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Deductive Reasoning
Deductive reasoning is a type of reasoning which draws a conclusion that follows with logical necessity from a given set of premises. This deductive scheme of a formal argument consisting of premises is also known as a hypothetical syllogism. Deductive reasoning differs from inductive reasoning in which the former requires premises with restricted information to validate the conclusion, while the latter is a logical process where a conclusion is proposed that contains more information than the observations or experience on which it is based. The value of applying deductive reasoning methods to our everyday thinking is that our thinking becomes more systematic and less prone to deception.

Conditional problems of deductive reasoning typically consist of (a) the conditional rule, the major premise, in which two propositions p, the antecedent, and q, the consequent, are linked in the form ‘‘if p, then q’’ (p→q), and (b) a minor premise which is p, q, or one of their negations (¬), and (c) a conclusion. A deductive conclusion often requires at least two premises, and is only based upon the information presented in those given premises. This deductive reasoning design (hypothetical syllogism) is built around a hypothetical statement which can take the form “IF… THEN”. There is no available access to outside information other than the premises taken together, although content is usually manipulated through background knowledge related to perceived necessity and/or sufficiency of p for q. Different arguments may have the same form, or structure.

Two examples of conditional problem forms for deductive reasoning are presented below:

Example 1:

1.	All X are Y. 	 	 (Premise 1)

2.	All Y is Z.		         (Premise 2)

3. ∴, X is Z.  	 (Conclusion)

Example 2:

1.	IF… THEN. 			(Premise 1)

2.	IF.				(Premise 2)

3. ∴,  THEN. 		(Conclusion)

Two examples of worded conditional problems for deductive reasoning are as follows:

Example 1:

1.	All men are mortal.

2.	All humans are men.

3. ∴, All humans are mortal.

Example 2:

1.	If it is spring, then the birds are chirping.

2.	It is spring.

3. ∴, The birds are chirping.

Such hypothetical syllogisms are guaranteed to yield a valid conclusion only when the original premises are valid. Deductive inferences often force the reasoner to ignore practical world knowledge and focus analytically upon the premises supplied.

Basic Rules of Logic: Modus Ponens and Modus Tollens
A hypothetical syllogism has only two terms – the antecedent and the consequent. The antecedent is the “IF” part of the statement. It states the condition under which the “THEN” part is true. The consequent is the “THEN” part, the consequence of what follows from the antecedent if the “IF” part is true.

Modus Ponens: Affirming the Antecedent
Modus Ponens (known as “affirm the antecedent” in Latin) is a logistic principle that whenever a conditional statement and its antecedent are given to be true its consequent may be validly incidental.

Modus ponens can be indicated this way:

1.	If A then B.

2.	 A.

3. ∴, B.

An example of a valid modus ponens syllogism is presented below:

1.	If I am Chinese, I am human.

2.	I am Chinese.

3. ∴, I am human.

The conclusion is valid when the antecedent is affirmed; given that the second premise affirms the antecedent “I am Chinese”, the conclusion “I am human” must be valid.

Modus Tollens: Denying the Consequent
Modus tollens (known as “the way of negation” in Latin) is another form of a valid hypothetical syllogism by denying that the consequent is true. These arguments deny the consequent of a hypothetical statement. If there is a real connection between the antecedent and the consequent, and the consequent is false, then the antecedent must be false. Alternatively, if the consequent is true, then the antecedent is true.

Modus tollens can be indicated this way:

1.	If A then B.

2.	Not A.

3. ∴, Not B.

An example of a valid modus tollens syllogism is presented below:

1.	If I am Chinese, I am human.

2.	I am not human.

3. ∴, I am not Chinese.

The conclusion is valid only when the consequent is denied; given that the second premise denies the consequent “I am human”, the conclusion “I am not Chinese” must be valid.

Validity
Any argument that doesn’t have a deductively valid form is said to be deductively invalid. An argument is valid if and only if it is not possible that all of its premises are true and its conclusion is false. Alternatively, the conclusion must be true if its premises are all true. There are many deductively invalid arguments, but only a few occur so frequently they have been termed. Two instances of deductively invalid arguments are the fallacy of denying the antecedent and the fallacy of affirming the consequent.

Fallacy of denying the antecedent:

Form:

1.	If A, then B.

2.	Not A.

3. ∴, Not B.

Example:

1.	If abortion is murder, then it’s wrong.

2.	Abortion isn’t murder.

3. ∴, Abortion isn’t wrong.

Fallacy of affirming the consequent:

Form:

1.	If A then B.

2.	B.

3. ∴, A.

Example:

1.	If Obama is president, then a liberal is now president.

2.	A liberal is now president.

3. ∴, Obama is president.

It is clear that the conclusion does not follow the premises. Notice how, for both fallacies, the second premise and the conclusion are “switched” with one another as well as the “affirm” or “deny” factor compared to the logical structure of modus ponens and modus tollens, respectively. One structural change to the deductive argument can lead it to be invalid.

Truth
Another large factor for a good argument is that all of its premises must be true. In order for a deductive argument to be ‘good’, validity is not enough. Even when some of the premises are false, the argument can still be valid if it follows the logical order. Consider the following deductive argument:

Example:

1.	No fathers are female.

2.	Sam is a father.

3. ∴, Sam is not female.

It is clear that this argument satisfies the validity requirement. However, it is unknown if the second premise is true; Sam may have no children or Sam may be female, so the second premise is false. This example makes it clear that validity of the argument is different than truth of the argument.

Soundness
Fogelin & Sinnott-Armstrong concluded that when an argument meets both standards of validity and truthfulness, it is said to be sound. If it fails to meet even one oft these standards, it is said to be unsound. A major advantage of having a sound argument is that it must always have a true conclusion, given that all of the premises are true and, since it is valid, it is impossible for the conclusion to be false.

Development and Deductive Reasoning
Life experience facilitates the emergence of deductive reasoning abilities. Since deductive reasoning calls upon an ability to abstract from pragmatic experience, is more difficult for younger children. Deductive reasoning has been viewed as a skill that emerges without training. It is supposed that such skills learned indirectly by students in traditional content areas such as science and mathematics. Deductive reasoning abilities are improved by acquiring an enormous amount of well-organized, domain-specific knowledge and processing strategies can improve performance within a domain by facilitating the ability to recognize important problem features quickly, to access chunks of relevant problem-solving strategies, and to solve problems efficiently and correctly.

Evolutionary Approaches for Deductive Reasoning
According to Leda Cosmides, an American psychologist who helped develop the field of evolutionary psychology with husband John Tooby, states that “these innate information-processing mechanisms that comprise the human mind were not designed to solve arbitrary tasks, but are instead, adaptations: mechanisms designed to solve the specific biological problems biological problems posed by the physical, ecological, and social environments encountered by our ancestor during the course of human evolution”. They argued that understanding the nature of the problems they were “designed” to solve is important to understand cognitive mechanisms themselves. It was found that when it came to solving deductive logical problems, the correct logical choices vastly increased when problems involved a social contract rule (i.e. “cheater detection”) compared to the abstract logical structure of the Wason selection task. Examples of the two are presented below:

(a) Abstract Problem

You have been hired as a clerk. You job is to make sure that a set of documents is marked correctly, according to the following rule: “If the document has a D rating, then it must be marked code 3.” You have been told that there are some errors in the way the documents have been coded and that you need to find the errors. Each document has a letter rating on one side and a numerical code on the other. Here are four documents. Which document(s) do you need to turn over to check for errors?

[D]    [F]      [3]      [5]

(b) Drinking Age Problem (Social Contract Rule)

You have been hired has a bouncer in a bar and you must enforce the following rule: “If a person is drinking vodka, then he or she must be over 20 years old.” The cards depicted in the figure contain information about four people in the bar. One side of each card lists a person’s age and the other side specifies what he or she is drinking. Which card(s) do you need to turn over to make sure that no one is breaking the law?

[BEER]    [SODA]      [25]      [17]

The reasoning behind the difference in performance between the social contract rule design and the abstract design is that human cognitive mechanisms were not needed and therefore not formed to specifically address such abstract problems. In particular, human cognitive functions are believed to have been significantly altered in the Pleistocene era, beginning approximately two million years ago. This time period was also known as the environment of evolutionary adaptation (EEA), where human cognition was adapted to deal with problems present in that time - detecting individuals who take resources that are not rightfully theirs. Our ancestors did not have to know how to deal with abstract problems because such problems were never encountered in the EEA. In turn, Cosmides concluded that:

1.	The human mind must contain algorithms that produce and operate on cost-benefit representations of exchange interactions.

2.	The human mind must include inferential procedures that make one very good at detecting cheating on social contracts.

Individual Differences in Deductive Reasoning
Individual differences research can provide evidence relevant to the rationality debate: the dispute as to whether humans are rational. People make many errors when faced with reasoning tasks, and the issue is whether these errors come from internal factors (e.g. inherent irrationality) or extraneous factors (e.g. misunderstanding task). In syllogistic reasoning, there is a belief bias, whereby individuals ignore the logic and give the response that corresponds to their prior beliefs. There is also good evidence that deductive reasoning abilities correlates with logical performance on syllogisms (deductive arguments).