Starting with Intuition

How do we define a fact? Some are so fundamental that they are universally recognized as self-evident—what we refer to as intuition. For instance, the statement 1 + 1 = 2 is such a truth. It's immediately apparent to us. Another way to frame intuition is as an understanding gleaned at a glance. René Descartes emphasized this type of insight, suggesting that it is a cognitive tool unavailable to non-human animals, which lack the capacity for such reasoning.

Consider the sighting of a single bird. It's evident that there is only one. Now, introduce a second bird, and a new concept emerges: that of "two." The complexity increases if we differentiate the species, such as a crow and a chicken. If we categorize them simply as birds, we acknowledge two. However, if we recognize their differences, we specify one crow and one chicken. At this point, we are dealing with conjecture, as we cannot confirm whether an animal like a monkey possesses the same pattern recognition abilities. Confusing conjecture with established fact can lead us astray in our pursuit of knowledge.

Now, let's revisit the concept of 1 and 1 yielding two. Recognizing that there is a single bird, and subsequently that two birds exist, are both intuitive truths.

Deduction

While recognizing these patterns may seem simple, it is part of our reasoning toolkit. A monkey might grasp the difference between one and many and could select one banana from a group, but it likely cannot comprehend numerical concepts like 2, 3, or 4. Whether a monkey can recognize these patterns remains a conjecture.

Now, let's explore a more intricate fact: 1 + 3 = 2 + 2. This may feel intuitive, but it relies on memory rather than pure intuition. If we take numbers like 325 + 428, the result isn’t immediately obvious; it requires a logical progression. When we deduce that 325 + 428 equals 753 and that 456 + 456 also equals 753, we arrive at our conclusion. Thus, the statement 1 + 3 = 2 + 2 derives from two previously established truths: 1 + 3 = 4 and 2 + 2 = 4. The equivalence of 4 = 4 is an intuitive fact.

Introducing Induction

To derive a conclusion such as 1 + 3 = 2 + 2, we need more than intuition; we employ deduction, which involves deriving remote facts from established ones. This logical chain allows us to form complex conclusions based on a series of interrelated truths.

Deduction is any conclusion that isn't self-evident and is reached through a series of known facts. Intuition represents direct knowledge, while deduction involves a series of established truths, as articulated by Descartes.

Real-life details often lack clarity, necessitating extensive reasoning to draw conclusions. Mathematics, particularly algebra and geometry, is rich in such established truths. For example, the fact that a triangle has three sides is irrefutable, as is the fact that a sphere has a single surface. This abundance of evident truths is why some philosophers gravitate toward mathematics.

However, deduction alone cannot address every inquiry; we also require induction, or enumeration. Induction becomes crucial when drawing conclusions from extensive data where self-evident truths are insufficient. For instance, if we heat water steadily and monitor its temperature, we expect a continuous increase until it reaches boiling point. Therefore, if we leave water on the stove for an hour, we cannot assume that the temperature will rise indefinitely; it will only do so until it reaches 100 degrees Celsius.

What about faith? Some individuals, including leaders in the USA, have claimed electoral outcomes as a matter of faith, asserting that the election was stolen based on belief rather than evidence. In India, opposition to the government can often appear illogical, with some viewing the Modi administration as incapable of doing anything right, driven by ideology rather than fact.

It is essential to recognize that faith cannot replace factual evidence. Any assertion not supported by intuition or deduction is questionable. Descartes suggested that divine revelation might provide certainty, especially regarding obscure matters, as it stems not from the intellect but from will.

Questions like whether the election was indeed stolen or if the second COVID-19 wave in India stemmed from governmental negligence cannot be resolved through faith alone. We must construct a chain of specific facts and engage in logical reasoning to ascertain the truth behind these claims. Intuition must play a role in linking each fact, ensuring that our reasoning tools do not falter, lest we be overwhelmed by the loudest grievances, jeopardizing our democracy.