What is logical reasoning: Definition and 5 Discussions

Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case. Together, they form an argument. Logical reasoning is norm-governed in the sense that it aims to formulate correct arguments that any rational person would find convincing. The main discipline studying logical reasoning is logic.
Distinct types of logical reasoning differ from each other concerning the norms they employ and the certainty of the conclusion they arrive at. Deductive reasoning offers the strongest support: the premises ensure the conclusion, meaning that it is impossible for the conclusion to be false if all the premises are true. Such an argument is called a valid argument, for example: all men are mortal; Socrates is a man; therefore, Socrates is mortal. For valid arguments, it is not important whether the premises are actually true but only that, if they were true, the conclusion could not be false. Valid arguments follow a rule of inference, such as modus ponens or modus tollens. Deductive reasoning plays a central role in formal logic and mathematics.
For non-deductive logical reasoning, the premises make their conclusion rationally convincing without ensuring its truth. This is often understood in terms of probability: the premises make it more likely that the conclusion is true and strong inferences make it very likely. Some uncertainty remains because the conclusion introduces new information not already found in the premises. Non-deductive reasoning plays a central role in everyday life and in most sciences. Often-discussed types are inductive, abductive, and analogical reasoning. Inductive reasoning is a form of generalization that infers a universal law from a pattern found in many individual cases. It can be used to conclude that "all ravens are black" based on many individual observations of black ravens. Abductive reasoning, also known as "inference to the best explanation", starts from an observation and reasons to the fact explaining this observation. An example is a doctor who examines the symptoms of their patient to make a diagnosis of the underlying cause. Analogical reasoning compares two similar systems. It observes that one of them has a feature and concludes that the other one also has this feature.
Arguments that fall short of the standards of logical reasoning are called fallacies. For formal fallacies, like affirming the consequent, the error lies in the logical form of the argument. For informal fallacies, like false dilemmas, the source of the faulty reasoning is usually found in the content or the context of the argument. Some theorists understand logical reasoning in a wide sense that is roughly equivalent to critical thinking. In this regard, it encompasses cognitive skills besides the ability to draw conclusions from premises. Examples are skills to generate and evaluate reasons and to assess the reliability of information. Further factors are to seek new information, to avoid inconsistencies, and to consider the advantages and disadvantages of different courses of action before making a decision.

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  1. robertphy

    B How to pick some numbers out of 13 integers, by a 4 digits code

    This is the question I read in a Math quizzes book: - you have the first 13 integers from 1 to 13 - someone gives you a code made of at most 4 digits (0 to 9) - you decipher the code and tell him exactly which numbers he wanted from the list each number can be picked only once For example. case...
  2. robertphy

    Suggestions for using Math Puzzles to stimulate my math students

    The question is: my students (K9-12) have received the (sadly) usual routine based Math pseudo-education, before me teaching them. The best way to curb the tide is to use Math puzzles, to re-ignite their love of Math, lost in kindergarten. Now, which book would you suggest to fight the battle...
  3. M

    B Logic Problem: Figuring Out How Many Apples Each Man Ate

    Hey, I'm new to these forums, so thanks in advance for any help I get! :D 4 men sat around a table that had a dish with 11 apples in it. By the time their discussion was over, all the apples had been eaten. Each man had at least one apple, and each man knew that fact. Each man knew the number...
  4. S

    What could the ancient-Greek approach reveal, using our hindsight?

    I saw a post on Quora recently, about Epicurus and his argument for the existence of indivisible atoms. The logic was faulty sadly. Could we, with modern knowledge of what there is, come up with ancient Greek style arguments - going from every day observations, without microscopes or...
  5. P

    Got these image puzzles at university and couldn't solve half of them

    Hey everyone, At university yesterday we were shown about 25 of these puzzles during a lecture about logical reasoning and I solved about half of them without much issue but the ones in the image have me stumped: How do I solve the 10 in the image? You have to look at the 4 on the left and...
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