LOGICAL REASONING

Logical reasoning

Logical reasoning is a system of making conclusions based on a set of grounds or information. Normally, logical reasoning is subdivided into two main types known as deductive and inductive reasoning. Whereas the principles of logic can be used to form a strong argument for or against a conclusion, the system has a lot of vulnerabilities, which includes the potential for false grounds, fallacies, and intentional distortion of reason.

To make a conclusion with the use of logical reasoning, evidence or facts ought to be first presented. For example, if a grocer wants to know if he is selling more beets than turnips, he may collect evidence about the amount of the two vegetables in latest shipments, how many have been sold, and if any product loss has occurred as a result of theft or damage. If his information shows that he sold 52 turnips and 75 beets in the same month, with no loss as a result of theft or damage, he can logically conclude that he sells more beets than turnips based on the evidence.

The type of reasoning in the above instance is referred to as deductive reasoning. This type of logic takes place when the information adds up to a distinct, irrefutable conclusion. Given that the information is correct, deductive reasoning can show an absolute truth or fact. Inductive logic, by contrast, makes use of information or premises to determine a highly probable, but not total, conclusion. Whereas inductive logical reasoning can be far more difficult to comprehend than deductive reasoning, it commonly forms the bulk of the majority of logic-based arguments.

One type of inductive reasoning takes care of conclusions that have to do with the future. If the grocer from the first instance given wants to know whether he will sell more turnips or beets over the next month, an absolute answer is not possible to get hold of, for the fact that it is a game of chance. Based on his past sales, the grocer might suppose that since he sold more beets in January, he will also sell more in February; nevertheless, if an E.coli outbreak in beets at the beginning of February makes people afraid of buying any, his former conclusion may be false. Making use of his sales records and knowledge of buying trends, he may be able to deduce an inductive argument that suggests a high probability of selling more beets than turnips, but his premises cannot add up to an complete guarantee.

Logical reasoning can be a good servant but a poor master. Whereas the principles of making use of accurate information to draw a strong conclusion may be very good, they often times break down when they are made use of incorrectly. A logical fallacy happens when an erroneous or unconfirmed conclusion is drawn from premises. There are dozens of forms of logical fallacies that serve as tripwires and pitfalls to good logical reasoning . Take time to learn how to make a sound, and convincing argument.

Definition of Logical Reasoning

Logical reasoning is the process of making use of a rational, systematic series of steps based on sound mathematical procedures and given statements to come to a conclusion. Geometric proofs make use of logical reasoning and the definitions and properties of geometric figures and terms to state definitively that something is constantly true. In logical reasoning, an if-then statement (as well referred to as a conditional statement) is a statement formed when one thing means another and can be written as and read as “If P then Q.” A contra positive is the provisional statement formed when negating both sides of the implication and could be written asand read as “If not Q, then not P.” Anything that is not established is referred to as a conjecture.

Logical reasoning is the process which makes use of arguments, statements, information and proverbs to decide if a statement is true or false,. This leads to logical or illogical reasoning. In today’s logical reasoning, three various kinds of reasoning can be differentiated as deductive reasoning, inductive reasoning and abduction reasoning and are based on deduction, induction and abduction respectively.

Deductive Reasoning

Deductive reasoning emanates from the philosophy and mathematics and is the most observable type of reasoning. Deduction is a method for applying a common rule (major premise) in particular situations (minor premise) of which conclusions can be drawn. For instance,

Major premise: All humans are mortal

Minor premise: Socrates is human

Conclusion: Socrates is mortal

Straight away the observable and straightforwardness of the conclusion can be drawn from the premises above the example of deductive reasoning. Observe that deductive reasoning no fresh information is provided, it only rearranges information that is previously known or given into a new statement or conclusion.

Inductive Reasoning

The exact opposite of deductive reasoning is inductive reasoning. In this type of logical reasoning particular conclusions are generalized to general conclusions. A well-known hypothesis is ‘all swans are white’. This conclusion was derived from a large amount of observations without observing any black swan. Inductive reasoning, nevertheless is a risky form of logical reasoning since the conclusion can easily be mistaken when, looking at the swans model, a black swan is spotted. Nevertheless, in the modern day, inductive reasoning is the most frequently used type of reasoning in physics and philology.

Abductive Reasoning

Abductive reasoning is the third type of logical reasoning and is rather comparable to inductive reasoning, due to the fact that conclusions drawn here are based on probabilities. In abductive reasoning, it is assumed that the majority of reasonable conclusion is as well the correct one. For instance:

Major premise: – The jar is filled with yellow marbles

Minor premise: – I have a yellow marble in my hand

Conclusion: –  The yellow marble was taken out of the jar

The adductive reasoning example vividly illustrates that conclusion might look obvious; however, it is solely based on the most believable reasoning. This type of logical reasoning is mainly used within the field of science and research.

Formal and Informal Logic Reasoning

In addition to these 3 types of logical reasoning, it is as well possible to make a difference between formal reasoning and informal reasoning. Formal reasoning is a type of logical reasoning based on valid premises and thus valid conclusions; therefore, it is a form of deductive reasoning. It makes available no new information, but just rearranges already known information to a new conclusion.

In addition to this formal reasoning we as well have informal reasoning. This type of logical reasoning possesses all the elements of formal reasoning, like the deduction part; nevertheless, it as well includes probabilities and truths about premises and conclusions. It can be said that informal reasoning is connected to abductive reasoning, one of the other three types of logical reasoning explained above

Linking these two forms of logical reasoning together with the three various forms results in the following differences in logical reasoning:

1. Deductive

a. Formal deductive reasoning

b. Informal deductive reasoning

2. Inductive

a. Formal inductive reasoning

b. Informal inductive reasoning

3. Abductive

a. Formal abductive reasoning

b. Informal abductive reasoning

Wrong can be Right Logically

Within logical reasoning it can occasionally occur that the premises and conclusion look as if clearly wrong, but are logically speaking correct when applying one of the types of logical reasoning stated above. Notice that conclusions are drawn based on logical reasoning and not on the validity of the context of particular premises or conclusions. For instance:

Major premise: –  Eating a lot makes you lose weight

Minor premise: – Craig is obese

Question: –  What can we do to make Craig lose weight?

Conclusion: –  We can make Craig eat a lot

By mere observation of the context of the words, you would think that this conclusion is incorrect, for the fact that you are aware that from everyday life, eating a lot does not make you lose weight at all but rather makes you gain weight. Nevertheless, based on logical reasoning this conclusion is most certainly correct, since both premises are valid, which routinely makes the conclusion a valid conclusion. What you require to understand is that the correct answer to any given logical reasoning argument needs the proper identification of relationships between assertions (normally facts and opinions), not the correctness of those assertions.

Logical Reasoning in Aptitude Tests

Logical reasoning commonly is a very significant section in aptitude tests and/or IQ tests. Logical reasoning is universal and it is made use of in every form of reasoning, in every job, in every field and every day. Therefore, if you possess good logical reasoning skills you ought to be able to apply this everywhere. Better developed logical reasoning skills make you able to comprehend, examine, and to query arguments based on statements or questions. These skills are generally made use of to identify clues that make an argument weaker, or to identify a particular assumption. Logical reasoning can be tested in quite a few different ways, nevertheless on Fibonicci you would get the most significant and most commonly accepted type of logical reasoning known as syllogisms.

There is a special notation known as functional notation that is constantly used in mathematics when one variable is described in terms of another.  The notation f(x) [read f of x] is frequently used to name a second variable.  Instead of writing y = 3x + 2 you may write f(x) = 3x + 2 or g(x) = 3x + 2 or possibly even y(x) = 3x + 2.  You can make use of any letter.  This notation showcase that f or  g or y  is a function of the variable x, which means that it can be articulated in terms of x.  To find the value of f(2), merely replace every x with the value 2.  To obtain the value of f (4), substitute each x in the given formula  with the value 4.  To discover the value of f(-3), substitute each x in the formula with the value -3.  Observe that f(x) does NOT mean to multiply f times x.

Example 1

Given f(x) = 2x + 3. 

Find the values of  a) f(0), b) f(7), c) f(-5).

Answer: 

(a) f(0) means that x = 0.  Substitute the x with the value of 0.

f(x) = 2x + 3

 f(0) = 2(0) + 3 = 3

(b) f(7) means that x = 7.  Substitute the x with the value of 7.

f(x) = 2x + 3

 f(7) = 2(7) + 3 = 14 +  3  or 17

(c) f(-5) means that x = -5.  Substitute the x with the value of -5.

f(x)  = 2x + 3

f(-5) = 2(-5) + 3 = -10 +  3  or -7