| Introductions [1], [2], [3], [4], [5] | Francis Bacon | JS Mills | Advanced |
Inductive reasoning is a method of reasoning in which the premises are viewed as supplying some evidence, but not full assurance, of the truth of the conclusion. It is also described as a method where one's experiences and observations, including what is learned from others, are synthesized to come up with a general truth. Many dictionaries define inductive reasoning as the derivation of general principles from specific observations (arguing from specific to general), although there are many inductive arguments that do not have that form.
Inductive reasoning is distinct from deductive reasoning. If the premises are correct, the conclusion of a deductive argument is certain; in contrast, the truth of the conclusion of an inductive argument is probable, based upon the evidence given.
Deductive Reasoning vs. Inductive Reasoning
During the scientific process, deductive reasoning is used to reach a logical true conclusion. Another type of reasoning, inductive, is also used. Often, people confuse deductive reasoning with inductive reasoning, and vice versa. It is important to learn the meaning of each type of reasoning so that proper logic can be identified.
Deductive reasoning
Deductive reasoning is a basic form of valid reasoning. Deductive reasoning, or deduction, starts out with a general statement, or hypothesis, and examines the possibilities to reach a specific, logical conclusion, according to California State University. The scientific method uses deduction to test hypotheses and theories. "In deductive inference, we hold a theory and based on it we make a prediction of its consequences. That is, we predict what the observations should be if the theory were correct. We go from the general — the theory — to the specific — the observations," said Dr. Sylvia Wassertheil-Smoller, a researcher and professor emerita at Albert Einstein College of Medicine.
Deductive reasoning usually follows steps. First, there is a premise, then a second premise, and finally an inference. A common form of deductive reasoning is the syllogism, in which two statements — a major premise and a minor premise — reach a logical conclusion. For example, the premise "Every A is B" could be followed by another premise, "This C is A." Those statements would lead to the conclusion "This C is B." Syllogisms are considered a good way to test deductive reasoning to make sure the argument is valid.
For example, "All men are mortal. Harold is a man. Therefore, Harold is mortal." For deductive reasoning to be sound, the hypothesis must be correct. It is assumed that the premises, "All men are mortal" and "Harold is a man" are true. Therefore, the conclusion is logical and true. In deductive reasoning, if something is true of a class of things in general, it is also true for all members of that class.
According to California State University, deductive inference conclusions are certain provided the premises are true. It's possible to come to a logical conclusion even if the generalization is not true. If the generalization is wrong, the conclusion may be logical, but it may also be untrue. For example, the argument, "All bald men are grandfathers. Harold is bald. Therefore, Harold is a grandfather," is valid logically but it is untrue because the original statement is false.
Inductive reasoning
Inductive reasoning is the opposite of deductive reasoning. Inductive reasoning makes broad generalizations from specific observations. Basically, there is data, then conclusions are drawn from the data. This is called inductive logic, according to Utah State University.
"In inductive inference, we go from the specific to the general. We make many observations, discern a pattern, make a generalization, and infer an explanation or a theory," Wassertheil-Smoller told Live Science. "In science, there is a constant interplay between inductive inference (based on observations) and deductive inference (based on theory), until we get closer and closer to the 'truth,' which we can only approach but not ascertain with complete certainty."
An example of inductive logic is, "The coin I pulled from the bag is a penny. That coin is a penny. A third coin from the bag is a penny. Therefore, all the coins in the bag are pennies."
Even if all of the premises are true in a statement, inductive reasoning allows for the conclusion to be false. Here's an example: "Harold is a grandfather. Harold is bald. Therefore, all grandfathers are bald." The conclusion does not follow logically from the statements.
Inductive reasoning has its place in the scientific method. Scientists use it to form hypotheses and theories. Deductive reasoning allows them to apply the theories to specific situations.
Abductive reasoning
Another form of scientific reasoning that doesn't fit in with inductive or deductive reasoning is abductive. Abductive reasoning usually starts with an incomplete set of observations and proceeds to the likeliest possible explanation for the group of observations, according to Butte College. It is based on making and testing hypotheses using the best information available. It often entails making an educated guess after observing a phenomenon for which there is no clear explanation.
For example, a person walks into their living room and finds torn up papers all over the floor. The person's dog has been alone in the room all day. The person concludes that the dog tore up the papers because it is the most likely scenario. Now, the person's sister may have brought by his niece and she may have torn up the papers, or it may have been done by the landlord, but the dog theory is the more likely conclusion.
Abductive reasoning is useful for forming hypotheses to be tested. Abductive reasoning is often used by doctors who make a diagnosis based on test results and by jurors who make decisions based on the evidence presented to them.
Deductive Reasoning vs. Inductive Reasoning
https://www.livescience.com/21569-deduction-vs-induction.html
What Is Inductive Reasoning?
Learn the Definition of Inductive Reasoning With Examples, Plus 6 Types of Inductive Reasoning
There is one logic exercise we do nearly every day, though we’re scarcely aware of it. We take tiny things we’ve seen or read and draw general principles from them—an act known as inductive reasoning.
This form of reasoning plays an important role in writing, too. But there’s a big gap between a strong inductive argument and a weak one.
What Is Inductive Reasoning?Inductive reasoning, or inductive logic, is a type of reasoning that involves drawing a general conclusion from a set of specific observations. Some people think of inductive reasoning as “bottom-up” logic, because it involves widening specific premises out into broader generalizations.
What Is an Example of Inductive Reasoning?
Here is a basic form of inductive reasoning, with a premise based on concrete data and a generalized conclusion:
- All the swans I have seen are white. (Premise)
- Therefore all swans are white. (Conclusion)
In this example, the conclusion is actually wrong—there are also black swans. This is what’s called a “weak” argument. However, it’s easy to make the conclusion stronger, by making it more probable:
- All the swans I have seen are white. (Premise)
- Therefore most swans are probably white. (Conclusion)
3 Ways Inductive Reasoning Is Used
Inductive reasoning is used in a number of different ways, each serving a different purpose:
- We use inductive reasoning in everyday life to build our understanding of the world.
- Inductive reasoning also underpins the scientific method: scientists gather data through observation and experiment, make hypotheses based on that data, and then test those theories further. That middle step—making hypotheses—is an inductive inference, and they wouldn’t get very far without it.
- Finally, despite the potential for weak conclusions, an inductive argument is also the main type of reasoning in academic life.
6 Types of Inductive Reasoning
There are a few key types of inductive reasoning.
- Generalized. This is the simple example given above, with the white swans. It uses premises about a sample set to draw conclusions about a whole population.
- Statistical. This form uses statistics based on a large and random sample set, and its quantifiable nature makes the conclusions stronger. For example: “95% of the swans I’ve seen on my global travels are white, therefore 95% of the world’s swans are white.”
- Bayesian. This is a method of adapting statistical reasoning to take into account new or additional data. For instance, location data might allow a more precise estimate of the percentage of white swans.
- Analogical. This form notes that on the basis of shared properties between two groups, they are also likely to share some further property. For example: “Swans look like geese and geese lay eggs, therefore swans also lay eggs.”
- Predictive. This type of reasoning draws a conclusion about the future based on a past sample. For instance: “There have always been swans on the lake in past summers, therefore there will be swans this summer.”
- Causal inference. This type of reasoning includes a causal link between the premise and the conclusion. For instance: “There have always been swans on the lake in summer, therefore the start of summer will bring swans onto the lake.”
What Is the Difference Between Inductive Reasoning and Deductive Reasoning?
Inductive reasoning is one of the two main types of reasoning that people base their beliefs on. The other is deductive reasoning, or what’s sometimes known as a syllogism.
An example of deductive reasoning is:
“All birds have feathers and swans are birds. Therefore swans have feathers.”
Logicians often prefer a deductive argument, because it produces rock-solid conclusions. However, this form of thinking is only useful in some, limited circumstances. Usually, it involves the opposite of generalizing, as it starts with general principles and works progressively towards a specific conclusion. It is sometimes known as a “top-down” argument, in contrast to the “bottom-up” approach of inductive reasoning.
Instead of being weak or strong, deductive reasoning produces either a valid argument or an invalid one, based on whether the premises necessitate the conclusion.
What Is the Difference Between Inductive Reasoning and Abductive Reasoning?
There is a third process that is important in scientific reasoning, even though its conclusions can be unreliable. This process is abductive reasoning, which takes true premises and seeks the most likely explanation for them—like taking the best guess.
As with inductive reasoning, abductive reasoning presents an opportunity to develop theories that a person can go on to test further. For example:
“There are always swans on the lake in summer but not in winter. Therefore swans like warm water.”
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What Is Inductive Reasoning? Learn the Definition of Inductive Reasoning With Examples, Plus 6 Types of Inductive Reasoning - 2021 - MasterClass
Deduction & Induction
In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.
Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a “top-down” approach. We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data – a confirmation (or not) of our original theories.
Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a “bottom up” approach (please note that it’s “bottom up” and not “bottoms up” which is the kind of thing the bartender says to customers when he’s trying to close for the night!). In inductive reasoning, we begin with specific observations and measures, begin to detect patterns and regularities, formulate some tentative hypotheses that we can explore, and finally end up developing some general conclusions or theories.
These two methods of reasoning have a very different “feel” to them when you’re conducting research. Inductive reasoning, by its very nature, is more open-ended and exploratory, especially at the beginning. Deductive reasoning is more narrow in nature and is concerned with testing or confirming hypotheses. Even though a particular study may look like it’s purely deductive (e.g., an experiment designed to test the hypothesized effects of some treatment on some outcome), most social research involves both inductive and deductive reasoning processes at some time in the project. In fact, it doesn’t take a rocket scientist to see that we could assemble the two graphs above into a single circular one that continually cycles from theories down to observations and back up again to theories. Even in the most constrained experiment, the researchers may observe patterns in the data that lead them to develop new theories.
https://conjointly.com/kb/deduction-and-induction/
When you make a decision, you typically go through a subconscious process of filtering observations through your past experiences. For example, if you look outside and see a sunny sky, it’s reasonable to think you will not need an umbrella. Because many past sunny days have proven this thinking correct, it is a reasonable assumption. This thought process is an example of using inductive reasoning, a logical process based on specific experiences, observations or facts.
An essential tool in statistics, research and probability, inductive reasoning supports us in identifying patterns and making better decisions in the workplace. In this article, we explain how inductive reasoning works with examples of how to use it in your job search and other professional settings. We also explain how inductive reasoning differs from abductive and deductive reasoning.
What is inductive reasoning?
Inductive reasoning is a method of logical thinking that combines observations with experiential information to reach a conclusion. When you can look at a specific set of data and form general conclusions based on existing knowledge from past experiences, you are using inductive reasoning.
For example, if you review the population information of a city for the past 15 years, you may observe that the population has increased at a consistent rate. If you want to predict what the population will be in five years, you can use the evidence or information you have to make an estimate.
Examples of inductive reasoning
Even if you haven’t heard of inductive reasoning before, you’ve likely used it to make decisions in a professional environment. Here are a few examples of how you might apply the inductive reasoning process in a professional environment:
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After analyzing high-performing and successful employees in the marketing department, a recruiter recognizes they all graduated with a degree in business, marketing or journalism. She decides to focus on future recruiting efforts on candidates with a degree in one of those three disciplines.
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A salesperson notices when they share testimonials from current and past clients with their prospects, they’re 75 percent more likely to make a sale. Now they share testimonials with all prospects to improve their close rate.
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Taking time to review comments from past customers is always beneficial. In addition to a positive customer review you can share with future clients, it can also inform you of any problems past customers may be experiencing.
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After noticing assisted living center residents’ moods improve when young children visit, an activities leader develops a volunteer initiative with local schools to pair students with center residents.
By taking time to look for and identify patterns in positive business outcomes, you can inform future efforts and recreate your success.
Types of inductive reasoning
There are various ways to use inductive reasoning depending on the situation. Here are the three most commonly used types of inductive reasoning:
Inductive generalization
In this type of inductive reasoning, a situation is presented, you look at evidence from past similar situations and draw a conclusion based on the information available.
Example: For the past three years, the company has beat its revenue goal in Q3. Based on this information, the company will likely beat its revenue goal in Q3 this year.
Statistical induction
This type of inductive reasoning utilizes statistical data to draw conclusions.
Example: 90 percent of the sales team met their quota last month. Pat is on the sales team. Pat likely met his sales quota last month.
In this case, you are using statistical evidence to inform your conclusion. While statistical induction provides more context for a possible outcome or prediction, it is crucial to remember new evidence may vary from past research and can prove a theory incorrect.
Induction by confirmation
Induction by confirmation allows you to reach a possible conclusion, but you must include specific assumptions for the outcome to be accepted. This type of inductive reasoning is used often by police officers and detectives. Here’s an example:
Renee broke into a building.
Anybody who breaks into a building will have opportunity, motive and means.
Renee was in the area and had lock picks in his bag.
Renee likely broke into the building.
In this situation, you develop a theory, and to prove it true, you must have specific evidence. Knowing that Renee was in the area where the building was broken into and had a lock pick in his bag are strong points to him being the one who broke into the building. Understanding the various types of inductive reasoning allows you to better implement them in your day-to-day operations within the workplace.
When to use inductive reasoning
Inductive reasoning is not always the best way to reach a conclusion. Here are the pros and cons of using this decision-making method:
The benefits of inductive reasoning
Inductive reasoning allows you to work with a wide range of probabilities. The assumptions you make from presented evidence or a specific set of data are practically limitless. However, inductive reasoning presents you with a starting point so you can narrow down your assumptions and reach an informed conclusion.
Inductive reasoning also allows you to develop multiple solutions to one issue and utilize your research to evaluate another hypothesis. It allows you to leverage knowledge gathered from past experiences to form judgments and make decisions in new situations.
The limits of inductive reasoning
One weakness of inductive reasoning is also one of its most significant strengths—you are only able to establish theories based on limited evidence or knowledge. While it provides you with the opportunity to explore, it also limits the foundation available for you to use.
For example, if you observe 100 cats and notice they all hiss at dogs, you may conclude that every cat will hiss at dogs. While this is sound reasoning, the data you are using is limiting. Because you only observed 100 cats, your conclusion may not be true for every cat.
When using inductive reasoning, it’s important to recognize there is always room for error. While your guess or theory may be incorrect in some cases, you can use that information to help you continue your research.
While you can use data and evidence to back up your claim or judgment, there is still a chance that new facts or evidence will be uncovered and prove your theory wrong. That’s why it’s important to learn to use inductive reasoning skills in conjunction with other types of reasoning.
How to demonstrate your inductive reasoning skills
Professionals who possess logical thinking abilities—like inductive reasoning skills—are often better at decision-making efforts. That’s why you must highlight this skill throughout the job search and hiring process.
Inductive reasoning skills on your resume
While you can list this soft skill on a resume, it’s especially important if an employer specifically mentions inductive reasoning or critical-thinking skills in the job listing or description. Consider providing a specific example of when you used inductive reasoning skills in the workplace on your cover letter.
Inductive reasoning skills in an interview
During a job interview, an employer may ask about your decision-making process. Take time to think about specific instances when you used inductive reasoning, especially when it resulted in a positive outcome. Providing a clear example can help prove to employers you’re able to make insightful observations, retain information and apply your knowledge to make well-informed decisions on the job.
Inductive reasoning skills using the STAR method
Utilizing the STAR (Situation, Task, Action and Result) technique is an effective method for communicating your inductive reasoning skills to potential employers clearly and concisely. Here are the steps for using the STAR method:
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Describe the situation. Where were you working? What was your role in the project or
task?
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Describe the task. What was your specific responsibility? What problem or issue
did you face? What observations did you make?
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Explain in detail the action you took. What conclusion did you reach? How did you translate your
conclusion into an actionable solution?
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Share the result. How did your actions address the problem? What was the outcome, and how did it affect the company or team?
Understanding inductive reasoning and how to effectively apply this logical thinking process in your work environment is essential to success in any position. Learning to recognize your inductive reasoning skills will help you highlight them during your job search and make a positive impression on employers during the interview process.
Inductive reasoning vs. deductive and abductive reasoning
Reasoning skills are one of the most important soft skills employers seek in potential candidates. In addition to inductive reasoning, there are two other types of reasoning—abductive and deductive—that are important to understand and apply both in and outside of the workplace.
Inductive vs. deductive reasoning
Where inductive thinking uses experience and proven observations to guess the outcome, deductive reasoning uses theories and beliefs to rationalize and prove a specific conclusion. The goal of inductive reasoning is to predict a likely outcome, while the goal of deductive reasoning to prove a fact.
Both types of reasoning bring valuable benefits to the workplace. Employers specifically like to see inductive reasoning on applications because it highlights your aptitude for critical thinking and problem-solving. In addition to including it on your resume, note it in your cover letter and at the interview.
Example of inductive reasoning:
- "I get tired if I don’t drink coffee."
- "Coffee is addictive."
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"I am addicted to coffee."
Example of deductive reasoning:
- "Human beings need breath to live."
- "You are a human."
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"You must need breath to live."
Inductive vs. abductive reasoning
Abductive reasoning allows for more guessing than inductive reasoning. For abductive reasoning, you analyze information or observations that may not be complete. You can guess or hypothesize possible outcomes based on the available information.
The medical field often uses abductive reasoning when making diagnoses in the absence of information such as test results. For example, when a patient presents symptoms, medical professionals work to develop a logical answer or a diagnosis based on the minimal information they have to develop a conclusion.
While abductive reasoning allows for more freedom than inductive or deductive reasoning, it can also result in several incorrect conclusions before you uncover the true answer.
https://www.indeed.com/career-advice/career-development/inductive-reasoning
Francis Bacon - Father of Empiricism
The Idols
In Book I of the New Organon (Aphorisms 39-68), Bacon introduces his famous doctrine of the “idols.” These are characteristic errors, natural tendencies, or defects that beset the mind and prevent it from achieving a full and accurate understanding of nature. Bacon points out that recognizing and counteracting the idols is as important to the study of nature as the recognition and refutation of bad arguments is to logic. Incidentally, he uses the word “idol” – from the Greek eidolon(“image” or “phantom”) – not in the sense of a false god or heathen deity but rather in the sense employed in Epicurean physics. Thus a Baconian idol is a potential deception or source of misunderstanding, especially one that clouds or confuses our knowledge of external reality.
Bacon identifies four different classes of idol. Each arises from a different source, and each presents its own special hazards and difficulties.
1. The Idols of the Tribe.
These are the natural weaknesses and tendencies common to human nature. Because they are innate, they cannot be completely eliminated, but only recognized and compensated for. Some of Bacon’s examples are:
- Our senses – which are inherently dull and easily deceivable. (Which is why Bacon prescribes instruments and strict investigative methods to correct them.)
- Our tendency to discern (or even impose) more order in phenomena than is actually there. As Bacon points out, we are apt to find similitude where there is actually singularity, regularity where there is actually randomness, etc.
- Our tendency towards “wishful thinking.” According to Bacon, we have a natural inclination to accept, believe, and even prove what we would prefer to be true.
- Our tendency to rush to conclusions and make premature judgments (instead of gradually and painstakingly accumulating evidence).
2. The Idols of the Cave.
Unlike the idols of the tribe, which are common to all human beings, those of the cave vary from individual to individual. They arise, that is to say, not from nature but from culture and thus reflect the peculiar distortions, prejudices, and beliefs that we are all subject to owing to our different family backgrounds, childhood experiences, education, training, gender, religion, social class, etc. Examples include:
- Special allegiance to a particular discipline or theory.
- High esteem for a few select authorities.
- A “cookie-cutter” mentality – that is, a tendency to reduce or confine phenomena within the terms of our own narrow training or discipline.
3. The Idols of the Market Place.
These are hindrances to clear thinking that arise, Bacon says, from the “intercourse and association of men with each other.” The main culprit here is language, though not just common speech, but also (and perhaps particularly) the special discourses, vocabularies, and jargons of various academic communities and disciplines. He points out that “the idols imposed by words on the understanding are of two kinds”: “they are either names of things that do not exist” (e.g., the crystalline spheres of Aristotelian cosmology) or faulty, vague, or misleading names for things that do exist (according to Bacon, abstract qualities and value terms – e.g., “moist,” “useful,” etc. – can be a particular source of confusion).
4. The Idols of the Theatre.
Like the idols of the cave, those of the theatre are culturally acquired rather than innate. And although the metaphor of a theatre suggests an artificial imitation of truth, as in drama or fiction, Bacon makes it clear that these idols derive mainly from grand schemes or systems of philosophy – and especially from three particular types of philosophy:
- Sophistical Philosophy – that is, philosophical systems based only on a few casually observed instances (or on no experimental evidence at all) and thus constructed mainly out of abstract argument and speculation. Bacon cites Scholasticism as a conspicuous example.
- Empirical Philosophy – that is, a philosophical system ultimately based on a single key insight (or on a very narrow base of research), which is then erected into a model or paradigm to explain phenomena of all kinds. Bacon cites the example of William Gilbert, whose experiments with the lodestone persuaded him that magnetism operated as the hidden force behind virtually all earthly phenomena.
- Superstitious Philosophy – this is Bacon’s phrase for any system of thought that mixes theology and philosophy. He cites Pythagoras and Plato as guilty of this practice, but also points his finger at pious contemporary efforts, similar to those of Creationists today, to found systems of natural philosophy on Genesis or the book of Job.
k. Induction
At the beginning of the Magna Instauratio and in Book II of the New Organon, Bacon introduces his system of “true and perfect Induction,” which he proposes as the essential foundation of scientific method and a necessary tool for the proper interpretation of nature. (This system was to have been more fully explained and demonstrated in Part IV of the Instauratio in a section titled “The Ladder of the Intellect,” but unfortunately the work never got beyond an introduction.)
According to Bacon, his system differs not only from the deductive logic and mania for syllogisms of the Schoolmen, but also from the classic induction of Aristotle and other logicians. As Bacon explains it, classic induction proceeds “at once from . . . sense and particulars up to the most general propositions” and then works backward (via deduction) to arrive at intermediate propositions. Thus, for example, from a few observations one might conclude (via induction) that “all new cars are shiny.” One would then be entitled to proceed backward from this general axiom to deduce such middle-level axioms as “all new Lexuses are shiny,” “all new Jeeps are shiny,” etc. – axioms that presumably would not need to be verified empirically since their truth would be logically guaranteed as long as the original generalization (“all new cars are shiny”) is true.
As Bacon rightly points out, one problem with this procedure is that if the general axioms prove false, all the intermediate axioms may be false as well. All it takes is one contradictory instance (in this case one new car with a dull finish) and “the whole edifice tumbles.” For this reason Bacon prescribes a different path. His method is to proceed “regularly and gradually from one axiom to another, so that the most general are not reached till the last.” In other words, each axiom – i.e., each step up “the ladder of intellect” – is thoroughly tested by observation and experimentation before the next step is taken. In effect, each confirmed axiom becomes a foothold to a higher truth, with the most general axioms representing the last stage of the process.
Thus, in the example described, the Baconian investigator would be obliged to examine a full inventory of new Chevrolets, Lexuses, Jeeps, etc., before reaching any conclusions about new cars in general. And while Bacon admits that such a method can be laborious, he argues that it eventually produces a stable edifice of knowledge instead of a rickety structure that collapses with the appearance of a single disconfirming instance. (Indeed, according to Bacon, when one follows his inductive procedure, a negative instance actually becomes something to be welcomed rather than feared. For instead of threatening an entire assembly, the discovery of a false generalization actually saves the investigator the trouble of having to proceed further in a particular direction or line of inquiry. Meanwhile the structure of truth that he has already built remains intact.)
Is Bacon’s system, then, a sound and reliable procedure, a strong ladder leading from carefully observed particulars to true and “inevitable” conclusions? Although he himself firmly believed in the utility and overall superiority of his method, many of his commentators and critics have had doubts. For one thing, it is not clear that the Baconian procedure, taken by itself, leads conclusively to any general propositions, much less to scientific principles or theoretical statements that we can accept as universally true. For at what point is the Baconian investigator willing to make the leap from observed particulars to abstract generalizations? After a dozen instances? A thousand? The fact is, Bacon’s method provides nothing to guide the investigator in this determination other than sheer instinct or professional judgment, and thus the tendency is for the investigation of particulars – the steady observation and collection of data – to go on continuously, and in effect endlessly.
One can thus easily imagine a scenario in which the piling up of instances becomes not just the initial stage in a process, but the very essence of the process itself; in effect, a zealous foraging after facts (in the New Organon Bacon famously compares the ideal Baconian researcher to a busy bee) becomes not only a means to knowledge, but an activity vigorously pursued for its own sake. Every scientist and academic person knows how tempting it is to put off the hard work of imaginative thinking in order to continue doing some form of rote research. Every investigator knows how easy it is to become wrapped up in data – with the unhappy result that one’s intended ascent up the Baconian ladder gets stuck in mundane matters of fact and never quite gets off the ground.
It was no doubt considerations like these that prompted the English physician (and neo-Aristotelian) William Harvey, of circulation-of-the-blood fame, to quip that Bacon wrote of natural philosophy “like a Lord Chancellor” – indeed like a politician or legislator rather than a practitioner. The assessment is just to the extent that Bacon in the New Organon does indeed prescribe a new and extremely rigid procedure for the investigation of nature rather than describe the more or less instinctive and improvisational – and by no means exclusively empirical – method that Kepler, Galileo, Harvey himself, and other working scientists were actually employing. In fact, other than Tycho Brahe, the Danish astronomer who, overseeing a team of assistants, faithfully observed and then painstakingly recorded entire volumes of astronomical data in tidy, systematically arranged tables, it is doubtful that there is another major figure in the history of science who can be legitimately termed an authentic, true-blooded Baconian. (Darwin, it is true, claimed that The Origin of Species was based on “Baconian principles.” However, it is one thing to collect instances in order to compare species and show a relationship among them; it is quite another to theorize a mechanism, namely evolution by mutation and natural selection, that elegantly and powerfully explains their entire history and variety.)
Science, that is to say, does not, and has probably never advanced according to the strict, gradual, ever-plodding method of Baconian observation and induction. It proceeds instead by unpredictable – and often intuitive and even (though Bacon would cringe at the word) imaginative – leaps and bounds. Kepler used Tycho’s scrupulously gathered data to support his own heart-felt and even occult belief that the movements of celestial bodies are regular and symmetrical, composing a true harmony of the spheres. Galileo tossed unequal weights from the Leaning Tower as a mere public demonstration of the fact (contrary to Aristotle) that they would fall at the same rate. He had long before satisfied himself that this would happen via the very un-Bacon-like method of mathematical reasoning and deductive thought-experiment. Harvey, by a similar process of quantitative analysis and deductive logic, knew that the blood must circulate, and it was only to provide proof of this fact that he set himself the secondary task of amassing empirical evidence and establishing the actual method by which it did so.
One could enumerate – in true Baconian fashion – a host of further instances. But the point is already made: advances in scientific knowledge have not been achieved for the most part via Baconian induction (which amounts to a kind of systematic and exhaustive survey of nature supposedly leading to ultimate insights) but rather by shrewd hints and guesses – in a word by hypotheses – that are then either corroborated or (in Karl Popper’s important term) falsified by subsequent research.
In summary, then, it can be said that Bacon underestimated the role of imagination and hypothesis (and overestimated the value of minute observation and bee-like data collection) in the production of new scientific knowledge. And in this respect it is true that he wrote of science like a Lord Chancellor, regally proclaiming the benefits of his own new and supposedly foolproof technique instead of recognizing and adapting procedures that had already been tested and approved. On the other hand, it must be added that Bacon did not present himself (or his method) as the final authority on the investigation of nature or, for that matter, on any other topic or issue relating to the advance of knowledge. By his own admission, he was but the Buccinator, or “trumpeter,” of such a revolutionary advance – not the founder or builder of a vast new system, but only the herald or announcing messenger of a new world to come.
https://iep.utm.edu/bacon/#SH2i
Francis Bacon and the Origins of Experimentation
Scientific reasoning proceeds on the assumption that there are discernable causal relations between objects and events. What causality is, however, is not as clear as you might think.
Accurately determining causes and effects is not a simple task. We can often confuse the two, or misidentify one because we lack sufficient information. Mill’s methods are attempts to isolate a cause from a complex event sequence. medieval writers that led merely to individualistic and arcane insights became a foil against which he developed a new mode of extracting secrets from nature. His vast knowledge of ancient and contemporary writers, in combination with his judicial life in the service of Elizabeth I and James I of England, contributed elements to the language he used to describe his new method. Of equal importance to his metaphorical style, however, was his immersion in the cultural, social, and economic fabric of fin-de-sie`cle Europe and the physical settings of his everyday life.
To appreciate the significance of Bacon’s achievement, one must go beyond a textual analysis of the words he used in his published writings. It is necessary to examine the emergence of his nascent concept of the contained, controlled experiment. The ingredients of his idea included an active inquisitor (scientist) who posed a question, a subject/object that held the answer as a veiled secret, witnesses who could verify and if necessary replicate the experience, and a practical outcome that would improve the life of human- kind. Although ambiguity may exist about the meanings of some of Bacon’s terms, their relevance becomes clear if they are placed in the context of his times.
Here I explicate Bacon’s movement toward the concept of the contained, controlled experiment in ways not heretofore discussed by historians (who have mainly focused on his inductive method) and respond to critics such as Peter Pesic who have debated his metaphors and objectives.2 I respect and appreciate Pesic’s research arguing that Bacon did not use the words “nature on the rack” or “torturing nature to reveal her secrets,” although later authors have attributed those sayings to him.3 I argue, however, that Bacon’s concept of experiment entailed a nature constrained by the “violence of imped- iments” and transformed by “art and the hand of man.”4 I disagree with Pesic that the dominant assessment of Bacon’s approach to science historically was or should be that of a “heroic struggle” with nature,5 in which he confronts “her inherent greatness”6 and in which both “the scientist and nature . . . are tested and purified” (i.e., “wrestling with Proteus”).7 I show instead how the contained, controlled experiment emerges from Bacon’s early interest in the practical and mechanical arts; the role of his 1609 Wisdom of the Ancients in developing his tripartite division of nature as free, erring, and in bonds; and how particular settings in Bacon’s cultural milieu contribute to and illustrate exper- imentation. Bacon’s ultimate objective was to recover the “dominion over creation” lost in the Fall from Eden in order to benefit humanity in material terms.8 That dominion, however, was achieved by the constraint of nature through technology, a process that exacted heavy costs from nature itself.
Interpretations of Bacon and his role in the rise of experimental science have a long history and have been discussed in numerous books and articles. At one end of the spectrum is the view of the Frankfurt School philosophers, who see Bacon as initiating a tradition of human power and dominion over nature.9 Thus mechanistic science itself, as it emerged in the seventeenth century, may be seen as complicit in some of humanity’s current ecological, medical, and human survival problems.10 At the other end of the scale are those who view Bacon as the humble servant of nature who gave humanity new tools to uncover the truths of nature.11 A modicum of middle ground, however, may exist between the two perspectives when larger political and social issues underlying his concept of power are taken into consideration.
“THE DOMINION OF MAN OVER THE UNIVERSE”
Francis Bacon lived on the cusp between the Renaissance and the Enlightenment, during the expansion of preindustrial capitalism. All over Europe a new flurry of activities that transformed nature through machines and inventions was taking place. Tunneling into the earth for coal and metals, building forges for refining ores and hammering metals, constructing mills powered by wind and water, and erecting machines for lifting and boring provided humanity with a new sense of power over nature. The development of the coal and iron industries, the enclosure of the commons for wool production for the textile industry, the cutting of enormous tracts of timber for shipbuilding, and the expansion of trade changed the natural landscape. Knowledge of crafts, mechanics, inventions, and the properties of matter was essential to creating a storehouse of reliable, replicable infor- mation about the practical arts that would be available not just to the few, but to the many.12
A number of works of the late sixteenth century provided Bacon with ample illustration of the constraint of nature by technology and the arts that would undergird his emerging concept of experiment…
Francis Bacon and the Origins of Experimentation
https://warwick.ac.uk/fac/arts/history/students/modules/hi203/group2/bacon.pdf
https://www.sfu.ca/~poitras/isis_torture-of-nature_08.pdf
Putting Nature on the Rack
What was it that distinguished the modern scientific method inaugurated by Bacon, Galileo, Descartes, and Co. from the science of the medievals?
One common answer is that the moderns required empirical evidence, whereas the medievals contented themselves with appeals to the authority of Aristotle. The famous story about Galileo’s Scholastic critics’ refusing to look through his telescope is supposed to illustrate this difference in attitudes.
The problem with this answer, of course, is that it is false. For one thing, the telescope story is (like so many other things everyone “knows” about the Scholastics and about the Galileo affair) a legend. For another, part of the reason Galileo’s position was resisted was precisely because there were a number of respects in which it appeared to conflict with the empirical evidence. (For example, the Copernican theory predicted that Venus should sometimes appear six times larger than it does at other times, but at first the empirical evidence seemed not to confirm this, until telescopes were developed which could detect the difference; the predicted stellar parallax did not receive empirical confirmation for a long time; and so forth.)
Then there is the fact that the medievals were simply by no means hostile to the idea that empirical evidence is the foundation of knowledge; on the contrary, it was a standard Scholastic slogan that “there is nothing in the intellect that was not first in the senses.” Indeed, Bacon regarded his Scholastic predecessors as if anything too quick to believe the evidence of the senses. The first of the “Idols of the Mind” that he famously critiques, namely the “Idols of the Tribe,” included a tendency to take the deliverances of sensory experience for granted. The senses could, in Bacon’s view, too readily be deceived, and needed to be corrected by carefully controlling the conditions of observation and developing scientific instruments. And in general, the early moderns regarded much of what the senses tell us about the natural world -- such as what they tell us about secondary qualities like color and temperature -- to be false.
So, it is simply not the case that the difference between the medievals and the early moderns was that the latter were more inclined to trust empirical evidence. On the contrary, there is a sense in which that is precisely the reverse of the truth.
Where empirical evidence is concerned, the real difference might, to oversimplify, be put as follows. Both the medievals and the early moderns regarded sensory experience as a crucial witness to the truth about the natural world. But whereas the medievals regarded it as a more or less friendly witness, the moderns regarded it as a more or less hostile witness. You can, from both sorts of witness, derive the truth. But the methods will be different.
Hence, a friendly witness can more or less be asked directly for the information you want. That doesn’t mean he might not sometimes need to be prodded to answer. Even if he is honest, he might be shy, or reluctant to divulge something embarrassing, or just not very articulate. It also doesn’t mean that everything he says can be taken at face value. He may be forgetful, or confused, or just mistaken now and again. A hostile witness, by contrast, though he has the information you want, cannot with confidence be asked directly. Even if he is articulate, has a crystal clear memory, etc., he may simply refuse to answer, or may persistently beat around the bush, or may flat-out lie, seriously and repeatedly. Thus, he may have to be tricked into giving you the information you want, like the Jack Nicholson character in A Few Good Men. Or you may be tempted to threaten or beat it out of him, like one of the cops in L.A. Confidential would. So, you might say that whereas the medieval Aristotelian scientist has a conversation with nature, the early modern Baconian scientist waterboards nature. Hence the notorious Baconian talk about putting nature to the rack, torturing her for her secrets, etc.
Of course, this is melodramatic. And to be fair, Bacon himself seems not to have put things quite the way commonly attributed to him (i.e. the stuff about torture and the rack). All the same, the medievals and moderns do disagree about the degree to which the world of ordinary experience and the world that science reveals -- what Wilfrid Sellars called “the manifest image” and “the scientific image” -- correspond. For the Aristotelian, philosophy and science are largely in harmony with common sense and ordinary experience. To be sure, they get at much deeper levels of reality, and they correct common sense and ordinary experience around the edges, but they don’t overthrow common sense and ordinary experience wholesale. For the moderns, by contrast, philosophy and science are likely radically to conflict with common sense and ordinary experience, and may indeed end up overthrowing them wholesale.
(This is not a difference concerning whether to accept the results of modern science, by the way. It is a difference about how to interpret those results. For example, it is a difference over whether to regard modern science as giving us a correct but merely partial description of nature -- a description which needs to be supplemented by and embedded within an Aristotelian metaphysics and philosophy of nature -- or whether to regard modern science instead as an exhaustive description of nature, and a complete metaphysics in its own right.)
The early moderns’ attitude of treating nature as a hostile witness -- of thinking that the truth about nature is largely contrary to what ordinary experience would indicate -- is one of the sources of the modern tendency to suppose that “things are never what they seem,” that traditional ideas are typically mere prejudices, that authorities and official stories of every kind need to be “unmasked,” and so forth. Michael Levin has called this the “skim milk fallacy,” and I’ve often noted some of its social and moral consequences (e.g. here, here and here). But these are merely byproducts of a much deeper metaphysical and epistemological revolution.
http://edwardfeser.blogspot.com/2016/03/putting-nature-on-rack.html
J.S. Mill on Scientific Method
This post in the second in a series on Science, Technology, and
Society. The first post is here, and the following post is here. All posts in the series have previously appeared on the Partially
Examined Life group page on Facebook.
"We begin by making any supposition, even a false one, to see what
consequences will follow from it; and by observing how these differ from
the real phenomena, we learn what corrections
to make in our
assumption."
John Stuart Mill (1806 – 1873) was an English political and epistemic philosopher. His father, James Mill, was a respected philosopher in his own right, and raised his son to follow in his footsteps. Mill was thus equipped, by both nature and nurture, for the life of the mind. He did not disappoint – he is usually regarded as the most influential philosopher of Victorian Britain. He made important contributions to mathematics, logic, epistemology, psychology, ethics, liberalism, feminism, and – our subject here – the philosophy of science.
In A System of Logic (1843) Mill proposed what has since become the standard description of a scientific explanation, called the Covering Law Model. According to Mill, science is concerned with the discovery of regular patterns in experience (laws), and a scientific explanation of a fact is one that fixes its relationship to such laws. As we gain experience in detecting these laws, we observe that certain features of investigation are more conducive to discovery than others. We might, in other words, propose a law about the discovery of laws – the Scientific Method. This method is, simply, to use inference and inductive reason to create a set of hypotheses, and then to use deductive reason to derive from them likely consequences. We then perform an experiment, and on that basis we eliminate or revise our theories until we arrive at the true explanation.
This method rests on two assumptions: that of Determinism (a discoverable cause for the phenomena does in fact exist, and requires the phenomena to exist where it is present), and that of Limited Variety (that cause is embedded in some way within the available hypotheses.) We can infer that these assumptions are indeed applicable from the explanatory success of the laws already discovered (or in principle discoverable) on their basis. Each new discovery which expands upon and agrees with earlier discoveries provides confirmation both of them, and of the assumptions of Determinism and Limited Variety.
Although Mill is interested in logic, he does not believe that scientific discoveries must be grounded in logic – because logic is embedded in the deep structure of the universe, and because that structure is known principally through experience, we know that a law which accords with experience is logical. It is not necessary to work out the specifics.
Science proceeds, according to Mill, in two ways: by filling in the gaps between theories, and by rearranging structures of theories. For instance, we can know at what temperature water boils from experience, and we embed that experience within an elementary principle. However, if we want to discover the effect of air pressure on the temperature at which water will boil, we need to invoke additional theories about air pressure and the nature of the boiling process itself. A more general account of observation requires, in other words, a more complex structure of theories. Creating the elementary theories is a matter of “filling in the gaps” in our knowledge. If these theories seem to contradict (for instance, the confrontation between Newton’s and Einstein’s account of gravity), we can reasonably infer that there is a flaw in our structural arrangement. Locating and repairing this flaw then becomes the object of scientific investigation. A true and accurate structure of theories, then, will contain no gaps, and no contradictions.
Mill’s account of scientific investigations formed the foundation for both logical positivism and the theory of falsification in a later generation. It was, and remains, the standard account of scientific discovery.
.....................
Daniel Halverson is a graduate student studying the history of Science,
Technology, and Society in Nineteenth century Germany. He is also a
regular contributor to the PEL Facebook page.
https://partiallyexaminedlife.com/2015/03/06/science-technology-and-society-ii-j-s-mill-on-scientific-method/
Mills Methods Of Inductive Inference
Scientific reasoning proceeds on the assumption that there are
discernable causal relations between objects and events. What causality
is, however,
is not as clear as you might think.
Accurately determining causes and effects is not a simple task. We can
often confuse the two, or misidentify one because we lack sufficient
information. Mill’s methods are attempts
to isolate a cause from a complex
event sequence.
1 - The Method of Agreement - involves ascertaining a "common factor. The common factor should be one that is present whenever the effect is present.
Therefore A is the cause, or the effect, of w.
2 - The Method of Difference - involves evaluating two cases, one in which the effect is present, and one where it is absent. If when the effect is absent, the possible cause "X" is also absent, the test lends support to "X" as the cause.
"If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon."
A B C D occur together with w x y z
B C D occur together with x y z
——————————————————
Therefore A is the cause, or the effect, or a part of the cause of w.
3 - The Joint Method - involves combining the first two methods.
"If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance: the circumstance in which alone the two sets of instances differ, is the effect, or cause, or a necessary part of the cause, of the phenomenon."
A B C occur together with x y z
A D E occur together with x v w also B C occur with y z
——————————————————
Therefore A is the cause, or the effect, or a part of the cause of
x.
4 - The Method of Residues - involves "subtracting out" those aspects of the effect whose causes are known and concluding that the rest of the effect ("the residue") is due to an additional cause.
"Deduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents."
A B C occur together with x y z
B is known to be the cause of y
C is known to be the cause of z
——————————————————
Therefore A is the cause or effect of x.
5 - The Method of Concomitant Variation - involves showing that as one factor varies, another varies in a corresponding way.
"Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation."
A B C occur together with x y z
A± B C results in x± y z.
—————————————————————
Therefore A and x are causally connected
More
https://en.wikipedia.org/wiki/Mill’s_Methods
Inductive Logic
- First published Mon Sep 6, 2004; substantive revision Mon Mar 19,
2018
An inductive logic is a logic of evidential support. In a deductive logic, the premises of a valid deductive argument logically entail the conclusion, where logical entailment means that every logically possible state of affairs that makes the premises true must make the conclusion true as well. Thus, the premises of a valid deductive argument provide total support for the conclusion. An inductive logic extends this idea to weaker arguments. In a good inductive argument, the truth of the premises provides some degree of support for the truth of the conclusion, where this degree-of-support might be measured via some numerical scale. By analogy with the notion of deductive entailment, the notion of inductive degree-of-support might mean something like this: among the logically possible states of affairs that make the premises true, the conclusion must be true in (at least) proportion r of them—where ris some numerical measure of the support strength.
If a logic of good inductive arguments is to be of any real value, the measure of support it articulates should be up to the task. Presumably, the logic should at least satisfy the following condition:
Criterion of Adequacy (CoA):
The
logic should make it likely (as a matter of logic) that as
evidence accumulates, the total body of true evidence claims will
eventually come to indicate, via the logic’s measure of support, that false hypotheses are probably false and that true
hypotheses are probably true.
The CoA stated here may strike some readers as surprisingly strong. Given a specific logic of evidential support, how might it be shown to satisfy such a condition?Section 4 will show precisely how this condition is satisfied by the logic of evidential support articulated in Sections 1 through 3 of this article.
This article will focus on the kind of the approach to inductive logic most widely studied by epistemologists and logicians in recent years. This approach employs conditional probability functions to represent measures of the degree to which evidence statements support hypotheses. Presumably, hypotheses should be empirically evaluated based on what they say (or imply) about the likelihood that evidence claims will be true. A straightforward theorem of probability theory, called Bayes’ Theorem, articulates the way in which what hypotheses say about the likelihoods of evidence claims influences the degree to which hypotheses are supported by those evidence claims. Thus, this approach to the logic of evidential support is often called a Bayesian Inductive Logic or a Bayesian Confirmation Theory. This article will first provide a detailed explication of a Bayesian approach to inductive logic. It will then examine the extent to which this logic may pass muster as an adequate logic of evidential support for hypotheses. In particular, we will see how such a logic may be shown to satisfy the Criterion of Adequacy stated above.
Sections 1 through 3 present all of the main ideas underlying the (Bayesian) probabilistic logic of evidential support. These three sections should suffice to provide an adequate understanding of the subject. Section 5 extends this account to cases where the implications of hypotheses about evidence claims (called likelihoods) are vague or imprecise. After reading Sections 1 through 3, the reader may safely skip directly to Section 5, bypassing the rather technical account in Section 4 of how how the CoA is satisfied.
Section 4 is for the more advanced reader who wants an understanding of how this logic may bring about convergence to the true hypothesis as evidence accumulates. This result shows that the Criterion of Adequacy is indeed satisfied—that as evidence accumulates, false hypotheses will very probably come to have evidential support values (as measured by their posterior probabilities) that approach 0; and as this happens, a true hypothesis may very probably acquire evidential support values (as measured by its posterior probability) that approaches 1.
- 1. Inductive Arguments
- 2. Inductive Logic and Inductive Probabilities
- 3. The Application of Inductive Probabilities to the Evaluation of Scientific Hypotheses
- 4. The Likelihood Ratio Convergence Theorem
- 5. When the Likelihoods are Vague or Diverse
- List of Supplements
- Bibliography
- Academic Tools
- Other Internet Resources
- Related Entries
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