# Deduction vs. Induction TODO: * Clear up your internal confusion between: the *logical* representation of deduction and induction, and the scientific (turkey problem) of deduction and induction. ### Summary ## In General Reasoning, Argument, Writing ### Argument and Logical Reasoning A correctly formed **deductive [Argument](Argument.md)** is one whose form is such that the conclusion follows with *logical necessity* from its premises. In other words, if the premises are true the conclusion *must also be true*[^1]. If we have a correctly formed deductive argument, then one could not accept the premises and deny the conclusions without contradicting oneself. For example: * Since all senators in the US Senate are at least 35 years old (premise) * and John McCain is a US Senator (premise) * John McCain is 35 years or older (conclusion) The conclusion of any deductive argument simply spells out what is already implicit in the premises. If you can get one to accept the crucial premises, which *already include* the conclusion, then your work is done. The argument is indeed so strong that it's conclusion cannot be denied. An **inductive [Argument](Argument.md)** is one in which the premises are supposed to provide some evidence for the truth of the conclusion. However, the conclusion of an inductive argument does not follow with logical necessity from its premises, even if all the premises are true, because the conclusion is not already contained in the premises. Hence, in contrast to a deductive argument, the truth or acceptability of the relevant premises in an inductive argument does not force or guarantee the truth of its conclusion. For example: * Since Senator Stone is the most popular Democrat in the Senate (premise) * And he is very charming and articulate (premise) * And he has moved to a politically moderate position on most issues (premise) * And he always easily wins reelection to his Senate seat (premise) * And he is often mentioned by prominent journalist and other Democrats as a possible presidential candidate (premise) * Therefore, the Democrats will choose Senator Stone as their next presidential candidate (conclusion) The conclusion of any inductive argument is at best only probable, because the conclusion makes a claim that goes beyond the evidence provided in the premises. It is quite possible that an inductive argument may fail to take into account crucial information that would be relevant to the truth of the conclusion. For example, if Senator Stone didn't want to run for president, that fact could obviously affect the truth of the arguments conclusion. To summarize: > A correctly formed **deductive argument** is one whose form is such that the conclusion follows with logical necessity from its premises. A correctly formed **inductive argument** is one whose form is such that the premises provide good evidence for the truth of the conclusion, but the truth of the conclusion does not follow with logical necessity from its premises. In every day life we generally encounter inductive arguments. From *The 12 Secrets of Persuasive Argument*: > In inductive arguments, focus on the inference*. When a conclusion relies upon an inference and contains new information not found in the premises, the reasoning is inductive.* For example, if premises were established that the defendant slurred his words, stumbled as he walked, and smelled of alcohol, you might reasonably infer the conclusion that the defendant was drunk. This is inductive reasoning. In an inductive argument the conclusion is, at best, probable. The conclusion is not always true when the premises are true. The probability of the conclusion depends on the strength of the inference from the premises. **Thus, when dealing with inductive reasoning, pay special attention to the inductive leap or inference, by which the conclusion follows the premises.** <br> … There are several popular misconceptions about inductive and deductive reasoning. When Sherlock Holmes made his remarkable “deductions” based on observations of various facts, he was usually engaging in inductive, not deductive, reasoning. In *How to Deliver a TED Talk*: > No discussion of logic is complete without a refresher course in the difference between inductive and deductive reasoning. By its strictest definition, inductive reasoning proves a general principle—your idea worth spreading—by highlighting a group of specific events, trends, or observations. In contrast, deductive reasoning builds up to a specific principle—again, your idea worth spreading—through a chain of increasingly narrow statements. ### In Writing In clear writing we often raise a point that needs to then be answered via points below. This answering must be done *logically*. For instance, say that we state "This internet cafe will grow faster than the industry". We then need to answer the question, "*why*?". We must answer this question logically, either via a clear inductive or deductive argument; one or the other, but not both at once. A **deductive grouping** presents an argument in successive steps. The first idea makes a statement about a situation that exists in the world today. The second idea comments on the subject or predicate of that statement. The third idea states the implication of those two situations existing in the world at the same time. Thus the grouping would have the following form: * Men are mortal. * Socrates is a man. * Therefore Socrates is mortal. The move up a level of abstraction from a deductive grouping, you summarize the argument, with your summary resting heavily on the final point: "Because Socrates is a man her is mortal". An **inductive grouping**, by contrast, will take a set of ideas that are related simply by virtue of the fact that you can describe them all by the same plural noun (reasons for, reasons against, steps, problems, etc). The form of this argument would be: * French tanks are at the Polish border. * Russian tanks are at the Polish border. * German tanks are at the Polish border. To move upward here, you draw an *inference* based on your assessment of what is the same about the points - i.e., they are all warlike movements against Poland. Thus, your inference would be something like "Poland is about to be invaded by tanks." As we saw in an argumentative context, deductive reasoning has us state a final conclusion explicitly, but the conclusion was already implicit in the sub premises. Inductive reasoning requires us to make an *inference* based on our sub premises. This inference is our conclusion. ### FS Article * [See here](https://fs.blog/2018/05/deductive-inductive-reasoning/) ## In Science ### Scientific method * https://www.nathanieldake.com/Machine_Learning/08-Bayesian_Machine_Learning-01-Bayesian-Inference.html#2.2-A-Scientific-Perspective:-Induction-vs.-Deduction ### The Book of Why Pearl writes that Holmes' great skill was not deduction, but rather induction. The distinction being: $\text{Deduction: \;\; Hypothesis} \longrightarrow \text{Conclusion}$ $\text{Induction: \;\; Evidence} \longrightarrow \text{Hypothesis}$ Holmes would often induce several hypothesis, and then eliminate them one by on in order to deduce the correct one. We can classify this as falling into the scientific bucket. ### Information: The New Language of Science Our terms are defined as (pg. 136): $\text{Deduction: \;\; Hypothesis} \longrightarrow \text{Observation}$ $\text{Induction: \;\; Observation} \longrightarrow \text{Theory}$ Again, this is a scientific classification. A fantastic visualization is included below:  In it we see: * `E`: The variety of immediate senses Experiences. This includes all that our senses perceive, as well as anything we can access via the help of instruments. It is this plane of experience that anchors science to the material world and distinguishes it from speculative philosophy. * `A`: The system of axioms. These are the great fundamental laws of science such as the laws of thermodynamics, electromagnetism, evolution, newtons laws, and so on. * `Sweeping Arrow`: This arrow represents the **inductive leap** from observation and experiment to theory. This is not (as it is often assumed) a logical or methodical inference, but a "free invention of human intellect", as Einstein has referred to it. Feynman refers to it as a guess. Deutsch refers to it as conjecture. This leap connotes inspiration, imagination, invention, intuition, insight and instinct. Crucial to note here is that the inductive leap does not originate from any one point on the plane E, but it skims along it for a while, gathering evidence without a firm attachment to specific facts. * `Black arrows from A -> S, S', S''`: Inferred Propostions. These are rigorous mathematical *deductions* from the fundamental laws, such as the proof of Kepler's laws of planetary motion from Newton's Laws of Gravity. * `Dotted arrows from S, S', S'' -> E`: Experiments comparing theoretical predictions to actual observations. Note that 3 arrows come back down to the plane while only a single arrow went up. This implies the principle of *parsimony* (/posts/see [Occam's Razor](Occam's%20Razor.md)), which states that the simplest explanation is usually the right one. Einstein goes on to state: > The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypothesis or axioms. We see that `A` is supported via the sweeping arrow on the left, as well as the multiple rigid struts on the right. It is this *dual support*, representing the *interplay* of induction and deduction, that lends robustness to the axioms of modern science. Both induction and deduction, reasoning from the particular to the general, and back again from the universal to the specific, form the essence of scientific thinking. ### David Deutsch #### The Fabric of Reality From chapter 3, Problem Solving. Deutsch states (pg 57): > Thus observations of ever smaller physical effects have been forcing ever greater changes in our world-view[^2]. It may therefore seem that we are inferring ever grander conclusions from ever scantier evidence. The question raised is "what justifies the inferences drawn from these patterns?" It is not a matter of logical deduction! There is no way of *proving* from these or from any other observations that the external universe or multiverse exist at all. Solipsism posits that only one mind exists and that what appears to be external reality is only a dream in the mind. The challenge we run into is that Solipsism is *logically consistent* (i.e. from a deductive perspective of reasoning) with any possible observational evidence, it follows that we can deduce *nothing* about external reality from observational evidence. Deutsch puts this in plain, terrifying terms: > If scientific reasoning does not amount to sequences of logical deductions from the evidence, what does it amount to? Why should we accept it's conclusions? This is known as the **[Problem of Induction](Problem%20of%20Induction.md)**. The theory was that their exists a lesser but still worthy form of justification known as *induction*. Induction was thought to fall between perfect justification via deduction, and on the other hand weaker intuitive forms of reasoning that didn't even have evidence to back them up. In this inductivist theory of scientific knowledge, observations play two roles: 1. First, in the discovery of scientific theories 2. Second, in their justification A theory is supposed to be discovered via "extrapolating" or "generalizing" the results of observations. Visually this scheme looks like:  Induction has many flaws, of which I will list several: * The Turkey problem. Each feeding (observation) makes the turkey more certain that there will be a subsequent feeding. This is a form of inductive justification. This is all well and good until the day before Thanksgiving the turkey gets the ax. This is explored deeply by Nassim Taleb (and others prior) in the [Problem of Induction](Problem%20of%20Induction.md). The idea is that *more observations* can never justify a theory *with certainty*. * It is *impossible* to extrapolate observations to *form* new theories. It is impossible to extrapolate observations unless one has already placed them within an explanatory framework. For example, in the case of the turkey let us consider two explanations the that it may have for the farmers behavior of feeding it. A) It guesses that the farmer has benevolent feelings towards turkeys B) It guesses that the farmer plans to fatten the turkeys up for slaughter. Now, keeping these two explanatory behaviors in mind, consider how a turkey may extrapolate the occurrence of an increase in feedings. If it believes the benevolent farmer theory, A, it may extrapolate that the increase in feedings means the farmer's benevolence is increasing. On the other hand, if it believes in theory B, it may extrapolate that slaughter is imminent. >The fact that the *same observational evidence* can be "extrapolated" to give two *diametrically* opposite predictions according to which explanation one adopts, and cannot justify either of them, is true of all observational evidence under all circumstances. CONTINUE ### The Beginning of Infinity [^1]: Attacking Faulty Reasoning, pg. 20 [^2]: This is in reference to quantum interference leading us to posit the multiverse.