In the case of Sherlock Holmes, inductive reasoning was his ability to look at the evidence at hand and formulate new leads and hypothesis that would eventually help solve the case.

Example of Inductive reasoning

Both Induction and Deduction are necessary within casual inference because they are two ways of approaching a problem and often go hand in hand. Induction goes from evidence -> hypothesis while deduction works in the forward direction; cause (hypothesis) -> effect (theory, conclusion). Artificial Intelligence has started automating Induction and Deduction, an example is Bayesian networks. 

Stages of Casual Inference: Induction and Deduction

Children below the age of 9 show capability in reasiong about diverse evidence. By age 5, children were able to reason that more options will be more respresentitive of a person's favorite toy preference. In addition, the way that children categorize groups as diverse is different from how adults do. Children have less exposure, so small differences in belief or grouping might seem like large differences for children. 

Effect of age on inductive reasoning

Inductive reasoning refrence library

An example of inductive reasoning leading to a false conclusion can be seen in generalizing about fruit. If one observes that their favorite fruits, such as apples, bananas, and oranges, all grow on trees, they might inductively conclude that all fruits grow on trees. This generalization, while based on direct observations, is incorrect, as demonstrated by fruits like strawberries and blueberries which do not grow on trees.

Example of an Incorrect Inductive Generalization

A biologist observes that every swan they have seen in Europe is white, and every swan they have seen in North America is white. Based on these numerous observations, the biologist concludes that all swans in the world must be white. Which statement best analyzes the biologist's conclusion?

A good scientific hypothesis must be logically sound, indicating that it is based on structured reasoning, prior theories, or empirical observations rather than being an arbitrary guess. In most cases, researchers utilize deductive reasoning to derive a precise, testable hypothesis from a broader theory. Conversely, in the absence of an existing theory, they may employ inductive reasoning to develop a more general hypothesis drawn from specific research findings or empirical observations.

Logical Hypothesis

In the context of scientific research, what is the primary characteristic of inductive reasoning?

A researcher observes that across 15 separate studies, participants who sleep fewer than six hours per night consistently score lower on memory tasks. The researcher uses these findings to form the broader generalization that sleep deprivation impairs memory performance. Because this generalization is based on numerous consistent and accurate observations, it is guaranteed to be correct.

Inductive reasoning is a method that moves from specific empirical observations to broader generalizations. Scientists utilize this process to formulate theories and generate hypotheses. However, a key characteristic of inductive reasoning is that its conclusions are not guaranteed to be correct, even when based on multiple, accurate observations.

University of Michigan - Ann Arbor

Google

Logical reasoning is the process of using a rational, systematic series of steps based on sound certain mathematical procedures and statements to arrive at a conclusion. 

There are three types of the reasoning:
- Abductive Reasoning 
- Deductive Reasoning 
- Inductive Reasoning

Reasoning

Pearl, J., & Mackenzie, D. (2019). The Book of Why. Penguin : 
[search.lib.umich.edu/catalog/record/016899333?query=the+book+of+why&library=All+Libraries](https://search.lib.umich.edu/catalog/record/016899333?query=the+book+of+why&library=All+Libraries) 

Reference : The Book of Why (needs to be merged)

Goldstein, E. B. (2014). Cognitive psychology: Connecting mind, research and everyday experience. Nelson Education.


Cognitive psychology: Connecting mind, research and everyday experience

https://en.wikipedia.org/wiki/Logical_reasoning

Wikipedia logical reasoning

Spielman, R. M., Jenkins, W. J., & Lovett, M. D. (2020, April 22). Psychology (2nd ed.). OpenStax. https://openstax.org/books/psychology-2e/pages/1-introduction

OpenStax Psychology (2nd ed.) Textbook

https://kpu.pressbooks.pub/psychmethods4e/

KPU Research Methods in Psychology - 4th American Edition

Eliminating different hypothesis to draw a conclusion.  The conclusion logically follows from "premises".

Deductive reasoning

Abductive reasoning usually starts with an incomplete set of observations and proceeds to the most possible explanation for the group of observations. It is based on making and testing hypotheses using the best information available.

Abductive reasoning is useful for forming hypotheses to be tested.

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