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Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...
Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water is boiling." expresses a proposition since it can be true or false.
For example, when the conclusion of an argument is very plausible, the subjects may lack the motivation to search for counterexamples among the constructed models. [3] Both mental logic theories and mental model theories assume that there is one general-purpose reasoning mechanism that applies to all forms of deductive reasoning.
Conclusion/Consequent: All Greeks are mortal. Each of the three distinct terms represents a category. From the example above, humans, mortal, and Greeks: mortal is the major term, and Greeks the minor term. The premises also have one term in common with each other, which is known as the middle term; in this example, humans. Both of the premises ...
In this example, the dependent clauses preceding the comma (namely, "all men are mortal" and "Socrates is a man") are the premises, while "Socrates is mortal" is the conclusion. The proof of a conclusion depends on both the truth of the premises and the validity of the argument. Also, additional information is required over and above the ...
In the philosophy of logic and logic, specifically in deductive reasoning, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of inference called modus ponens takes two premises, one in ...
Deductive arguments are sometimes referred to as "truth-preserving" arguments. For example, consider the argument that because bats can fly (premise=true), and all flying creatures are birds (premise=false), therefore bats are birds (conclusion=false). If we assume the premises are true, the conclusion follows necessarily, and it is a valid ...
In modern usage, it has come to refer to an argument in which the premises assume the conclusion without supporting it. This makes it an example of circular reasoning. [1] [2] Some examples are: "People have known for thousands of years that the earth is round. Therefore, the earth is round." "Drugs are illegal so they must be bad for you.
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