Epistemic Status

The epistemic status of a proposition is the degree it’s supported by the evidence and reason

Outline

Epistemic Status

The epistemic status of a proposition is the degree it’s supported by the evidence and reason.

Basic Epistemic Statuses

“In our reasonings concerning matter of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of [probable] evidence. A wise man, therefore, proportions his belief to the evidence.” (David Hume, 1758)

Epistemic Operators

An epistemic operator is a sentential operator expressing a degree or range of evidential support.

It’s certain that
The probability is 1.0 that
It’s virtually certain that
It is beyond a reasonable doubt that
It’s reasonable to believe that
It’s very likely that
There’s clear and convincing evidence that
There is a preponderance of evidence that
It’s a toss-up whether
It’s an open question whether
There’s probable cause that illegal drugs are in the house.

It’s uncertain whether
It’s unknown whether
There’s a chance that
It’s possible that
It’s plausible that
It’s credible that
It’s doubtful that
It’s unlikely that
There’s a remote possibility that
It’s far-fetched that
It’s impossible that
The probability is zero that

Examples

It’s certain that 2+2=4.
It’s beyond a reasonable doubt that Russia interfered with the 2016 election in support of Trump.
In all likelihood Oswald acted alone in assassinating President Kennedy.
Echinacea probably does not prevent colds.
It’s reasonable to believe that Jefferson fathered at least some of Sally Hemings’ children.
The Tunguska Event of 1908 was most likely caused by a meteor.
The idea the CIA assassinated Kennedy is farfetched.
The nature of dark matter is an open question.
It’s unlikely the tumor is malignant.
His statistics are questionable.
Chances are he died instantly.
It’s doubtful the legislation will pass.
It’s impossible that Frederick Douglass founded the NAACP.

Epistemic Status is Based on Evidence

Epistemic status is based on, and relative to, evidence.
A standard deck of 52 cards is shuffled and placed face-down. The probability the top card is an ace is 4/52, based only on this information. But for someone who’s peeked at the top card, it’s either certain or impossible that the top card is an ace.
That is:
- The probability that the top card is an ace is 4/52, based only on the fact that the deck is a well-shuffled standard deck of 52 cards.
- It’s certain that the top card is an ace, based on the the peeker’s evidence that he saw that the top card was an ace.
- It’s impossible that the top card is an ace, based on the the peeker’s evidence that he saw that the top card was not an ace.

The Basic Epistemic Operators

Certain, Impossible, and Toss-up

Certainty and impossibility are the upper and lower bounds of epistemic operators, corresponding to probabilities one and zero.
A proposition is certain if its falsehood is impossible, if there’s no chance of it being false.
A proposition is impossible if it’s certainly false, if there’s no chance of it being true. As you read this sentence, for example, it’s certain you have a functioning brain and impossible you don’t.
Midway between the extremes is toss-up, where the probability of being true equals the probability of being false. Flip a coin and it’s a toss-up whether it lands heads.
Certainty logically entails truth, as GE Moore noted in “Certainty.”
Impossibility entails falsehood.
The epistemic operators between entail neither.
It is certain that is logically equivalent to:
- it is known that
- it is known for certain that
- it is an established fact that
Two Senses of Impossible
- Incapability Sense
  - It’s impossible to trisect an angle using only a straightedge and compass
  - It’s impossible for a human being to run 100 miles an hour.
  - It’s impossible that an object with mass be accelerated beyond the speed of light.
  - It’s impossible for Smith to rob a bank and be in jail at the time.
- Epistemic Sense
  - It’s impossible that Amy is in Alaska, since she’s right next to me here in Texas.
  - It’s Impossible that Smith robbed the bank, since he was in jail at the time.

Preponderance of Evidence and Very Likely

Certainty, impossibility and toss-up are points on the probability continuum. By contrast, preponderance of evidence and very likely are ranges of probabilities, line-segments rather than points.
A preponderance of evidence exists for a proposition if it’s more probable than not. There’s a preponderance of evidence, for example, that New Year’s resolutions to lose weight don’t survive past February. Preponderance of evidence is the standard of evidence in civil actions, where a plaintiff sues a defendant.
A proposition is very likely if its probability is significantly greater than 0.5, if it’s in all likelihood true. Flip a coin three times and it’s very likely it lands heads at least once.

Beyond a Reasonable Doubt

Beyond a reasonable doubt is the standard of evidence for criminal trials in the United States and Great Britain. It’s also the standard used in everyday affairs.
In the law reasonable doubt is described as the kind of doubt that would make a reasonable person hesitate to act in the most important of his affairs.
law.cornell.edu/wex/beyond_a_reasonable_doubt
- In a criminal case, the prosecution bears the burden of proving that the defendant is guilty beyond all reasonable doubt. This means that the prosecution must convince the jury that there is no other reasonable explanation that can come from the evidence presented at trial. In other words, the jury must be virtually certain of the defendant’s guilt in order to render a guilty verdict. This standard of proof is much higher than the civil standard, called “preponderance of the evidence,” which only requires a certainty greater than 50 percent.

Washington Post Fact Checker
- We will adopt a “reasonable person” standard for reaching conclusions. We do not demand 100 percent proof.
Beyond a reasonable doubt belongs to a family of terms expressing epistemic status.
- View A Matter of Degree
- Beyond a reasonable doubt is weaker than certain: everything certain is beyond a reasonable doubt, but not the reverse. As I leave work my belief my car is where I parked it is beyond a reasonable doubt, given that locked cars generally stay put. But it’s not certain, since even locked cars are stolen or towed.
- Beyond a reasonable doubt is stronger than very likely: every belief beyond a reasonable doubt is very likely, but not vice versa. It’s very likely you won’t roll two sixes, but not beyond a reasonable doubt.
Beyond a reasonable doubt seems synonymous with certain for all intents and purposes.
Reasonable doubt exists if there’s credible evidence the statement is false, if there’s a plausible, competing hypothesis.
A statement is either:
- true beyond a reasonable doubt, or
- false beyond a reasonable doubt, or
- an open question.
A person who states something as fact assumes the burden of proof, the burden of proving the statement beyond a reasonable doubt.

True and False are Not Epistemic Operators

It is true that and it is false that are not epistemic operators
- The epistemic status of a proposition depends on evidence.
- Truth and falsehood depend on reality.
Consider the hypothesis that Aunt Flo’s tumor is malignant. Its truth depends on whether the tumor is in fact malignant. Its epistemic status, by contrast, is a function of the evidence: symptoms, family history, blood tests, scans, biopsies.
Truth and falsehood depend on what’s real; epistemic operators depend on the evidence.

Epistemic Operators in the Law, Intelligence Assessment, and Philosophy

The Law

Beyond a reasonable doubt: This is the standard of evidence in a criminal trial. The prosecution has the burden of proof, i.e. to prove the defendant guilty beyond a reasonable doubt; otherwise the defendant is found innocent. The law doesn’t define the phrase.
- cornell.edu/wex/beyond_a_reasonable_doubt
Clear and convincing evidence: Weaker than beyond a reasonable doubt, this is the standard for removing a child from a home or terminating parental rights. The operator is sometimes said to mean substantially more probable than not.
- cornell.edu/wex/clear_and_convincing_evidence
Preponderance of evidence: This is the standard used in civil cases, where a plaintiff sues a defendant. The operator means more probable than not.
- cornell.edu/wex/preponderance_of_the_evidence
Probable cause: This is the standard used by police to arrest or search a person without a warrant.
- cornell.edu/wex/probable_cause
Reasonable suspicion: A police officer is justified in stopping and briefly detaining a person if there’s a reasonable suspicion of involvement in a crime
- cornell.edu/wex/reasonable_suspicion

Intelligence Assessment

National Intelligence Estimates are summaries of the intelligence assessments of sixteen agencies of the United States Government, including the CIA, the Department of Defense, and the Department of Justice.
Intelligence assessments have the form:
- We judge (assess) with high (moderate, low) confidence that X
- We judge (assess) with high (moderate, low) confidence that it is likely (unlikely, very likely, very unlikely, almost certainly, remotely possible, an even chance) that X
For example:
- We assess with low confidence that Iran probably has imported at least some weapons-usable fissile material, but still judge with moderate-to-high confidence it has not obtained enough for a nuclear weapon.
- We judge with moderate confidence that the earliest possible date Iran would be technically capable of producing enough HEU for a weapon is late 2009, but that this is very unlikely.
From a National Intelligence Estimate:

dni.gov/files/documents/Newsroom/Reports%20and%20Pubs/20071203_release.pdf

Philosophy

Theory of Knowledge, 3rd Edition, Roderick Chisholm

Basic Locution:
- Doxastic attitude A is at least as justified for S as doxastic attitude B, where doxastic attitudes are:
  - believing P
  - disbelieving P (believing ~P)
  - withholding P (neither believing nor disbelieving P)
Definitions
- Doxastic attitude A is more justified for S than doxastic B =df it is false that B is at least as justified for S as is A
- P is certain for S =df for every Q, believing P is more justified for S than withholding Q, and believing P is at least as justified for S as is believing Q
- P is obvious for S =df for every Q, S is more justified in believing P than in withholding Q
- P is evident for S =df for every proposition Q, believing P is at least as justified for S as withholding Q
- P is beyond reasonable doubt for S =df S is more justified in believing P than in withholding P
- P is epistemically in the clear for S =df S is not more justified in withholding P than in believing P
- P is probable for D =df S is more justified in believing P than in believing ~P
- P is counterbalanced for S =df S is no more justified in believing P than believing ~P and S is no more justified in believing ~P than believing P
Axioms
- A1: If A is more justified than B for S, then B is not more justified than A for S
- A2: If A is more justified than B for S and if B is more justified than C for S, then If A is more justified than C for S
- A3: If P&Q is beyond reasonable doubt for S, then believing P&Q is more justified for S than believing P and withholding Q.
- A4: If anything is probable for S, then something is certain for S.
- A5: If S knows that P, then, if S believes that he knows that P, S knows that he knows that P

Addenda

Knowledge

Two millennia ago Plato proved that knowledge is not the same thing true belief.
- “Suppose a jury has been justly persuaded of some matter which only an eyewitness could know, and which cannot otherwise be known; suppose they come to their decision based on hearsay, forming a true belief: then they have decided the case without knowledge.”
  - Plato’s Theaetetus
Thus the jurors form a true belief about some matter — let’s say that the defendant stole the jewels — but they don’t know that the defendant is guilty because their belief is based only on hearsay.
So, Plato concluded, knowledge is more than just true belief. But what more is it?
A plausible suggestion is that knowledge is true belief plus certainty.
That is, a person knows that P if and only if:
- it’s true that P
- the person believes that P
- it is certain that P, based on the person’s evidence.
Thus, to say that a witness knows that the defendant stole the jewels is to say, not only that the witness correctly believes that the defendant is guilty, but also that the witness has evidence that makes it certain the defendant is guilty.
View Analysis of Knowledge.

Prove, Show, Establish, Disprove, Refute

Arguments or evidence establish, show, or prove a proposition if they make it true beyond a reasonable doubt.
From Merriam-Webster Unabridged:
- Prove
  - 3a: to establish the truth of (as by argument or evidence) : demonstrate, show
    - unabridged.merriam-webster.com/unabridged/prove
- Show
  - 15a: to demonstrate or establish by argument or reasoning : prove
    - unabridged.merriam-webster.com/unabridged/show
- Establish
  - 6b: to prove or make acceptable beyond a reasonable doubt
    - unabridged.merriam-webster.com/unabridged/establish
Arguments or evidence disprove or refute a proposition if they make it false beyond a reasonable doubt.

Principle of Indifference and Indeterminate Probabilities

Easy Problem

An urn has 100 balls, 50 red, 50 white. You randomly select a ball. It’s clear that the probability the ball is red is 0.5, other things being equal. Or, in other words:
- The odds are even the ball is red.
- There’s a 50-50 chance the ball is red.
- It’s a tossup whether the ball is red.

Hard Problem

An urn has 100 balls, each red or white. But it’s unknown how many are red and how many are white. You randomly select a ball. What’s the probability the ball is red?

One Answer
- The probability the ball is red is 0.5.
  - The argument uses the Principle of Indifference:
    - Competing hypotheses are equally likely if there’s no evidence that one is more likely than another.
  - Since there’s no evidence that makes it more likely that the ball is one color rather than the other, red and white are equally likely.
- But the argument fails:
  - If it’s reasonable to believe there’s a 50-50 chance the ball is red, it’s reasonable to believe that at least one ball is red. The latter is false since it’s unknown how many are red and how many are white. It’s therefore not reasonable to believe the probability of the ball’s being red is 1/2.

A Better Answer
- The probability the ball is red is unknown and indeterminate.
  - The probability is unknown since the probability depends on the number of red and white balls in the urn, which is unknown.
  - The probability is indeterminate since there’s no way of determining the probability based on the evidence we have, which does not include evidence regarding the number of red and white balls.

Sentential Operators

A sentential operator is a word or phrase that generates an independent clause when combined other independent clauses.