# How to formalise inductive reasoning? [closed]

How can I formalise inductive reasoning or findings, for example, from grounded theory studies?

I understand deductive reasoning could use first-order logic to demonstrate the validity of an argument (truth of the premises guarantees the truth of the conclusion) but inductive arguments only provide probable support for the conclusion.

Would the best approach be to use Toulmin model of argumentation to formalise the inductive argument?

• You may want to take a look at this short video Dec 23, 2022 at 2:32
• This question is too broad for this group. There have been hundreds of attempts to formalize induction, and no answer can cover even a fraction of them. Dec 23, 2022 at 5:49
• @RodrigodeAzevedo the end of the video was interesting. At 3:48 he mentions combining the methods of inference so that it is possible to observe the [effect] of a phenomenon, then induce an explanation [cause] and in turn induce a [rule]. From this, it is possible to use deduction to predict new data elements. In the case of a grounded theory study once open, axial, and selective coding are complete and the core category has been inductively described this [rule] could now be used deductively and the argument formalised using FOL. Is that correct, or have I taken it a step too far? Dec 23, 2022 at 6:47
• @DavidGudeman apologies if my question is too broad; I am new to logic so trying to get my head around the mechanics. Out of the hundreds of attempts to formalise induction is there a method(s) that sounds out above the rest as widely accepted? Dec 23, 2022 at 7:14
• See Inductive Logic. Dec 23, 2022 at 7:49

How to Formalise Inductive Reasoning

I have been wondering along those same lines. In academia.edu, I have posted Induction and the Uniformity Principle; derivation of the principle from fundamental axioms. Here is the table of contents:

1.0 Introduction

2.0 The inductive process is a syllogism.

3.0 The Uniformity Principle is the major premise of the inductive syllogism

3.1 Introduction

3.2 Objection to the Uniformity Principle; the course of nature changes.

3.3 Objection to the Uniformity Principle; simple enumeration fails.

4.0 The Uniformity Principle is derived from three fundamental axioms.

4.1 The purpose of the axioms

4.2 The axioms of uniformity: Existence, Identity, Continuity

A. Existence

B. Identity

C. Continuity

4.3 The axioms are valid and support uniformity.

4.4 The three axioms are necessary and sufficient.

5.0 Uniformity permits the process of falsification that allows the content of the conclusion to be estimated.

6.0 Conclusion

I do not know how closely my analysis approximates that of Prof. Toulmin. However, I think that my one-step-at-a-time approach is similar to what he was looking for.

I hope this answer is useful.

• Thankyou Andrew. I will look at your post as it sounds very interesting Dec 23, 2022 at 6:48
• To be fair, in terms of formal logic, the inductive argument is not a syllogism (in the sense that formal logic uses it): see Syllogism: "That theory is in fact the theory of inferences of a very specific sort: inferences with two premises, each of which is a categorical sentence, having exactly one term in common, and having as conclusion a categorical sentence the terms of which are just those two terms not shared by the premises. " Dec 23, 2022 at 11:32
• Mill's dictum that “[E]very induction may be thrown into the form of a syllogism” must be read as "“[E]very induction may be thrown into the form of a formal deduction." Dec 23, 2022 at 11:33
• Having said that, the burden of proof relies of the "major premise, the so-called Uniformity Principle that, of course, cannot be grounded inductively. The issue IMO is: how can we derive so a general principle from more fundamental ones? Dec 23, 2022 at 12:42