It’s Christmas dinner, an allegory of abundance and a stage for opulence. Your neighbor at the table, probably a fourth cousin whose name you barely remember, is starting to show signs of giving up and is desperately seeking your complicit gaze. But with feigned nonchalance and reckless boldness, you act as if you’re still hungry, even though the amount of food you’ve just consumed could satisfy the caloric needs of the entire province of Isernia. Then, as the third hour of dinner strikes, a new, succulent course is brought out: a stuffed turkey.
At that moment, in a fleeting pang of consciousness – typically left at home during such occasions (otherwise, how else could one explain such an absurd amount of food?) – you wonder about the story behind the turkey in front of you.
This turkey lived on a farm where, from day one, it was fed regularly. The turkey noticed that food was brought every day at the same time, regardless of the season, weather, or other external factors.
Over time, it began to derive a general rule based on repeated observation of reality. It began to embrace an inductivist worldview, collecting so many observations that it eventually made the following assertion:
“Every day at the same time, they will bring me food.”
Satisfied and convinced by its inductivist reasoning, the turkey continued to live this way for several months. Unfortunately for the turkey, its assertion was spectacularly disproven on Christmas Eve when its owner approached as usual, but instead of bringing food, he slaughtered it to serve at the very Christmas dinner you are attending.
The Turkey and Inductivism
This sad story is actually a famous metaphor developed by Welsh philosopher Bertrand Russell in the early 20th century. It clearly and simply refutes the idea that repeated observation of a phenomenon can lead to a general assertion with absolute certainty. The story of the inductivist turkey dates back to a time when Russell opposed the ideas of the Vienna Circle’s neopositivists, who placed unconditional trust in science—particularly inductivism—and regarded it as the only possible means of acquiring knowledge.
The turkey’s example was later adopted by Austrian philosopher Karl Popper, who used it to support his principle of falsifiability. According to this theory—one of the 20th century’s most brilliant—science progresses through deductions that are never definitive and can always be falsified, meaning disproven by reality. There is no science if the truths it produces are immutable and unfalsifiable. Without falsifiability, there can be no progress, stimulation, or debate.
What Does This Mean for the Turkey?
Returning to the turkey’s situation, does this mean it’s impossible to draw conclusions based on experience? Of course not. The study of specific cases helps us understand the general phenomenon we’re investigating and can lay the groundwork for developing general laws. However, the truth of any conclusion we reach is never guaranteed. In simpler terms, if a flock of sheep passes by and we see 100 white sheep in a row, that doesn’t mean the next one will also be white. From an even more pragmatic perspective, no number of observations can guarantee absolute conclusions about the phenomenon in question.
Implications for Statistics and Inference
Statistics, and particularly inference—a core component of statistics—derive their philosophical foundations from this concept. The purpose of inference is to draw general conclusions based on partial observations of reality, or a sample.
For example, let’s say we want to estimate the average number of guests at a Christmas dinner. How would we do that? Let’s set aside the turkey for a moment, put down our forks and knives, and imagine we have a sample of 100 Christmas dinners where we count the number of guests. Based on a fundamental theorem of statistics known as the Central Limit Theorem, we can assert that the average number of guests observed in our sample is a correct estimate of the true population mean (provided the sample is representative and unbiased, but that’s a topic for another day). Moreover, the error in this estimate decreases as the sample size increases. In other words, the more dinners we include in our sample, the more robust and accurate the estimate becomes. Logical, right?
But how certain are we that our estimate is correct? Suppose we’ve determined that the average number of guests across 100 dinners is 10. From this observation, we can also calculate an interval within which the true average is likely to fall. With a sample of 100 units, we can assert with a certain level of confidence (typically 95%) that the true average number of guests is between 7 and 13. With a sample of 200 units, our estimate becomes more precise, narrowing the interval to 8 and 12. The larger the sample, the more accurate the estimate.
Absolute Confidence? The Turkey’s Warning
These estimates are valid with a 95% confidence level. But what if we wanted 100% confidence? Would it be possible? Here’s where our inductivist turkey makes its comeback. If we wanted 100% confidence, we would fall into the same trap as the turkey—attempting to draw conclusions with absolute certainty from a series of observations. As we’ve seen, at the turkey’s expense, this is impossible. The explanation is simple: even with a large and representative sample, it’s never possible to completely eliminate the influence of chance. There’s always a small probability that we’ll encounter an observation—like a Christmas dinner with more or fewer guests than our confidence interval predicts—that contradicts our estimates.
Thus, what statistics can offer in such cases is a very robust estimate of the parameter we’re studying (instead of the number of dinner guests, think about something more critical, like the average income of a population, the efficacy of a drug, or election polls). However, it can never provide absolute certainty about a phenomenon. This is because the world we live in is not deterministic but is partly governed by chance. In this sense, statistics is a science that demonstrates the “non-absoluteness” of other sciences, which is perhaps why it is often feared or disliked.
After all, statistics reached its peak development in the 20th century, the century of relativism—think of Einstein’s theory of relativity, Heisenberg’s uncertainty principle, or Popper’s criterion of falsifiability.
Now, it’s time to eat the turkey before it gets cold!
