Every scientific activity has some relationship, negative or positive, with the other ways of human thinking, which may occur in diverse instances, such as religion (i.e. hermeneutics), politics, medicine, media or more simply the individual man.
According to the definition given to scientific reasoning, its links to the other ways of thinking may be very different. I will not present here the different definitions we can use, but look in more detail to two major approaches: inductivism, in the sense given by Bacon, and deductivism, in the sense given by Hume and Popper. However the participants to this discussion are invited to introduce other scientific approaches.
For inductivism, Bacon said:
There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immovable, proceeds to judgement and to the discovery of middle axioms. And this way is now in fashion. The other derives from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried.
This new way leads to a true induction (as discovering principles from the study of their consequences), while the first leads to idols and false notions, which are used by the other ways of thinking. The discovered principles are not numerous, and without the laws of Galileo, Newton, Darwin, Einstein, et al., the facts observed would be different.
For deductivism, Hume revived the traditional meaning of induction (as generalization) which was clearly rejected by Bacon, and restored its deductive conception. This leads for example to the falsificationism of Popper, which accepts different hypotheses in order to try to falsify them. These hypotheses can easily be drawn from other ways of thinking, if they don’t contradict our observations, but they may be as numerous as them.
The joined document examines the interrelationships between scientific and non-scientific thinking about inoculation and vaccination against smallpox, and is part of a more detailed paper not yet published. For the Baconian idols, you may have a look to the paper I presented with Jakub Bijak, Robert Franck and Eric Silverman on: Are the four Baconian idols still alive in demography?, at the Chaire Quetelet 2013.
I would appreciate an exchange of ideas on this topic, as well from natural sciences as from social sciences.