Syllogistic Reasoning-Categorical Syllogisms PDF

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Syllogistic Reasoning: Categorical Syllogisms Syllogistic reasoning Syllogistic Reasoning is the other key type of deductive reasoning which is based on the use of syllogisms. Deductive arguments sometimes take a form called a syllogism. Syllogisms Syllogisms derive from the Greek word syllogismos, meaning conclusion or inference. It is deductive arguments that involve drawing conclusions from two premises-major premise and minor premise.

The following is an example of a syllogism: All men are mortal Socrates is a man Therefore, I am mortal

MAJOR PREMISE

MINOR PREMISE

CONCLU SIONS

This draws a clear picture of how one statement, when known to be universally true, should point perfectly to another clear claim, thus drawing an accurate conclusion. In logic, syllogism aims is to identify the general truths in a particular situation What is a Categorical syllogism?  

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The most well-known kind of syllogism. It is an argument consisting of exactly three categorical propositions (two premises and a conclusion) in which there appear a total of exactly three categorical terms, each of which is used exactly twice.The first two premises are given and presumed to be true. The third categorical proposition is the conclusion. A categorical proposition is termed "valid" if the premises are sufficient support to prove the conclusion true. The premises are always presumed to be true. To avoid confusing oneself, the use of factually true premises is useful when examining a syllogism.

In fact, each term represents all, none, or some of the members of a particular class or category. To determine whether the conclusion follows logically from the premises, the reasoner must determine the category memberships of the terms. Parts of Categorical syllogism

A. Major Term- the predicate of the conclusions (animals with hearts) B. Minor Term- the subject of the conclusions (dogs) C. Middle Term- the term repeated in the premises, but not in the conclusions (mammals) MP1- All mammals are animals with hearts MP2- All dogs are mammals C- All dogs are animals with hearts Moods of Categorical syllogism  The moods of a categorical syllogism- the letters of the three propositions that compose the syllogisms All mammals are animals with hearts All dogs are mammals All dogs are animals with hearts

EAE

AAA

No mammals are animals with hearts All dogs are mammals No dogs are animals with hearts

Some mammals are animals with hearts All dogs are mammals Some dogs are animals with hearts

IAI

 An example of a categorical syllogism would be as follows: All cognitive psychologists are pianists. All pianists are athletes. Therefore, all cognitive psychologists are athletes.

No geese are felines. Some birds are geese. Therefore, some birds are not felines.

Four kinds of Premises: 1. Statements of the form “All A are B” sometimes are referred to as universal affirmatives, because they make a positive (affirmative) statement about all members of a class (universal). Example:

All cognitive psychologists are pianists. All pianists are athletes. Therefore, all cognitive psychologists are athletes.

Note: All is A is B then all B is A therefore when the statement is positive then the conclusions must be positive 2. Universal negative statements make a negative statement about all members of a class (e.g., “No cognitive psychologists are flutists.”). The possible conclusions are: No A is B No B is A Some A is not B Some B is not A

Example: No geese are felines. Some birds are geese. Therefore, some birds are not felines.

Note: When NO comes in statement, SOME-NOT should follow in conclusion. 3. Particular affirmative statements make a positive statement about some members of a class (e.g., “Some cognitive psychologists are left-handed.”). 4. Particular negative statements make a negative statement about some members of a class (e.g., “Some cognitive psychologists are not physicists.”). How do people solve syllogisms? Various theories have been proposed as to how people solve categorical syllogisms. 1. Using atmosphere bias. There are two basic ideas of this theory: a. If there is at least one negative in the premises, people will prefer a negative solution. b. If there is at least one particular in the premises, people will prefer a particular solution. For example, if one of the premises is “No pilots are children,” people will prefer a solution that has the word no in it. 2. Using a semantic (meaning-based) process based on mental models. A mental model is an internal representation of information that corresponds analogously with whatever is being represented. Mental model theories postulate that human beings reason, not on the basis of form, but on the basis of content. They can construct mental models of situations both when they perceive a real event and when they understand discourse. The mental processes underlying reasoning are therefore semantic, not syntactic.

Aids and Obstacles to Deductive Reasoning

In deductive reasoning, as in many other cognitive processes, we engage in many heuristic shortcuts. These shortcuts sometimes lead to inaccurate conclusions . In addition to these shortcuts, we often are influenced by biases that distort the outcomes of our reasoning. Heuristics in Deductive Reasoning Heuristics in syllogistic reasoning include overextension errors. In these errors, we overextend the use of strategies that work in some syllogisms to syllogisms in which the strategies fail us. For example, although reversals work well with universal negatives, they do not work with other kinds of premises. We also experience foreclosure effects when we fail to consider all the possibilities before reaching a conclusion. In addition, premise-phrasing effects may influence our deductive reasoning, for example, the sequence of terms or the use of particular qualifiers or negative phrasing. Premise-phrasing effects may lead us to leap to a conclusion without adequately reflecting on the deductive validity of the syllogism. Biases in Deductive Reasoning Biases that affect deductive reasoning generally relate to the content of the premises and the believability of the conclusion. They also reflect the tendency toward confirmation bias. In confirmation bias, we seek confirmation rather than disconfirmation of what we already believe. Suppose the content of the premises and a conclusion seem to be true. In such cases, reasoners tend to believe in the validity of the conclusion, even when the logic is flawed (Evans, Barston, & Pollard, 1983). Confirmation bias can be detrimental and even dangerous in some circumstances. For instance, in an emergency room, if a doctor assumes that a patient has condition X, the doctor may interpret the set of symptoms as supporting the diagnosis without fully considering all alternative interpretations (Pines, 2005). This shortcut can result in inappropriate diagnosis and treatment, which can be extremely dangerous. Enhancing Deductive Reasoning 1. Avoid heuristics and biases that distort our reasoning. 2. Engage in practices that facilitate reasoning. 4. Training and practice seem to increase performance on reasoning tasks. References: Sternberg, R,J, & Sternberg, K. (2011) Cognitive Psychology 6th edition https://www.mesacc.edu/~barsp59601/text/103/notes/syllogisms.pdf http://www.philosophypages.com/lg/e08a.htm#:~:text=A%20categorical%20syllogism %20is%20an,which%20is%20used%20exactly%20twice.&text=The%20other %20premise%2C%20which%20links,we%20call%20the%20minor%20premise. https://courses.lumenlearning.com/atd-epcc-introethics-1/chapter/syllogisms/...