Our ancestors have contemplated the world ever since they had the capacity for abstract thought. However, higher thought functions evolved as untamed instincts harnessed to the senses and emotions. Only in the last few millennia did philosophers start to think about thinking. They recognized that thought was most accurate when imagination is disciplined by reason. Reason can reveal universal truths that do not depend on culture, opinion, or coercion. Sometimes people have changed the world just by changing the way we think about it.
Ancient Greeks, especially Aristotle, systematized formal logic. Logic is the study of truth as captured by language. It is highly abstract, so logical rules apply equally to apples, oranges, and thoughts about oranges. The adjective “formal” here means that the veracity of an argument can be analyzed based on its form, no matter what the argument is about.
The basic unit of logic is a sentence that represents a true or false fact. Facts can be qualified and quantified with terms such as sometimes and for every. They can be connected with conjunctions like and / or / not. Some connections are conditional, for instance, “If fact A is true, then fact B is false.” These simple connections lead to rules about how the mind must work in order to follow reality. Aristotle analyzed formal logic during the Athenian democracy. In a democracy, citizens debate to persuade each other to action. Aristotle recognized that clever rhetoricians could convince each other of false facts with illogical tactics: by appealing to emotions or popular opinion, or by making faulty arguments sound convincing. 2 His main contributions were the analysis of syllogisms and logical fallacies (faulty reasoning). A syllogism connects two factual premises together to deduce a third fact, a conclusion:
|Correct||Some Antiques are Bronze,|
and All Bronze Corrodes.
Therefore, some Antiques Corrode.
|Some Albums have Ballads,|
and Ballads always make me Cry.
Therefore, some Albums make me Cry.
|Some As are Bs
All Bs are Cs
Some As are Cs
|Incorrect||Some Appetizers have Berries,|
and Some Berries make me Choke.
Therefore, some Appetizers make me Choke.
|Some As are Bs
Some Bs are Cs
Some As are Cs
An argument that follows the upper form will be correct, whether it’s about antiques, albums, or anything. By merely changing the “all” to “some”, we get the lower fallacy. The “appetizers” argument is faulty, even if some appetizer really does make me choke! 1
It’s easy to fool people with bad logic, because the human mind understands examples and personal experience best; it takes extensive training to think in purely abstract terms. Many people buy fallacious arguments, especially ones that support predisposed beliefs. Not only do we filter evidence, but we often filter logic itself!
An orderly system of logic gave philosophers and scientists much better guidance to move academic progress forward. Logical statements have a “mechanical” flavor to them, in that they lead to conclusions automatically. In very recent centuries, engineers learned how to program logical sequences into machines, which progressed into computers. Even the phone in your pocket is part of a long tradition going back to Aristotle.
Logic alone is not enough to understand the world. Consider this argument:
Oranges are rich in Vitamin C
Vitamin C effectively prevents colds
Oranges effectively prevent colds
This syllogism is logically correct, but that only means that its conclusion is as good as its premises. We have to test those premises in the real world. First, we can’t ascertain whether oranges are rich in vitamin C just by thinking about oranges. We have to analyze some oranges in a lab.
It’s even more challenging to test whether vitamin C effectively prevents colds. Inductive reasoning from examples may suggest a hypothesis: “I have been getting colds less often since taking my vitamin C tablets. Maybe the vitamin C is preventing colds.” An experiment is the best way to test this prediction. By comparing people who take vitamin C to those who don’t, a scientist can get a pretty good idea of the vitamin’s efficacy. The clearest and most convincing results will be mathematical, for example by describing percentages and time durations. Observations, induction, experiments, and mathematical modeling are key elements of what we now call the scientific method.
Ancient Greeks showed some mindfulness of induction and observations, but they were not good scientists by today’s standards. They proposed many laws of nature that were flat-out false but went unchallenged for millennia. Medieval Moslem scientists were more experimental and mathematical, and started overturning some classical ideas. 2 3Renaissance Europeans continued developing science as a form of inquiry.
By 1650, it was well established that quality of knowledge is not measured by the person who expounds it but by the method he follows. Science was seen as an evolving body of hypotheses that lost or gained strength based on evidence. A hypothesis should also be falsifiable: it should make predictions that can be tested as true or false. 4
16th century Polish astronomer Nicolaus Copernicus used meticulous observations to propose the radical notion that the Earth goes around the sun. Copernicus’ model was imperfect, so much so that we might call his discovery a lucky guess. Nevertheless, it was confirmed, refined, and mathematized after another century of scientific observations. The power of science to uncover such a grand but invisible order made a great impression throughout Europe. The movement it inspired is now neatly summarized as the scientific revolution.
Since astronomy is mostly observational, it lent itself to early rapid development as a body of science. The same was true of anatomy. With dissections, scientists such as Vesalius and Harvey were able to discover basic realities about the structures and functions of organs.
The Renaissance’s trailblazing experimental scientist was Galileo. 3 He used man-made experimental setups to systematically force nature to give him answers. For instance, it is difficult to take precise measurements of falling balls, so Galileo slowed them down by rolling them down ramps. His observations led to broad laws of nature and mathematical descriptions of movement and solid / fluid mechanics.
The generation after Galileo saw a flurry of activity in many fields. Scientists made revolutionary discoveries in hydraulics, optics, electricity and magnetism, geology, and biology. The mathematics to describe nature matured very quickly into calculus and other advanced methods. Scientific academies and journals formed around each discipline. This accelerated the pace of science well beyond what isolated medieval thinkers had accomplished.
Isaac Newton 4 tied together many strands of scientific progress with mathematical principles. His universal laws of motion and gravitation were the most far-reaching. Aristotle had taught that Earthly objects have very different natures from heavenly objects. Newton showed that the same laws apply to motion in the heavens as on Earth. The moon’s circular orbit is a combination of straight-line motion in two directions: falling toward Earth (gravity, like an apple from a tree) and flying off tangentially into space (inertia, like a puck on frictionless ice).
Mathematical laws also greatly delimited the role of magic willpower in nature. If particles and planets moved in patterns that could be predicted on paper, nature’s laws seemed more like indifferent properties of numbers than any divine plan. Post-Newtonian scientists spoke of a “clockwork” universe, one that did not operate at God’s whim but that could be precisely understood with close study.
Although Europe’s leading scientists up to and including Newton were devoutly Christian, some discoveries were starting to conflict with scripture 5 or church doctrine. 5 Churches banned numerous scientific works for heresy. 6 Europe entered a confusing period when reason and authority gave different answers.
Outside of clockwork and astronomy, most phenomena are complicated and difficult to predict. Probability is the reasoned way to deal with the unknown. In medieval thought, understanding the unknown was a matter of interpreting signs from nature. To determine whether a sick man would survive, an oracle might say that a flock of ravens foretells his death, whereas a doctor might say that death is more likely when the patient’s nose perspires. Obviously, some signs were more accurate than others. Signs led to the concept of evidence, and the reliability of evidence was called probability. 7
17th century mathematicians 6 realized that some probabilities could be quantified by counting equally likely events. Tools of chance – dice, playing cards, roulette wheels – provide the simplest illustrations. There are about 3,000,000 ways to deal a poker hand. Roughly 5,000 of these hands constitute a flush. Thus, the probability of getting a flush is 5,000 / 3,000,000 or about one in 600. Interpretation 1: In a casino full of 600 gamblers, about one of them would hold a flush. Interpretation 2: It is rational for a gambler to bet $1 for a $600 prize in the event he is dealt a flush. Understanding these interpretations helped make lotteries, insurance, law, and pensions fairer and more efficient. Managing risk wisely became an integral part of capitalistic investment, wealth management, and state budgets.
An essential step in calculating probabilities is to have accurate tallies of data. For instance, if the state issues annuities to millions of men, it needs to know the probability that each man will survive each year to collect his payment. This probability is determined by examining voluminous record books. Statistics, the study of data, was pioneered concurrently with probability. The earliest known case study was John Graunt’s analysis of England’s Bills of Mortality. This tome listed christenings, deaths, and immigrations through the centuries. Graunt was able to determine fundamental facts such as that England’s children were born 51% male, and that plagues rarely lasted more than two years.
Without examining data, such valuable but subtle truths would otherwise be invisible. Most people get their understanding of the world through direct personal experience. Any one person’s experience, though, is too limited and biased to get the full picture of reality. Conventional wisdom, too, can be mistaken. For instance, the English once believed that plagues struck whenever a new king was crowned. Data proved that this was false superstition. 8 Science and society have become increasingly data-driven ever since – a characteristic that is only accelerating in the computer age.
Back to Section 3.VII: The European Age
Continue to Section 3.IX: Summary
- Galileo (1610), public domain. https://commons.wikimedia.org/wiki/File:Galileo%27s_sketches_of_the_moon.png ↩
- Michael Shenefelt and Heidi White, If A, Then B: How the World Discovered Logic, Columbia University Press (2013). Chapters 1 and 2 give a unique discussion of how Aristotle’s formulation of logic was influenced by his environment. Section 2.5 in particular discusses “The Separation of Logic from Rhetoric”. ↩
- David Charles Lindberg, “Chapter 4: Alhazen and the new intromission theory of vision”, Theories of Vision from al-Kindi to Kepler, pp. 60 ff., University of Chicago Press (1976), https://books.google.com/books?id=-8A_auBvyFoC&pg=PA60#v=onepage&q&f=false (accessed 10/06/19). ↩
- 20th century American philosopher Karl Popper defined science by falsifiable hypotheses. Stephen Thornton, “Karl Popper” in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (ongoing since 11/13/1997), https://plato.stanford.edu/entries/popper/ (accessed and saved 12/11/16, archived 10/17/19). ↩
- Dan Hardin, “All 281 Geocentric References of the Holy Bible”, Gateway Anabaptist Church (1/29/2014), http://www.gatewayanabaptistchurch.com/2014/01/29/all-281-geocentric-references-of-the-holy-bible/ (accessed, saved, and archived 10/12/19). ↩
- Scientists on the Catholic church’s Index of Prohibited Books included Kepler, Galileo, Descartes, Francis Bacon, and Pascal. For the Church’s arguments against Galileo, see Ernst Krause, “The Struggle Regarding the Position of the Earth”, The Open Court 14(8):449-474 esp. at 459 (August, 1900), http://opensiuc.lib.siu.edu/cgi/viewcontent.cgi?article=1214&context=ocj (accessed, saved, and archived 10/12/19). ↩
- Ian Hacking, The Emergence of Probability, Cambridge University Press (2006), Chapter 5, “Signs”. ↩
- John Graunt, “Chap. VI: Of the Sickliness, Healthfulness, and Fruitfulness of Seasons”, Natural and Political Observations Made Upon the Bills of Mortality (1662, 5th edition London, 1676) p. 369, reprinted at https://en.wikisource.org/wiki/Natural_and_Political_Observations_Made_upon_the_Bills_of_Mortality_(Graunt_1676)/Chapter_6 (accessed and saved 10/13/19). ↩
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