[Aristothelean induction] flies from the senses and particulars to the most general axioms, and from these principles proceeds to judgment and the discovery of the middle axioms.
Francis Bacon, Novum Organum, Aphorism 19
[induction] cursorily skims experience and particulars
Francis Bacon, Novum Organum, Aphorism 22
The Aristotelian method became quite popular because it represents the natural way human mind work if it is left to itself. Nevertheless, Bacon points out that our minds are full of prejudices and these might deceive our mind. These prejudices take the form of idols.
There are four types of Idols, explained from the 38th to the 62nd aphorism:
Idols of the Tribe
Idols of the Tribe have their root in the human race and its nature, for it’s similar to a distorting mirror: it distorts our perceptions.
For example, human mind is prone to believe there is more order in nature than it is actually disposed to discover, this often ends up producing dogmas and fallacious theories. Individuals, once they have formed an opinion, they attempt in every possible way to make their theory work. Once we have an idea of something, we try to distort everything we know in order to make it correspond to our idea. By following this idol, senses often become inadequate and they can easily be deceived.
This interpretation reminds of the definition of pseudo-sciences by Karl Popper.
Idols of the Cave
Idols of the Cave are a consequence individuals’ personal weaknesses in reasoning, due to their particular personalities, likes and dislikes. Idols related to education, formation, readings, customs, etc.
Idols of the market place
Idols of the Market Place occur when people interact with each other;
this is the place where idles are produced by the use of languages and their interaction. Words are normally used in their common meaning, but meanings are often conflicting because we have different purposes.
Idols of the Theatre
Idols of the Theatre derive from the academic dogmas and not asking questions about the world. Dogmas often end up creating fictional worlds, not necessarily justified. They penetrate in our minds
Persuasive but not necessarily justified theories.
Anticipation of nature
Being led to draw conclusions from premises not infected by idols is defined by Bacon as anticipation of nature (or anticipation of mind). This helps our way to get to scientific knowledge.
We anticipate nature as we expect it to be, without focusing on
Induction by enumeration
It’s bad induction to infer principles of science through simple enumerations, namely through simple experience, for it relies on isolated observations, which don’t lead to enough knowledge and understanding.
If we were to perform observations without a method, a guidance, we may be able to draw conclusions, but without a substantial and reliable evidence. Therefore, a good guidance is needed to get to accountable conclusions.
Bacon here gives some sort of counterfactual reasoning: if we could progress by looking at single observations, we should get an idea of the direction of science, but in his opinion at his time it was completely without an order.
Those who have handled the sciences have been either Empiricists or Rationalists. Empiricists, like ants, merely collect things and use them. The Rationalists, like spiders, spin webs out of themselves. The middle way is that of the bee, which gathers its materials from the flowers of the garden and field, but then transforms and digests it by a power of its own.
Francis Bacon, Novum Organum, Aphorism 95
Interpretation of nature
first lights the candle, and then by means of the candle shows the way; commencing as it does with experience duly ordered and digested, not bungling and erratic, and from it educing axioms, and from the established axioms again new experiments.
We go from a well organized experience to the principles and then we draw the principles again: this is the good induction that is draw by a guidance:
a step-by-step methodical assistance to the senses. Our senses require a guidance because they can easily misinform us. As an educated lawyer, Bacon says we need to vex and interrogate nature as if we were interrogating a witness. In a certain sense we may say we need to provoke nature, stimulating it to give us information.
This is the method he prefers to the Aristotelian induction by enumeration; Bacon’s method rely on experience and what he calls gradual induction.
it shall analyze experience and take it to pieces, and by a due process of exclusion and rejection lead it to an inevitable conclusion.
[Good induction proceeds by] rejections and exclusions, and then after a sufficient number of negatives, come to a conclusion on the affirmative instances.
Francis Bacon, Novum Organum, Aphorism 105
Facts are particulars, various, diffuse. They must be arranged in a suitable order
Francis Bacon, Novum Organum, Book II, Aphorism 10
Bacon’s method relies on two main factors:
experience and gradual induction
Experience amounts to facts arranged in a suitable order, not only plain and passive observation, without an order. To achieve this, we need the device of rules that allow us to classify facts.
This should be done by using tables:
- Tables of absence and presence
- Tables of deviation
- Tables of degrees or comparison
Subsequently, we collect all of these instances in histories, which are records of instances of facts and they concern either natural occurrences or artificial creations of experiments. Some sort of general surveys.
At this point, everything is left to the interpretation of gradual induction. This process provides a well prepared experience to apply induction in a good way. Only if we do this Induction can take its proper course.
As an example, Bacon applies his whole method to heat, after concluding the experiment, he concludes that heat is motion. He gets to this result by discarding many apparently good candidates and assumptions, using his inductive method.
Bacon revolutionizes the perspective of scientific reasoning by introducing his interpretation of induction. Bacon’s text is full of metaphors and images. There are two vintages to gradual induction:
- It produces an hypothesis
- It allows further testing to establish the results with greater confidence.
The aim—and the supposed result—is to provide
not elegant and probable conjectures, but certain and demonstrable knowledge.
Bacon’s rules of induction became the best way to discover the truth of premises that in the Aristotelian format were somewhat taken for granted.
Thus, we can attribute a better evidence to the premises, which can lead us to better conclusions.
We now have demonstrable knowledge that is different from the Aristotelian one.
Bacon wants, in his scientific method, to rely on an idea of indubitability rather than infallibility, namely focusing on what can be proven about an idea rather than what can be attached to it. Infallibility is not attainable by humans
In the New Organon, Bacon proclaims we should rely on his method because it is the best available one; according to him, we have a method that can lead us to good results, independently of individual skills: if this method is followed correctly, its conclusions cannot be doubtable.
This is a new territory of debate and study: Bacon must convince the scientific world that his method is good to follow, while having to face the very long Aristotelian tradition.
Bacon nevertheless he’s prudent by agreeing that the results his method brings about are not taking us to infallible certainties, because infallibility is proper of logic, which is proper of deduction.
Still, Bacon gives us reasons to believe that it is possible to reach some formal certainties, by filling his book with further tools that should make us more comfortable with the ideas he suggests.
Bacon suggests that conclusions well accompanied by evidences are to be considered more comfortable, more certain. Again: by using the word “certain” Bacon means empirical indubitability rather than logical infallibility.
- Is this optimism really motivated?
- How reliable is induction even in this laboriously described manner?
In the former, starting by a universal statement and getting to specific ones, while in the latter we go from a number of singular statements up to a universal one.
The principle of induction
If a large number of instances have been observed under a wide variety of conditions, and if all those observed ones without exceptions possessed a certain property, then all instances have that property.
Is meant to be legitimate and explain how by going from the observation of particular instances to a generalization which includes all of those instances and possibly all of the instances yet to be realized. The principle of induction makes significant not only the instances I observed up to now but the ones I’ll observe in the future. A projaction is entailed in this principle.
Logically speaking the problem comes therefore from expectations: if I see a lot of whit swans, I may easily conclude that all swans are white. This shows how in everyday life human’s nature is inductive.
This not only happens in everyday life, but in science, too: the normal number of chromosomes, the laws of gravitation, come from singular observations later generalized.
We are entering a slightly dangerous field, since with induction we can struggle to make a statement certain, but we will never be completely sure about its absolute truth; we are limited by the possible falsification laying a single specific instance or observation.
We are forced to bet on the assumption that the past and the present will be similar to the future. We assume that the present data is sufficient to understand the future.
At the same time, we are brought to base our assumptions on a wide enough set of observations and instances, but how wide is wide enough?
How justified are this assumptions? How risky and how well granted are they?
From a logical point of view:
In an induction, starting from a true premise may lead us to a false conclusion: there is no logical contradiction in stating that all swans are white up to now and successively affirming that not all swans are white.
Logic cannot guide us through this process of understanding.