As historian Geoffrey Cantor writes,
That Faraday expounded an empiricist view of science all commentators agree. Yet there are many incompatible strands within empiricism.
Faraday modified his views over the years, going from an initial allergy to mathematics to a tolerance of it. “Faraday’s rather complex, and apparently inconsistent, view on scientific method,” may be due to this metamorphosis.
Questions about the proper method for pursuing science were very important to him and he felt obliged on numerous occasions to expound his views on this subject so as to defend himself and his scientific work against alternative, but false, conceptions of science.
Cantor notes that there may be some distance between Faraday’s “methodological pronouncements” and “the actual methods he employed in the laboratory.” But the distance, if any, is slight, for “the two were closely related.” If someone had asked him “why he held those views,” he most probably would have answered that he was forced to hold them by the weight of empirical evidence, and if his methods and views changed slightly over the years, it would be because of the discovery of new evidence.
Faraday expressed a distaste for imagination, arguing that fantasy has no role in science, and coming close to echoing Newton’s famous hypotheses non fingo. Yet, for a thinker who largely rejected any role for imagination in scientific method, Faraday’s method centered around images: the etymological connection between ‘image’ and ‘imagination’ is not without cause. Cantor argues that Faraday doesn’t exile imagination completely and that Faraday retains a tightly-governed “proper role of the imagination.”
The famous near-absence of equations in many of Faraday’s writings, and his numerous drawings and diagrams attest to the visual nature of his thought. By contrast, other scientists of Faraday’s era, as well as before and after his era, had embraced the marriage between mathematics and natural sciences — especially between mathematics and physics.
Newton (1642 - 1727) clearly is an example of this marriage, yet Newton attached some importance to visualization. Indeed, John Hutchinson (1674 - 1737) criticized Newton’s inclusions of diagrams in scientific texts. Hutchinson wrote that Newton’s diagrams were “a cobweb of circles and lines to catch flies in.”
To be sure, it can be argued that a visual approach and a mathematical approach to electromagnetism are not that different, because the fields which Faraday described in words and pictures can also be captured in equations. But to that argument it can be replied that diagrams and drawings might offer a more intuitive understanding than equations, and that the intuitive understanding might be in some ways deeper and might offer more insights into the workings of electromagnetism.
Jim Al-Khalili describes Faraday’s skills:
What Faraday lacked in formal scientific training, particularly in mathematics, he made up for by his exceptional talent as an experimentalist. And although he was initially distrustful of mathematics, regarding it as obstructing rather than helping our understanding of the workings of Nature, he would, later in life, change his view in the light of the work of James Clerk Maxwell. In fact, Maxwell himself regarded Faraday as being an excellent theoretician and claimed this was the reason he was able to put Faraday's theories into the language of analytical mathematics.
Faraday’s search for principles, and his formulations of what those principles are or might be, were shaped in part by his Sandemanian and Glasite beliefs, as Geoffrey Cantor notes:
In his writings Faraday made repeated attempts to express the divinely fashioned natural economy in terms of metascientific principles, most importantly his principle of the conservation of forces. In his work of the 1820s and early 1830s the economy of nature was more implicit than explicit. By the late 1830s, however, it was beginning to emerge in a variety of different metascientific statements and to take on a more fixed form. Only with his far more explicit formulation of the principle of force conservation in the mid-1850s do we see it proposed as an incorrigible principle and one which must take precedence over all scientific theorizing.
The conservation of forces would seem to be, at first glance, a quantitative and therefore mathematical concept. Yet it seems that Faraday might have arrived at it visually.
