 Reason is the capacity to think, understand and form judgments through a process of inference that is guided by some form of logic. It is one of the ways by which thinking leads from one idea to a related idea and generates knowledge that is based upon a coherent set of rules. When looking at the different types of reasoning, philosophers have come to define two primary and distinct kinds, called deductive and inductive reasoning. Induction and deduction differ in both structure and in the strength of their conclusion. Concerning structure, in a generalized sense, deductive reasoning is reasoning downwards from a premise to a specific conclusion, whereas inductive reasoning is bottom up where we start with a number of specific instances and then move towards a more general conclusion. With respect to the strength of conclusion, deductive reasoning leads to certainty, whereas inductive reasoning leads to probability. In inductive arguments, the conclusion is constrained within the premise. This is, in a sense, a closed system, a form of thinking inside the box. As we follow a well-defined set of steps according to a well-defined set of rules, leading directly from premise to conclusion. In contrast, induction is more like thinking outside the box, we're inferring from what we know to what might be true. Deduction is a process of reasoning from a given statement to a conclusion through a well-formed set of steps. It typically involves reasoning from the general to the particular, but not always. For example, our premise might be that good students pass exams, and that Kate is a good student, therefore Kate will pass the exam. We can see how the original premise leads directly to the conclusion. In deductive reasoning, the conclusion is derived from the original premise, and thus every deductive argument is either valid or invalid, and this can be mathematically proven. If in the above example, the final statement does not prove valid, that is to say Kate does not pass the exam, then we'd have to go back and check the premise as either one of them must be incorrect. Proofs are examples of deductive reasoning. In mathematics, a proof is a deductive argument for a mathematical statement. In principle, a proof can be traced back to self-evident or assured statements, which are known as axioms. An axiom is a statement or proposition that is regarded as being established, accepted or self-evidently true. A proof, because it is deductive, must demonstrate that a statement is always true, rather than enunciate many confirmatory cases. An unproved proposition that is believed to be true is known as a conjecture. A classical example of an axiomatic system, Euclid's method consists of assuming a small set of intuitively appealing axioms and deducing many other propositions or theorems from these axioms. Unfortunately, most events in the world cannot be summed up into nice neat proofs. In the everyday world, deduction involves a requirement for a large amount of general information in order to give one a specific conclusion that may be certain but is often quite obvious and not very helpful. And thus, in addition to being able to reason logically from a given statement to another in a deductive fashion, one also needs to be able to take what one has experienced before and use that to infer general theories to predict what might happen in the future. This is inductive reasoning and it is the type of reasoning we use all day, every day. Induction is very different from the analytical method of deduction. It is more a process whereby general propositions are established based upon a limited amount of particular instances. It typically involves passing from the particular to the general, saying something new based on what we already know. Polling would be a good example of this. We often take polls of a population to draw a conclusion about the whole population. In this process, we're gathering data from a limited number of instances, a small subset of the population and we then use that data to draw conclusions about the whole population. As we are generalizing from what we know to what might be true, induction cannot be certain. It can only have varying degrees of strength, which can be interpreted statistically. Inductive reasoning may be almost 100% true, but never be proven certain like deductive conclusions. Its application in the world rests on the assumption that there are unchanging effects produced by natural causes, and a general induction is made by discovering apparent uniformities which form the basis for generalizations. With induction, we can only ever achieve probabilities never mathematical certainties like deduction. Induction involves taking samples from the past and projecting them onto future events. It is based on the insight that the future often resembles the past. Thus, inductive reasoning, in its broadest sense, includes all inferral processes that expand knowledge in the face of uncertainty. The process of induction has been the great method of modern science, and through it many of the great celebrated achievements of science have been made. Thus it was by induction that Newton discovered the principles of gravity, and Darwin came to the theory of evolution. Sometimes the world works on predictable rules of inference, but sometimes it does not. Sometimes the future is not the same as the past, and unlikely events do in fact occur. To solve this, we need a similar but different form of reasoning called abduction. Abductive reasoning is often described as being inference to the best explanation. Abductive reasoning is a form of logical inference which goes from an observation to a theory which accounts for that observation, ideally seeking to find the simplest and most likely explanation and this is the essence of scientific inquiry. It involves the gathering of data and the formulation of theories and conjectures to explain that data. Abduction works by taking in data and ruling out the impossible explanations until one is left with only with the most plausible options given the evidence. It is a form of logical inference which goes from an observation to a theory which accounts for the observation, ideally seeking to find the simplest and most likely explanation. For example, in a billiard game, after seeing the red ball moving towards one, we may have ducked that the cue ball struck the red ball and that's why it's moving. The strike of the cue ball would account for the movement of the red ball. It serves as a hypothesis that explains our observation. Given the many possible explanations for the movement of the red ball, our abduction does not leave us certain that the cue ball in fact struck the red ball. But abduction is still useful in serving to orientate us in our surroundings. Despite many possible explanations for any physical process that we observe, we tend to abduct a single explanation or just a few explanations for a process in the expectation that we can better orientate ourselves in our surroundings and disregard some possibilities. Abductive reasoning can also be called reasoning through successive approximation. Under this principle, an explanation is valid if it is the best possible explanation to a set of known data. The best possible explanation is often defined with regard to simplicity and elegance. According to Vohan and Schick, abduction uses five criteria, testability, fruitfulness, scope, simplicity, and conservationism. When figuring out the best explanation, we consider two or more hypotheses, then compare them based on their criteria, whichever one fits best overall is the best explanation. The difference between abductive reasoning and inductive reasoning is a subtle one. Both use evidence to form guesses that are likely but not guaranteed to be true. However abductive reasoning looks for cause and effect relationships while induction seeks to determine general rules. Another form of reasoning is analogical reasoning. An analogy is a comparison between two phenomena which highlights respects in which they are thought to be similar. Analogical reasoning is any type of thinking that relies upon an analogy. An analogical argument is an explicit representation of a form of analogical reasoning that cites accepted similarities between two systems to support the conclusion that some further similarities may exist. Analogical reasoning involves lateral thinking between two distinct things. We're transferring a statement about one distinct phenomenon to another phenomenon. Analogical reasoning is reasoning horizontally. Imagine trying to explain to a child what a lion is. One might say it's like a big cat. Thus one is creating an analogy between the two, a horizontal link. We might likewise see this analogical process of reasoning in how a court of law will rule a particular way on a case based upon other similar cases that is ruled upon in the past. Analogical thinking is ubiquitous in human cognition and communications where analogies are used in explaining new concepts. Domains such as electricity or molecular motion which cannot be directly perceived are often taught by analogy to familiar concept domains such as water flow or billiard ball collisions. Analogy is a cognitive process of transferring information or meaning from a particular subject, the analog or source, to another, the target. In a narrow sense, analogy is an inference or argument from one particular to another particular as opposed to deduction, induction or abduction where at least one of the premises or conclusion is a general statement.