vein diagram and the final result is that Some dwellers are bats (I to I), as the universal principle type four in the analytical method depicts(given above), that with two particular sentences only I to I is available. Therefore, only one conclusion is achievable. Nothing else is considered.

Extra syllogism question based on syllogism reasoning and principles

Syllogism questions are an effective way to understand the concept of syllogism for better understanding and knowledge grasp.

1) Find the possible conclusion among the two inferences.

Statements:

No bird is a dweller.

Some birds are flyers.

Conclusions:

1. a) Flyers that are birds are not dwellers.
2. b) No flyer is a dweller

The possible conclusion among both will be Flyers that are birds are not dwellers. This reference can be better understood by the illustration of the Venn diagram below.

Conclusion

The important aspects of syllogism are tried to be covered in the following article with a possible utility of syllogism reasoning and the necessities required to solve syllogism questions. The vital importance and emergence of syllogism theories have also been mentioned quite briefly.