Inference - Making Sense of Statements
Summary
Inference is the process of drawing logical conclusions from established statements, and the validity of an inference depends on the accuracy of its premises and the logical soundness of the reasoning process.
Inference is the process of drawing conclusions from known statements whose truth values are established, and these statements are referred to as premises. By applying existing principles, new statements, known as conclusions, are derived from the given premises. This process of drawing conclusions is often referred to as reasoning or argumentation.
Validity of an Argument
An argument is considered valid if its premises are true, leading to a true conclusion. Conversely, an argument is deemed invalid if its premises are true but the conclusion is false.
Example
Consider the following statements:
- Premise 1: All humans are mortal.
- Premise 2: Sita is a human.
Inference (Conclusion): Sita is mortal.
Explanation
We know that all humans are mortal (Premise 1). We also know that Sita is a human (Premise 2). Applying the principle that if all humans are mortal, and Sita is a human, then Sita must be mortal.
Validity Check
If Premise 1 and Premise 2 are true (which they are in this case), then the conclusion (Sita is mortal) is valid.
Invalid Example
Now, consider the following invalid example:
- Premise 1: All birds can fly.
- Premise 2: Penguins are birds.
Inference (Incorrect Conclusion): Penguins can fly.
Explanation
Premise 1 states that all birds can fly. Premise 2 states that penguins are birds. However, the conclusion that penguins can fly is incorrect because penguins are an exception to the generalization that all birds can fly.
Validity Check
In this case, even though Premise 1 and Premise 2 are true, the conclusion is invalid due to the specific nature of penguins.