Introduction to solve math problems deductive reasoning
Deductive reasoning is one of the two essential forms of suitable reasoning. The reasoning constructs or evaluates deductive reasoning. While deductive reasoning argues from the general to exacting , similarly inductive reasoning argues from the specific to a general instance. Deductive arguments may be valid or invalid,and sound or unsound, but that are not true or false. Whenever we turn up for the conclusion using facts, definitions, rule, or properties, then it is so called Deductive Reasoning.
Types of reasoning:
The types of reasoning are
• AbductionAnalogical reasoning
• Cause-and-effect reasoning
• Cause-to-effects reasoning.
o Effects-to-cause reasoning
o The Bradford Hill Criteria
o Comparative reasoningConditional
o reasoningCriteria reasoning.
• Decompositional reasoning
• Deductive reasoning
• Exemplar reasoning
• Inductive reasoning
• Modal logic
• Traditional logic
• Pros-vs-cons reasoning
• Set-based reasoning.
• Systemic reasoning
Example for Deductive Reasoning
1.To determine (a × b...
example, Skloot states, “As Cliff and Fred lowered Henrietta’s coffin into her grave and began covering her with handfuls of dirt, the sky turned black as strap molasses. The rain fell thick and fast. Then came long rumbling thunder…” and Henrietta’s cousin Peter, stated, “We shoulda knew she was trying to tell us something with that storm” (92). Skloot, includes this casual argument because it illustrates how Henrietta’s family believes Henrietta created the storm. Skloot also uses deductive reasoning, which goes from general to specific. For example, she states, “First, HeLa didn’t grow from one of Henrietta’s cells. It grew from a sliver of her tumor, which was a cluster of cells. Second, cells often behave differently, even if they’re all from the same sample, which means some grow faster than others” (99). Skloot uses deductive reasoning to explain how HeLa began and uses specific evidence. Skloot uses both types of reasoning in her book to create a stronger argument.
There is nothing inherently wrong with this method. However, it does become a problem when a deductive argument is attempting to bring something into existence. We simply cannot do that, for it goes against the common sense laws of logic. Gaunilo offered us an example famously known as the “Isle of the Blessed” (Peterson 173). In this example, he attempts to use the same deductive form Anselm uses to bring an island into existence. “Because it is better that such a perfect island exists in reality than simply in the mind alone, this Isle of the Blest must necessarily exist” (Pojman 42).
Rene Descartes Method of Doubt was simply his mathematical method in discovering the unanswered questions about the universe. He wanted to prove every unknown question and be certain that he could prove his truths with knowledge given only by mathematical proof. "Common Sense", which Descartes refers to as natural reason, is the understanding of all humans with many given subjects. He feels that in some common sense areas, one should just be expected to know what all humans are assumed to know and therefore, does not need to be mathematically proven.
Deduction is the third characteristic of rationalism, which is to prove something with certainty rather than reason. For example, Descartes attempted to prove the existence of God through deductive reasoning in his third meditation. It went something like this: “I have an idea of a perfect substance, but I am not a perfect substance, so there is no way I could not be the cause of this idea, so there must be some formal reality which is a perfect substance- like God. Because only perfection can create perfection, and though it can also create imperfection- nothing that is imperfect can create something that is perfect.
There are two main types of arguments: deductive and inductive. A deductive argument is an argument such that the premises provide (or appear to provide) complete support for the conclusion. An inductive argument is an argument such that the premises provide (or appear to provide) some degree of support (but less than complete support) for the conclusion. If the premises actually provide the required degree of support for the conclusion, then the argument is a good one. A good deductive argument is known as a valid argument and is such that if all its premises are true, then its conclusion must be true. If all the argument is valid and actually has all true premises, then it is known as a sound argument. If it is invalid or has one or more false premises, it will be unsound. A good inductive argument is known as a strong (or "cogent") inductive argument. It is such that if the premises are true, the conclusion is likely to be true.
The term inductive reasoning refers to reasoning that takes specific information and makes a broader generalization that is considered probable, allowing for the fact that the conclusion may not be accurate. An example of inductive reasoning is: All observed children like to play with Legos. All children, therefore, enjoy playing with Legos. Relying on inductive reasoning throughout everyday life is just a part of human nature. If someone were to take into consideration every plausible outcome of a given situation, they would never get anything done or been stricken with worry. The simple principle of induction (SPI) states that:
The problem of induction has a close relation with the inductive reasoning and such expression as “a posteriori”. There are two distinct methods of reasoning: deductive and inductive approaches. A deductive argument is the truth preserving in which if the premises are true than it follows that the conclusion will be true too. The deductive reasoning goes from the general to the specific things. On the other hand, an inductive argument is an argument that may contain true premises and still has a false conclusion. Induction or the inductive reasoning is the form of reasoning in which we make a conclusion about future experience or about presence based on the past experience. The problem of induction also has a connection with the expressions as “a priori” and “a posteriori”. The truth in a priori statement is embedded in the statement itself, and the truth is considered to be as common knowledge or justification without the need to experience. Whereas, in order to determine if a pos...
...undervalued the use of inductive reasoning, more modern logicians have embraced the value of this type of thinking and acknowledge that both inductive and deductive reasoning can be used to arrive at more thorough and accurate truths about our world and the situations that occur within it.
In this argument, if “employees have a duty of loyalty to the companies that employ them” is considered the p and “it is rational for employees to expect companies to recognize and fulfill a duty of loyalty to their employees” will be the q. It continues to follow that q is false as it is not rational for employees to expect companies to recognize and fulfill loyalty to their employees. The logical form ends with not p as “It is false that employees have a duty of loyalty to the companies that employ them”. It is known that this argument is deductively valid but in order to show that the conclusion is also true, it must be true that the argument is deductively sound. An example of a deductively valid argument would be as following: Premise 1) All mammals have four feet; Premise 2) Lions are mammals; Conclusion) Therefore, Lions have four feet. Premise 1 in this argument is true, mammals do have four feet, Premise 2 is also true, Lions are mammals, and therefore the conclusion is also true that Lions have four feet. With these true premises leading to a true conclusion help us understand
...h not justifiable enough to be relied. Even though the inductive reasoning has been a success in the determination of events and instances that have occurred in the past, philosophers still argue about its appropriateness, in the modern society (Earman, 2006, p.36). The problem of induction has been analyzed through various philosophical studies with the aim of finding a justifiable answer to the dilemma. The uncertainty of inductive reason forms the basis of myriad questions that engulf the justification of the approach. According to some philosophers, it is possible that some unknown phenomenon might occur, leading to justification with a known phenomenon. As aforementioned, falsification and irrationalism are some of the solutions to the induction problem. It is, therefore, imperative for individuals to falsify the beliefs through hypothesis and empirical testing.
Reasoning is the action of constructing thoughts into a valid argument. This is probably something you do every day. When you make a decision, we are using reasoning. By taking different thoughts and thinking why you should go with one thought over another. Inductive and deductive reasoning are both propositional logic. Propositional logic is the branch of logic that studies ways of joining and simplifying entire propositions, statements to hold more complicated propositions or statements. This means it uses a combination od facts to come up with a conclusion.
A sound deductive argument, within the context of finding a definite answer, requires that, “it is both valid, and all of its premises are actually true.” (“Validity and Soundness”) In other words, a deductive argument is sound if the ‘things’ that it is standing on are real, and it relates these things in a way that logically leads to the argument’s conclusion. For example, a sound deductive argument could follow that, “If I fill up my car with gas, I will not wind up with an empty tank. I have filled my car up with gas, therefore I will not wind up with an empty tank.” Since the premise that a car needs gas to stay ‘full’ is true, and the premise and conclusion of the argument are logically related, the argument
...erlock Holmes. “It’s not an easy task, that constant cognitive vigilance, the eternal awareness of our own limitations and the resulting strategic allocation of attention” (Konnikova, "Do You See like Dr. Watson or Observe like Sherlock Holmes"). It is not easy for some people to think just like him but it is something that can be acquired by constant practice and dedication. Holmes teaches us how to be mindful to our surroundings and apply it in our lives. He also shows us how to make great connections about the things that we see and the things that we know already and from there deduce the possible cause. The use of deductive reasoning as a convention is crucial because not all readers possesses extraordinary intellect like Holmes but as we, the readers go through the novel, learn to expand these abilities ourselves and learn to apply them in our everyday lives.
Reasoning is a way of knowing; it is the process of forming ideas based on previous knowledge. It is rational, and therefore by reasoning, events appear to be logical and consistent. Whether reasoning can expose truth is determined...