A deductively valid argument is one in which the conclusion must be absolutely, positively true if the premises are true.

Deductive arguments come in two forms: Syllogistic and Chiasmic. A syllogism is a deductive argument in which each premise follows from the previous one by means of **a logical connector** such as "therefore," "so," or "thus." A chiasmus is a deductive argument in which the conclusion follows from **the first premise** by means of a logical connector and the second premise follows from the conclusion by means of another logical connector.

Syllogisms and chiasmcs can be simple or complex. A simple syllogism has only three terms (or propositions), while a complex syllogism includes four or more terms. Similarly, a simple chiasmus has only two propositions, while a complex chiasmus may include **three, four, or even all five propositions**.

Every syllogism and chiasmcs contains a major premise and a minor premise. The major premise is the first sentence or statement in the argument that gives information about the subject matter under discussion. The minor premise is the next sentence or statement in the argument that builds on the information given in **the major premise**.

- Which of the following is true of a deductively valid argument?
- What is a logical argument that shows a statement is true?
- Which of the following is a valid logical argument?
- What does it mean to say a deductive argument is valid?
- What is correct about deductive reasoning?
- What does "deductive" mean in philosophy?
- What is a valid and sound argument?

If all of the premises are true and the conclusion follows logically from **those premises**, a deductive argument is called valid. If not, it is called an inductive argument.

A deductive argument proves a hypothesis or claim because all the steps in the argument lead to a conclusion that must be true if the premise(s) are. For example, if we were to argue that all swans are white by observing one particular black swan, we have made a logical error because even though all swans are white, this particular swan is not. A valid deductive argument would produce a true conclusion even if the premise(s) are false. For example, if we were to argue that all swans are white by observing one particular black duck, we would still reach the correct conclusion that this particular swan is indeed white. Valid arguments can be easy to construct using logic laws such as "all animals with four legs walk around on earth, therefore cows also walk around on earth" or "if pigs could fly, then they would be birds," which are both examples of syllogisms.

A deductive argument is considered to be valid if and only if it is written in such a way that it is impossible for the premises to be true while the conclusion remains false. In effect, an argument is valid if the truth of the premises assures the truth of the conclusion logically. For example, the argument "All dogs are mortal; Socrates is a dog; therefore, Socrates must die" is valid because the fact that all dogs are mortal guarantees that Socrates will die.

An inductive argument is considered to be valid if and only if it contains either a full proof or strong evidence to support **its conclusion**. A full proof is defined as a sequence of propositions each of which is either a premise or its own consequence, that is, a proposition that can be deduced from the previous one in the sequence. An indirect proof is considered to be a full proof since it can be used to prove **any other proposition** by mathematical induction. For example, the inductive proof that every natural number greater than 2 must contain a prime number as a factor can be used to show that all real numbers greater than 2 are also divisible by **at least one prime number**.

Arguments based on analogy are usually not considered to be valid because an analogy is never sufficient by itself to prove or disprove anything.

For example, suppose we were to argue: All dogs bark; therefore, all cats meow.

This argument is valid because the truth of the first sentence (all dogs bark) guarantees the truth of **the second sentence** (all cats meow). Even if some dogs did not bark, this would not change the fact that all dogs do bark, which means that all cats must meow as well. In **other words**, because all dogs bark, so too must all cats meow.

Deductive arguments are often simple to understand and easy to verify or refute. They are called "deductive" because the conclusion follows directly from the facts or assumptions taken for granted by the argument-builder.

Arguments that use logic instead of mathematics to prove or disprove claims are called "logical." These arguments examine what can be inferred from given information or facts. They require that one consider each possibility and eliminate those possibilities that cannot possibly be true. Only then can one conclude with certainty which possibility remains.

For example, let's say I claim that all bumblebees are white.

The argument is deductive if the arguer believes that the validity of the premises absolutely proves the truth of the conclusion. An argument is valid if the premises cannot all be true without also being true in the conclusion. A good argument is one in which the truth of all of the premises causes the conclusion to be true. If you accept this definition, then deductive arguments are exactly those for which this property holds.

Deductive arguments are easy to identify because they always contain a chain of **logical steps**: a series of statements where each statement uses as **its subject** **some part** of the previous statement. For example, if someone were to argue that all bakers are artists because everyone who bakes art, we could then conclude that "so too are painters". The word "therefore" would not be necessary here because the implication is clear from the first sentence.

In addition to valid arguments, many philosophers also include examples of good arguments in their writings on logic. For example, George Berkeley and David Hume both argued that sensory experience is all we can truly know with certainty, so anything beyond what our senses tell us is mere speculation. However, despite these two opinions holding such different views on what logic is able to prove, both thinkers accepted the validity of the argument "all objects of sense experience are physical, therefore objects of sense experience must be physical."

Logicians have developed rules and strategies for constructing **good arguments**, just as mathematicians do for constructing good proofs.

A deductive argument is one that the arguer intends to be deductively valid, that is, to give a guarantee of the validity of the conclusion if the premises are true. A typical example is a syllogism with all categorical propositions (each premise and conclusion), such as **this one**: All men are mortal; Socrates is a man; therefore, he is mortal.

Deduction is the process of going from facts, definitions, or assumptions about something to another truth-value-bearing statement by means of these items. For example, assuming that all men are mortal, it follows that Socrates is mortal. In formal logic, deduction is the process of moving from a set of premisses to a conclusion by means of logical connectors such as "therefore".

In philosophy, deduction plays a crucial role in many areas of inquiry, including mathematics, science, and logic itself. Mathematics and logic were the first disciplines to develop methods and systems for proof by induction or elimination, but only mathematicians have needed a method for proving deductions. As part of their effort to systematize knowledge about the world, philosophers have used deduction to prove important results in ethics, aesthetics, politics, and other subjects.

A logical argument is sound if and only if it is both valid and true in all of its premises.