2. NITIN RANA PARIKSHIT GAUR PURNENDU PuLKITPAL SINGH RISHAB RAJ RITIKA GAUTAM Group MEMBERS ARE -

3. Deductive reasoning is sometimes referred to as top-down logic. Its counterpart, inductive reasoning, is sometimes referred to as bottom-up logic. Where deductive reasoning proceeds from general premises to a specific conclusion, inductive reasoning proceeds from specific premises to a general conclusion. The Greek philosopher Aristotle, who is considered the father of deductive reasoning, wrote the following classic example: All men are mortal.Socrates is a man.Therefore, Socrates is mortal. In Aristotle’s example, sometimes referred to as a syllogism, the premises of the argument -- that all men are mortal and that Socrates is a man -- are self-evidently true. Because the premises establish that Socrates is an individual in a group whose members are all mortal, the inescapable conclusion is that Socrates must likewise be mortal.

4. “Deductive reasoning is a logical process in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true”.

6. Two Methods of Reasoning by Harvey Bluedorn. Copyright 1995. All rights reserved. An Introduction to Inductive and Deductive Logic Fixing Flawed Thinking We often suppose that the other guy's thinking is flawed, without even considering whether the real problem is actually with our own thinking. We tend to elevate our limited observations and our plausible opinions to the level of sure facts and infallible conclusions. Faith indeed has a part in logic, but too often we give it the wrong part. We know what we want to believe, and we conclude that it therefore must be true. But t’ain’t necessarily so. We need to recognize what method of reasoning we are using, and what are the limits of that method of reasoning.

8. Reasoning can run in two opposite directions. Deductive reasoning moves from a general premise to a more specific conclusion. Inductive reasoning moves from specific premises to a general conclusion. These two methods of reasoning will produce two different kinds of results. Two Methods Of Reasoning

11. Let's look at inductive reasoning first. Inductive reasoning moves from the particular to the general. It gathers together particular observations in the form of premises, then it reasons from these particular premises to a general conclusion. The most common form of inductive reasoning is when we collect evidence of some observed phenomena (e.g. examining 10,000 dogs for fleas), then we draw a general conclusion about all such phenomena based on our collected evidence (e.g. whether all dogs have fleas). In an inductive argument, the conclusion goes beyond what the premises actually say. For example, if I observe 10,000 dogs, and every dog has fleas, I may conclude "All dogs must have fleas." The conclusion is a conjecture or a prediction. Further evidence may support or deny my conclusion. The 10,001st dog may not have fleas. Therefore, with an inductive argument, anyone can affirm all my premises (10,000 dogs with fleas, yet deny my conclusion (all dogs have fleas) without involving himself in any logical contradiction. What I say in my conclusion is possible, It may even seem very probable. Nevertheless, it is not a necessary conclusion. If someone said,

12. "Some dogs may have fleas, but I don't believe all dogs have fleas," there is no logical response I could make. The logical certainty of my conclusion is entirely dependent upon my correct interpretation of the evidence and the consistency of the evidence with the remainder of the phenomena which was not, is not, or may never be observed. Maybe I had fleas, and I inadvertently transferred them to each of the 10,000 dogs, so the 10,000 dogs actually had no fleas except when I examined them. I would have to examine all dogs at all times under thoroughly monitored conditions in order to "prove" my conclusion. But this would be an impractical task. Therefore it is unlikely my conclusion will ever be proven. It can, however, be disproven. Find one dog without fleas. Then you will be left with the conclusion which I should have arrived at to begin with, "Some dogs have fleas." Maybe most dogs, or nearly all dogs have fleas. But all I know for certain is that some dogs have fleas. Remember, an inductive argument concludes more than the premises actually warrant.

13. We use inductive reasoning all of the time. It is very useful. But we must recognize its limits. Most inductive reasoning is not based upon exhaustive evidence, and therefore the form is incomplete. (10,000 dogs is not all dogs.) Unless the evidence or observations are exhaustive (I examine all dogs for fleas), the conclusion is only a guess. It may be a good guess. The strength of the inductive argument is increased as it approaches completeness. If the evidence I accept represents all possibilities within the whole, my inductive conclusion will be correct. The more I can demonstrate that the evidence is truly representative, the more compelling will my conclusion be. "10,000 dogs of every age and variety chosen at random from every country on the earth were examined under controlled conditions, and all of them had fleas. Therefore, it seems likely that all dogs have fleas."

14. Deductive reasoning moves from the general to the particular. It takes a general premise and deduces particular conclusions. A "valid" deductive argument is one in which the conclusion necessarily follows from the premise. (All dogs have fleas. This is a dog. Therefore this dog has fleas.) The premise may not be "true" but the form of the argument is nevertheless "valid". (If all dogs do have fleas, and if this is a dog, then this dog must necessarily have fleas.) An "invalid" deductive argument will contain something in the conclusion wholly new and independent from those things mentioned in the premise of the argument. (If all dogs have fleas, then my dog must have ticks. But ticks are not mentioned in the premise.) Sometimes it is not so obvious that something new has been introduced in the conclusion. (Only man is a rational being. Therefore, no woman is a rational being

15. Sources of Deductive Premises If one believes all the premises in a valid deductive argument, he must believe the conclusion. The premise of a deductive argument may come from several sources. In order to evaluate the truth of the deductive argument, it is important to recognize the source of its premises.

16. The conclusion of an inductive argument may be used as the premise of adeductive argument. The weakness of most inductive arguments is that they begin with incomplete premises. (10,000 dogs is not all dogs.) One may arrive at a false inductive conclusion (All 10,000 dogs examined had flees, therefore all dogs have fleas.). He may use this false conclusion as the premise of a valid deductive argument (Since all dogs have fleas, therefore this dog must have fleas). If the premise is false, the conclusion is false. (This dog may indeed have fleas, but it is not a necessary consequence of the fact that all dogs have fleas, because all dogs do not necessarily have fleas, only 10,000 dogs had fleas at the time they were tested.) Scientists commonly arrive at inductive conclusions on the basis of inadequate information, then argue deductively from their induction.

17. Invalid and False Inductive argument : All living creatures have a genetic code. Therefore all living creatures are genetically related. Valid but False Deductive Argument: All living creatures are genetically related. Man is a living creature. Therefore man is genetically related to all other living creatures.

18. If A = B and B = C, then A = C.All apples are fruits, all fruits grow on trees; therefore, all apples grow on trees.William is a bachelor, all bachelors are single; hence William is single.Since all humans are mortal, and I am a human, then I am mortal. All dolphins are mammals, all mammals have kidneys; therefore all dolphins have kidneys. Since all squares are rectangles, and all rectangles have four sides, so all squares have four sides. If Dennis misses work and at work there is a party, then Dennis will miss the party.All numbers ending in 0 or 5 are divisible by 5. The number 35 ends with a 5, so it is divisible by 5.The Earth is a planet, and all planets orbit a sun, therefore the Earth orbits a sun.To earn a master’s degree, a student must have 32 credits. Tim has 40 credits, so Tim will earn a master’s degree.All birds have feathers and robins are birds, so robins have feathers.It is dangerous to drive on icy streets. The streets are icy now so it is dangerous to drive now.All cats have a keen sense of smell. Fluffy is a cat, so Fluffy has a keen sense of smell.The elm is a tree and all trees have bark, so elms have bark.Snakes are reptiles and reptiles are cold-blooded; therefore, snakes are cold-blooded.Cacti are plants and all plants perform photosynthesis; therefore, cacti perform photosynthesis.Red meat has iron in it and beef is red meat, so beef has iron in it.Acute angles are less than 90 degrees and this angle is 40 degrees so this angle is acute.All noble gases are stable and helium is a noble gas, so helium is stable.Magnolias are dicots and dicots have two embryonic leaves; therefore magnolias have two embryonic leaves.Elephants have cells in their bodies and all cells have DNA, so elephants have DNA.All cars have at least two doors and a Ford Focus is a car, so the Ford Focus has at least two doors.All horses have manes and the Arabian is a horse; therefore Arabians have manes.Other Patterns of Deductive Reasoning