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The Self-Indicating Assumption (SIA) claims that learning "I am Eric" should shift your credence toward worlds with more observers. But SIA proponents also acknowledge that it doesn't matter whether you're Eric, Sarah, or John, every specific identity gives the same probability. This seems to reveal a contradiction. You cannot treat something as evidence while simultaneously admitting its specific content is irrelevant. I'm going to show that this isn't a quirk of SIA, it's a logical incoherence.
What Makes This Critique Different
You might have encountered other criticisms of SIA, arguments about infinite populations, measure theory, or the Presumptuous Philosopher problem. This argument takes a different approach.
I'm not arguing that SIA leads to counterintuitive conclusions. Many philosophical positions that I espouse have counterintuitive implications. I'm arguing that SIA contains an internal tension. It simultaneously treats identity information as relevant evidence and as irrelevant.
I'm not introducing exotic scenarios. This argument uses the simplest possible case: God flips a coin and creates one or two people. If there's a problem with SIA's reasoning, we should be able to see it clearly in this basic setup.
Most importantly: This argument requires no advanced mathematics, no probability theory beyond basic Bayesian reasoning, and no contentious philosophical assumptions. It focuses on a simple question: Can you extract evidence from information you acknowledge is irrelevant?
If this argument succeeds, it suggests SIA has a foundational problem, not just edge-case difficulties.
The Setup
Here's the classic thought experiment:
At the beginning of the universe, God flips a fair coin. If Heads, he creates one room with one human. If Tails, he creates two rooms, each with one human. You wake up in a room knowing this setup but nothing else.
The Halfer Position: The coin was fair, and learning "I exist" gives you no new information. P(Heads) = 1/2.
The SIA Position: You should reason as if randomly selected from all possible observers. There are three possible "observer-slots" (one in Heads-world, two in Tails-world), so P(Heads) = 1/3.
The Identity Symmetry Problem
Ask an SIA proponent what probability they'd assign in each case:
The probability doesn't change based on which specific person it is. SIA proponents themselves acknowledge that identity doesn't matter to their calculation. Every possible identity gives the same 2/3 answer.
But if the specific identity is irrelevant to the probability, if it makes no difference whether the observer is Eric, Sarah, or John, then the identity information is doing no evidential work. They're really just responding to "someone exists with some identity," which was already certain under both Heads and Tails.
This is the core contradiction: SIA treats "I am Eric" as evidence that should shift your credence to 2/3, while simultaneously acknowledging that the specific identity "Eric" (as opposed to "Sarah" or "John") is completely irrelevant to the calculation. How can something be evidence if that something doesn't matter?
The Logical Chain
Let's trace through what SIA is committed to:
Step 1: "Someone exists" → Does this change the odds from the initial 50/50?
SIA proponents would correctly answer: "No, it stays 50/50, because someone existing was guaranteed under both Heads and Tails." (Basic stats rule)
Step 2: "Someone with an identity exists" → Does this change the odds?
It can't. Whoever exists must have some identity. This is just a necessary specification of "someone exists."
Step 3: "Eric exists" (or Sarah, or John) → Does this change the odds?
SIA says: "Yes! Now it's 2/3 for Tails."
But wait. We just established that:
You cannot go from 50/50 to 2/3 by adding information that you simultaneously claim is irrelevant. This appears to be a fairly direct problem. This is SIA extracting Bayesian evidence from a tautology, from learning that whoever exists is someone in particular, which was guaranteed to be true.
The Ball Analogy
Here's why this reasoning fails. Imagine a jar filled with balls of different colors. We flip a coin:
You learn: "A black ball was picked."
Does this tell you anything about the coin flip? No! Yes, black balls are more likely to be picked under Tails (two chances vs. one), but some ball with some color was guaranteed to be picked either way. The specific color is irrelevant to the coin flip probability.
Here's why this matters empirically: If a person applies SIA-style reasoning “I'm more likely to observe a ball under Tails, so each ball I see gives 2/3 probability to Tails” they would predict approximately 33 Heads and 67 Tails after 100 flips. But the actual result would be 50/50. The SIA reasoning produces falsifiable, empirically wrong predictions. This isn't just a philosophical disagreement, it's a reasoning error that would lose you money if you bet on it.
The same logic applies to personal identity:
The ball example shows why "necessary specification" isn't evidence. When something must necessarily be true (some color must be picked, some identity must exist), learning which particular specification obtained tells you nothing.
The Math Doesn't Care Who Does It
Here's the argument that makes escape impossible.
Eric knows: "Eric exists."
Outside observer knows: "Eric exists."
These are identical pieces of information. They must lead to identical conclusions. Math doesn't change depending on who's doing the calculation.
Yet SIA claims:
This is, to say the least, perplexing. They have the same information about the world. They must reach the same conclusion about the same coin flip.
The Indexical Illusion
SIA proponents will object: "But Eric has special indexical information! He knows he's this observer, not just that some observer exists. He knows 'I am Eric.'"
This is a linguistic illusion created by first-person pronouns. Let's examine what each party actually knows by removing pronouns:
Eric knows:
Outside observer who learns "Eric exists in a room" knows:
These are identical! Statement (3) is simply the law of identity, tautology that holds in all possible worlds and conveys zero information.
The illusion arises from the first-person pronoun. When Eric thinks "I am Eric," it feels like he's learned something special. But "I" is just how Eric refers to Eric. Strip away the grammatical packaging and you're left with "Eric is Eric", which tells us nothing about the world.
Your subjective perspective isn't information about the world, it can't change the actual probability of a past coin flip.
Consider a concrete scenario: Eric wakes up and calculates P(Tails) = 2/3 using SIA. He then calls an outside observer and says, "I'm Eric, I exist in room A". Thereby transferring his indexical information.
Should the outside observer now also update to 2/3?
If yes: Then what information justified the update? Not the specific identity "Eric", SIA itself acknowledges that any identity (Eric, Sarah, John) would yield the same 2/3 probability. So the observer is updating on "someone with some specific identity exists," which reduces to "someone exists with some identity" and that was guaranteed under both Heads and Tails. The observer is extracting evidence from the fact that whoever exists turned out to be someone in particular, which had to be true.
If no: Then the same information ("Eric exists in room A") produces different probabilities depending on who holds it. Eric concludes 2/3, the observer concludes 1/2. But evidence doesn't work this way. If "Eric exists" is genuine evidence about the coin flip, it must have the same evidential force regardless of who learns it.
The dilemma reveals SIA's core problem: Eric can fully communicate his indexical information "I am Eric, and I exist" to the observer. They now share the same facts. If SIA claims this produces different probabilities for the two of them, it's treating evidence as somehow non-transferable, which violates basic principles of how information works. Evidence is about the world, and facts about the world don't change their meaning when communicated from one person to another.
The "Observer Slot" Objection
SIA proponents might refine their objection: "Eric doesn't just know 'Eric exists', he observes that he is in this particular observer slot. He has first-person access to being this observer, not just knowledge that this observer exists."
This doesn't help for two reasons.
First: What makes "observer slots" special?
SIA applies its sampling logic only to observers. If God flips a coin and creates either one $100 bill or two $100 bills, SIA proponents wouldn't claim that "being" a $100 bill gives evidence for two bills existing. The same goes for colored balls, envelopes, or any other entities.
Why should observer slots work differently? What is it about consciousness or subjective experience that changes the underlying statistics? If SIA requires that observers are metaphysically special. That there's something about being a conscious entity that makes sampling logic apply in a way it doesn't for physical objects. It then seems to be smuggling in dualist assumptions, or some other unstated assumption about observers. Most SIA proponents are physicalists who would reject Cartesian dualism in other contexts. But without such assumptions, there's no principled reason why "observer slots" should behave differently from "dollar slots" or "ball slots."
The burden is on SIA to explain this asymmetry. Absent a compelling justification, "observer slots" are just another type of countable entity, and the logic that fails for dollars should fail for observers too
Second: The observer knows Eric is in this particular observer slot.
Let's be precise about what "being in an observer slot" means:
What Eric observes:
What the outside observer knows upon learning "Eric exists in room A and is having experiences":
The outside observer knows everything on Eric's list. Statement (4) "these are Eric's experiences" is not special information. It's just the fact that Eric's experiences are Eric's experiences. Of course Eric's experiences belong to Eric. That's what makes them Eric's experiences. This is, once again, a tautology.
The key point: There is no additional fact called "I am in this observer slot" beyond the fact "Eric is in this observer slot." The first-person perspective doesn't add information, it's just Eric's way of referring to Eric.
Consider: If the outside observer can deduce P(Tails) = 1/2 from "Eric exists in room A," but Eric should deduce P(Tails) = 2/3 from the same facts, then you're saying that being the person the facts are about changes the math. But math doesn't work that way. Your identity as the subject of the facts doesn't change what the facts imply.
SIA wants to claim that "experiencing being Eric" gives Eric evidence that "knowing about Eric" doesn't give the outside observer. But experiencing being Eric just is being Eric. And the outside observer knows Eric is Eric. And as long as we are not trying to deduct anything from Eric’s personal life, there's no epistemic gap here, just a grammatical one.
Preempting Objections
"But you're ignoring indexical information"
No. I just showed that "indexical information" reduces to "Eric is Eric," which is a tautology. The outside observer also knows Eric is Eric. There's no special knowledge here.
"But the outside observer doesn't know which room they'd see if they looked"
Neither does Eric! Eric doesn't know if there's another room. The outside observer who learns "Eric exists" knows everything Eric knows. They must reach the same conclusion.
"You're just assuming the halfer position"
No. I'm showing an internal inconsistency in SIA. I'm not arguing for an alternative theory. I'm showing that SIA contradicts itself by treating identity as both evidentially relevant and evidentially irrelevant.
Conclusion
SIA seems to fail because it contains a logical contradiction at its core:
The Identity Symmetry Problem: SIA treats specific identities (Eric, Sarah, John) as evidence that should shift probabilities to 2/3, while simultaneously acknowledging through its symmetric treatment of all identities that the specific identity is irrelevant to the calculation. This is incoherent, you cannot claim something is evidence while also claiming its specific details don't matter.
The Information Identity Problem: Eric and an outside observer who both know "Eric exists" have identical information. They must reach identical conclusions. SIA's claim that they should differ reveals it's trying to extract evidence from subjective perspective rather than from facts about the world.
The result: SIA updates on tautologies. It treats "whoever exists is someone" as evidence for more observers, when this was guaranteed to be true regardless. It extracts information from non-information.
The halfer position emerges as the only coherent answer. The coin was fair, someone was guaranteed to exist with some identity, and learning which identity you happen to be tells you nothing about the coin flip that created you. The pronoun "I" creates an illusion of special knowledge, but once we strip away the linguistic packaging, we see that you know exactly what an outside observer knows: that you exist, and that you are you, a tautology that provides no evidence about anything.
Notes :
I developed this argument independently after getting confused by the math-heavy critiques of SIA I found online. If anyone knows of similar arguments in the literature, I'd be curious to see them. I am a relative novice to the discussion and would like to strengthen my argument by engaging.
I used AI translation tools to assist in rendering my original French text into English. All reasoning and arguments are my own. I am bilingual and will interact in the comments but I wanted my main post to sound as smooth as possible to the audience here.
I’m a native French speaker. In French academic writing, arguments are often presented more directly; I’ve tried to keep that clarity here while respecting the more collaborative tone of LessWrong discussions. I do not wish to come off as too confident, I am not a veteran of this debate and I know it, I post it with full humility.