# Deductive and Inductive argument difference

I am looking for the precise definition of deductive and inductive argument. I have grade 11 logic textbook, which characterizes deductive argument as that for which, the conclusion is implicit in the premises i.e. the conclusion does not go beyond the evidence in the premises. So in symbolic terms, can I define deductive argument as follows- Let P={P1,P2, P3, P4,......Pn} be the set of propositions along with usual logical operators and parentheses. Then sequence A1, A2, A3,....., Am| A, where A1, A2,...,Am, A are well defined formulas formed by P, is said to be deductive argument if for the sets, S={x| for some k from 1 to m, x is a proposition in Ak} T=Set of all the propositions present in A, T is subset of S is true. But then, is [1.p implies q 2.p Therefore, q or r]; not a deductive argument? Thank you.

• A deductive argument is a proof of the conclusion from the premises. Jul 5, 2023 at 16:09
• An inductive argument is an argument supporting a claim, hypothesis using evidence. Jul 5, 2023 at 16:10
• To Mauro Allegranza, hello sir, thank you for your comment. I wish to know about following argument- 1) Alex is a teacher. 2) Alex is a good man. Therefore, Alex is a good teacher. So is this "invalid deductive argument" or "bad inductive argument"? Thank you sir. Jul 5, 2023 at 17:19
• That is not valid however you take it. The word 'good' is what Peter Geach called an attributive adjective and it cannot be used in this way. By contrast, adjectives like 'yellow' are predicative, so it is OK to go from "this is yellow; this is a book; therefore, this is a yellow book". Also, your textbook definition of deductive argument is poor: deductive validity is not about what is implicit in the premises but about what follows from them by necessity or about what is provable from them. Jul 5, 2023 at 19:02
• As to attempting to express validity symbolically, it is much more complex than your attempt. Validity can be understood in terms of what is provable, using a formal deductive system, or in terms of semantic consequence, using model theory. Jul 5, 2023 at 21:30

Deductive argument: those arguments where there is a guarantee of transmission of truth. If the premises are true, the conclusion must be true. Of course this is not a guarantee of the presence of truth itself.

Every A is B. Every B is C. Thus, every A is C.

Fallacy: An argument which presents as deductive but is invalid, i. e., it is possible that the premises are truth but not the conclusion.

Every A is B. Every B is C. Thus, every C is A.

Inductive argument: an argument which does not guarantee the transmission of truth but gives support to the conclusion that is desired to claim. Most of the inductive arguments involve the concept of probability.

95% of the times that it's raining there are thunders. Tomorrow will rain. Therefore, tomorrow will be a thunder.

Note that strictly every inductive argument is invalid, but this doesn't mean that they are useless. Actually most of the arguments used in the everyday life are inductive.

This argument

[1.p implies q 2.p Therefore, q or r]

is valid because of the modus ponens and addition rule

• Thank you so much for your answer. I need help in the following argument- 1)Alex is a good man. 2) Alex is a teacher. Therefore, Alex is a good teacher. Should it be called "invalid deductive argument" or "bad inductive argument". Thank you. Jul 8, 2023 at 4:29
• As you presented I think it is a bad inductive argument. But honestly the definitions of good man and goot teacher are not clear. If you add a premise saying 'every good man Is a good teacher' then its deductive and valid
– tac
Jul 8, 2023 at 12:47
• I upvoted your answer. But tac, regarding the comments, you're missing the premise (2) that Alex is a teacher. @user2513050: Think about what your statements mean, logically. (1) means Good(Alex) ∧ Man(Alex). (2) means Teacher(Alex). (3) ("Alex is a good teacher") means ___? And check for yourself whether (3) can be deduced to be true given that (1) and (2) are both true. Apr 2 at 9:58