How do you get from understanding the uninformative proposition ‘No unmarried man is married’ to understanding the informative proposition ‘No bachelor is married’? The move can be expressed in a syllogism.
- No unmarried man is married.
- A bachelor is an unmarried man.
- Therefore, no bachelor is married.
This syllogism makes explicit what is implicit in the informative ‘No bachelor is married’ – foremost, premiss (2): that a bachelor is an unmarried man. Premiss (2) contains the information. Premiss (2) nominates the synonymy of ‘bachelor’ and ‘unmarried man’. Premiss (2) therefore legitimates the synonym substitution of ‘bachelor’ for ‘unmarried man’. But this does not explain the identity of ‘bachelor’ and ‘unmarried man’, so let’s assume a pure nominalism whereby we establish that to be a bachelor is to be an unmarried man. Establishing synonymy, this form of syllogism can thus be called a syllogism establishing synonymy.