The 1,200-Voter Survey: Hume's Problem in an Ajmer Classroom
A Class 12 student in Ajmer surveys 1,200 of the city's roughly 180,000 registered voters over three evenings, drawing names with a random-number table. His sample predicts the winning margin to within 1.5 percentage points, comfortably inside the stated margin of error. At the viva, three claims are made. (a) 'The survey proves the general law that young voters turn out at a lower rate.' (b) 'The margin-of-error figure is pure mathematics, so the prediction itself is a priori knowledge.' (c) A classmate who has been reading Charvaka material says the survey is just perception of 1,200 people and is therefore the only defensible kind of knowledge, while the law in (a) is inference and worthless. The teacher has 40 minutes and must use the three sentences to teach the difference between a posteriori generalisation, a priori reasoning and the problem of induction. She also has to correct (b) without letting the class conclude that all reasoning is empirical.
1. Diagnose claim (a) using Hume. What does the sample establish and what does it not establish?
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What the sample establishes. Twelve hundred observations give Hume a constant conjunction inside the sample: young voters and lower turnout have been found together so far. That is all that has been observed, and it is enough to state a frequency with a margin of error, conditional on the sample being genuinely random.
What it does not establish. The step from 1,200 observed to 180,000 unobserved voters assumes that the unobserved resemble the observed - the uniformity of nature. Hume's point is that this principle is neither a relation of ideas nor an impression; any attempt to prove it uses the very induction it is meant to justify, so the argument is circular. Nor is there any impression of necessary connection: the student saw voters, not the must that makes the pattern hold tomorrow. Claim (a) then commits a second, separate error: it converts a statistical estimate into a universal law.
Kant's reply, for contrast. Kant would say the principle is not a lucky generalisation but an a priori condition of having any experience of an ordered world. That secures the possibility of empirical law, not the truth of this prediction.
2. Is claim (b) correct? Separate the a priori element from the a posteriori element in the prediction.
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Split the claim. The arithmetic of a confidence interval is a priori: given the premises about sample size and variance, the margin of error follows by calculation and could not be otherwise. Hume would call this a relation of ideas; Kant would call the mathematics synthetic a priori.
But the prediction is not a priori. The full statement - 'the winning margin will fall within 1.5 points' - contains an empirical premise: that the sample was drawn randomly and is representative. That premise is known only from experience and could fail: a biased list, a holiday, a monsoon, a ward left out. A conditional whose antecedent is empirical is not a priori knowledge of the world; it is a priori reasoning applied to empirical data.
Why the correction matters. If the class concludes that because (b) is wrong all reasoning is empirical, it has swapped one error for another. The conditional 'if the sample is random, the estimate falls within the stated error' is a piece of a priori reasoning, and it is what makes the survey worth doing. The rationalist would push further and claim the uniformity of nature as an a priori principle of sufficient reason; the empirical answer is that the premise must be checked, not assumed.
3. How should the teacher answer the classmate's remark in (c)?
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The tu quoque. If his Charvaka principle is that only perception counts, then the survey's headline - a prediction about 180,000 voters - is not perception and must be discarded. What he saw was 1,200 people answering questions. The step from those to the city is inference, and it is exactly the step he has just declared worthless. His remark therefore refutes the survey rather than defending it.
The more careful Charvaka reply. A consistent Charvaka need not reject all reasoning in practice; he can hold that inference is unreliable because vyapti can never be established beyond the observed cases, which is Hume's problem in Sanskrit dress. On that version the survey survives only as a record of what was seen, and its predictive claim is a gamble rather than knowledge.
What the teacher should draw out. Nyaya would answer that vyapti is established by repeated observation, the absence of a counter-instance, and the upadhi test - which is precisely the dispute the class should be having, and it connects the Ajmer survey to the Indian materials on inference rather than leaving them in a separate chapter.