Accessing Truth
Different fields of study use distinct methods to determine and verify truth: science relies on the scientific method, while mathematics uses logic. Misuse of terms like 'logic' and 'mathematically' in arguments often reflects a desire for irrefutable proof but can be misleading.
THE IDEA
ACCESSING TRUTH
All areas of research and study are concerned with uncovering truths about the world. It might be the earth, the weather, the outer reaches of the universe, birds, electricity, brains, blood, people thousands of years ago, numbers, or something else. Depending on what you’re studying, you’ll need different ways of determining what is true, and of convincing other people that you’re right. Anyone can make claims about what they think is true, but unless they back up their claims in some way, maybe nobody will believe them, and rightly so.
So different subjects have different ways of accessing truth.
Scientific truth is determined using the scientific method, which is a clearly defined framework for deciding how likely something is to be correct. It usually involves forming a theory, gathering evidence, and rigorously testing the theory against the evidence.
Mathematical truth is accessed by logic. We can still use emotions to feel it, understand it, and be convinced of it, but we use only logic to verify it. This distinction is important and subtle. In a way, we do access mathematical truth using emotions, but it doesn’t count as true until we have verified it using logic.
The word “logic” is sometimes thrown around in disagreements to try and give an argument weight. “Logically this has to be true”, or “Logically that can’t be right”, or “You’re just not being logical!” The word “mathematically” also gets thrown around in this way. “Mathematically, they just can’t win the election.” Unfortunately these uses are often meaningless, more of a last-ditch way to try and shore up a weak argument. While the abuse of these words devalues them and so makes me sad, I am an optimist and so I choose to find something heartening in this as well: I am heartened to think that at some level people know that logic and mathematics are irrefutable and so should conclusively end an argument. If their names are being taken in vain to vanquish an opponent, at least this means there is some sense in which their power is being acknowledged.
When to use it
Evaluating competing claims in a scientific debate by distinguishing between empirical evidence and logical necessity.
Teaching critical thinking by contrasting how truths are established in different academic disciplines.
Analyzing political or advertising rhetoric that invokes 'logic' or 'mathematics' to appear objective.
Designing an interdisciplinary curriculum that helps students understand why a mathematical proof is different from a scientific theory.
FROM THEORY TO EVERYDAY LIFE
In practice
Scientific Truth vs Mathematical Truth
In science, determining whether a new drug is effective requires forming a hypothesis, conducting double-blind trials, and analyzing statistical significance. In mathematics, proving that the square root of 2 is irrational relies on logical deduction from axioms, not empirical evidence.
Misuse of 'Logic' in Everyday Arguments
Someone might say, 'Logically, my team will win the championship because they have the best players.' This uses 'logically' as rhetorical emphasis, not as a formal logical proof. The actual truth depends on many variables beyond talent.
A MOMENT TO REFLECT
Put it to work.
Think of an argument in which someone used the word logically. What premises and evidence supported the claim, and did the conclusion follow from them?
How does the scientific method differ from other ways of knowing, such as tradition or personal experience?
When you encounter a statistic or mathematical claim in the news, how can you evaluate whether it is used correctly or as rhetorical shorthand?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)