Logic and Discovery
Valid deduction reveals consequences already implied by its premises. Cheng compares this with discovery: an artifact or café can be new to the person finding it even though it already existed. Long chains of reasoning can reveal implications that were far from obvious at the start.
THE IDEA
LOGIC AND DISCOVERY
A valid logical implication preserves truth: if its premises are true, its conclusion must be true. Saying it out loud doesn’t exactly add new information, but it does add new insight. This is why in normal language logical implications can sound a bit stupid, as the immediate new insight is often horribly obvious. Take the example “If you have white privilege then you have privilege.” The “you have privilege” part of the sentence is the logical conclusion that automatically has to be true. It doesn’t add any new information, but rather, it gives a different view point on the same thing; in this case the new view is the broader context of different types of privilege.
In this way logic is really about shedding new light on things rather than discovering new things. In a way, this is no different from, say, an archaeologist digging up an artefact. That artefact was already there, it’s just that digging it up brings it to light. We get new insights but only because before that we were a bit ignorant. If we dig up a pot or the foundations of a building from hundreds of years ago, someone did already know about it, they just happen to be long dead.
Sometimes you might go on holiday abroad and “discover” a cute little café down some backstreet. Of course, you didn’t actually discover something new – some other people already knew about it (the owners and all the people who already go there). But it’s new to you. Sometimes people think they’ve “discovered” an amazing new singer, but they turn out to be extremely famous already, just not to the person who thinks they’ve just discovered them, and then everyone else rolls their eyes.
Logical conclusions are not new facts. Just like America was there all the time before white people reckon they “discovered” it, logical conclusions are true all along whether or not a human notices it. With “If you have white privilege then you have privilege” the conclusion is rather obvious, but the power of logic builds up when you string together a series of logical conclusions one after another, gradually getting you somewhere further from when you started. For example, we could string these implications together:
- If you are white then you have white privilege.
- If you have white privilege then you have privilege.
We now have the implication “If you are white then you have privilege.”
Sometimes the revelation happens suddenly, like unearthing spadefuls of dirt until suddenly hitting treasure. Sometimes it happens gradually, like in the wonderful example of the guy who swapped a paper clip for a house.
When to use it
In a debate, understanding that logical conclusions are not new facts can help focus the discussion on the truth of the premises rather than debating the conclusion.
When teaching logic or critical thinking, use the analogy of discovery to explain why logic is powerful: it makes implicit knowledge explicit.
In problem-solving, build logical chains from known facts to uncover hidden implications and reach novel solutions.
When evaluating an argument, checking both whether its premises are supported and whether its conclusion follows from them.
FROM THEORY TO EVERYDAY LIFE
In practice
White Privilege and Privilege
The statement 'If you have white privilege then you have privilege' is a logical implication. The conclusion 'you have privilege' automatically follows from the premise, but reframing the idea in terms of privilege highlights the broader context of different types of privilege.
Swapping a Paper Clip for a House
The paper-clip-for-a-house story illustrates how a series of small steps can reach an unexpected destination. The trades are an analogy for a chain of reasoning, rather than logical implications: each trade depends on someone agreeing to it, whereas a valid inference follows necessarily from its premises.
A MOMENT TO REFLECT
Put it to work.
Can you think of a time when someone presented a logical conclusion as a new discovery, but it was actually already implicit in the premises?
How can recognizing that logical conclusions are not new facts change the way you argue or reason with others?
What is the value of logical reasoning if it only reveals what is already true? When might that be particularly useful?
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)