4 ms·

Inconsistency implies falsity

by jrlocke 11y ago

Karunamon 11y ago
Humans are not logically consistent animals.
- imaginenore 11y ago
  Some of us try to be.
  - loco5niner 11y ago
    Not one succeeds.
  - AlexandrB 11y ago
    You'd have to be omniscient first. Otherwise you may always be inconsistent when judged against context you're not aware of.
njharman 11y ago
Nope, it doesn't. Things can be inconsistent and/or false there is no inherent correlation.
- JadeNB 11y ago
  But a collection of true statements cannot be inconsistent, so inconsistency does imply falsity. (Perhaps you are arguing against the converse, that falsity implies inconsistency, or against the claim that inconsistency and falsity are equivalent?)
  - njharman 11y ago
    Less arguing and more curious about your logic. Maybe I don't understand definition of inconsistent you're using. I'm using informal, layman's definition. To me True and Inconsistent must have nuances of meaning or there wouldn't be two words. Here are two true statements that seem inconsistent to me. "Norm said 2+2=4" "Norm said 2+2=5" It is true Norm said both those things. Norm's ability to do arithmetic (or possibly tell the truth, or etc) is not consistent.
    - JadeNB 11y ago
      The statements "2 + 2 = 4" and "2 + 2 = 5" are not consistent (unless 4 = 5), which is OK; the second one is not true (unless 4 = 5). The statements "Norm said '2 + 2 = 4'" and "Norm said '2 + 2 = 5'" are consistent. (A sufficient but not necessary definition of consistency of a collection of statements is that there is a model—let's leave the meaning of that vague—in which they hold. If we are sufficiently vague about what 'model' means, then we may take the real world to be one.) As you say, together (if true, and if taken to be true expressions of Norm's beliefs) these consistent statements imply the inconsistency of Norm's beliefs. That is a good thing; it is useful to be able to judge the consistency of statements about inconsistency, just as it is to be able to judge the truth of statements about falsity. (For example, I think that you will agree that the fact that "2 + 2 = 5" is false does not make "Norm said '2 + 2 = 5'" false.) To me, the nuanced distinction between truth and consistency comes in the facts that (1) the latter is weaker than the former ("Norm said '2 + 2 = 4'" and "Norm can do basic arithmetic" are consistent, even if they are not both true), and (2) that the latter is of interest mainly about collections of statements; the truth of a group of (non-mutually referential) statements is determined by the truth of each individual statement, but the same is not true for consistency.
JadeNB 11y ago
I think that this is Karunamon (https://news.ycombinator.com/item?id=9534654)'s https://news.ycombinator.com/item?id=9534654)'s point: an inconsistent collection of statements contains at least one false statement; but a collection of statements, all of which are false, is guaranteed to be consistent, so consistency is no guarantor of truth (and indeed may obtain with more falsehood in place than inconsistency).
- dragonwriter 11y ago
  > a collection of statements, all of which are false, is guaranteed to be consistent "Hillary Clinton is exactly 8 years old", "Hillary Clinton is exactly 9 years old". A collection of statements, all of which are false, is not guaranteed to be consistent.
  - JadeNB 11y ago
    > A collection of statements, all of which are false, is not guaranteed to be consistent. Hmm. You are right, to be sure. I guess I was carelessly generalising from the fact that anything follows from a false statement.
    - dragonwriter 11y ago
      I think you are misremembering the rule that any statement of the form if X then Y is true if X is false as "anything follows from a false statement" which isn't correct.
      - JadeNB 11y ago
        > any statement of the form if X then Y is true if X is false This is indeed precisely what I meant by "anything (Y) follows from a false statement (X)"—although maybe "everything follows from a false statement" sounds better. This is precisely why an inconsistent logic can prove everything. This principle is sometimes also called ex falso quodlibet (https://en.wikipedia.org/wiki/Ex_falso_quodlibet https://en.wikipedia.org/wiki/Ex_falso_quodlibet). Of course, giving it another name doesn't make it any more (or less) true, but it may make it sound more familiar and less dodgy! I know I muffed up the first statement pretty badly, which doesn't inspire confidence; but, as a mathematician, I'm pretty sure about this one. :-)
dragonwriter 11y ago
Laws are not claims, so "inconsistency implies falsity" is irrelevant in the context of law, however accurate it might be in terms of the truth values of a collection of claims. (And, anyhow, what actually is being discussed isn't actual consistency or inconsistency in the law, but the ability to construct a consistent set of principles supporting the law that is more general than the specific laws that the principles support. The issue isn't that the laws at issue are actually inconsistent, is that the author feels that the specific laws should be justified by more general principles than the laws themselves, and that (for the laws in question) those principles should address only the degree of danger of the activity, and the more general principles the author infers from each of the laws in question, based on the premise that the justifying principle must consider only safety, are when taken together, are inconsistent. This isn't really about consistency, its about whether the actual content of the law fits a particular preference of the author which involves more than just logical consistency.)

Inconsistency implies falsity

by jrlocke 11y ago

Inconsistency implies falsity

Karunamon 11y ago

Humans are not logically consistent animals.

imaginenore 11y ago
Some of us try to be.
- loco5niner 11y ago
  Not one succeeds.
- AlexandrB 11y ago
  You'd have to be omniscient first. Otherwise you may always be inconsistent when judged against context you're not aware of.

njharman 11y ago

Nope, it doesn't. Things can be inconsistent and/or false there is no inherent correlation.

JadeNB 11y ago
But a collection of true statements cannot be inconsistent, so inconsistency does imply falsity. (Perhaps you are arguing against the converse, that falsity implies inconsistency, or against the claim that inconsistency and falsity are equivalent?)
- njharman 11y ago
  Less arguing and more curious about your logic. Maybe I don't understand definition of inconsistent you're using. I'm using informal, layman's definition. To me True and Inconsistent must have nuances of meaning or there wouldn't be two words. Here are two true statements that seem inconsistent to me. "Norm said 2+2=4" "Norm said 2+2=5" It is true Norm said both those things. Norm's ability to do arithmetic (or possibly tell the truth, or etc) is not consistent.
  - JadeNB 11y ago
    The statements "2 + 2 = 4" and "2 + 2 = 5" are not consistent (unless 4 = 5), which is OK; the second one is not true (unless 4 = 5). The statements "Norm said '2 + 2 = 4'" and "Norm said '2 + 2 = 5'" are consistent. (A sufficient but not necessary definition of consistency of a collection of statements is that there is a model—let's leave the meaning of that vague—in which they hold. If we are sufficiently vague about what 'model' means, then we may take the real world to be one.) As you say, together (if true, and if taken to be true expressions of Norm's beliefs) these consistent statements imply the inconsistency of Norm's beliefs. That is a good thing; it is useful to be able to judge the consistency of statements about inconsistency, just as it is to be able to judge the truth of statements about falsity. (For example, I think that you will agree that the fact that "2 + 2 = 5" is false does not make "Norm said '2 + 2 = 5'" false.) To me, the nuanced distinction between truth and consistency comes in the facts that (1) the latter is weaker than the former ("Norm said '2 + 2 = 4'" and "Norm can do basic arithmetic" are consistent, even if they are not both true), and (2) that the latter is of interest mainly about collections of statements; the truth of a group of (non-mutually referential) statements is determined by the truth of each individual statement, but the same is not true for consistency.

JadeNB 11y ago

I think that this is Karunamon (https://news.ycombinator.com/item?id=9534654)'s https://news.ycombinator.com/item?id=9534654)'s point: an inconsistent collection of statements contains at least one false statement; but a collection of statements, all of which are false, is guaranteed to be consistent, so consistency is no guarantor of truth (and indeed may obtain with more falsehood in place than inconsistency).

dragonwriter 11y ago
> a collection of statements, all of which are false, is guaranteed to be consistent "Hillary Clinton is exactly 8 years old", "Hillary Clinton is exactly 9 years old". A collection of statements, all of which are false, is not guaranteed to be consistent.
- JadeNB 11y ago
  > A collection of statements, all of which are false, is not guaranteed to be consistent. Hmm. You are right, to be sure. I guess I was carelessly generalising from the fact that anything follows from a false statement.
  - dragonwriter 11y ago
    I think you are misremembering the rule that any statement of the form if X then Y is true if X is false as "anything follows from a false statement" which isn't correct.
    - JadeNB 11y ago
      > any statement of the form if X then Y is true if X is false This is indeed precisely what I meant by "anything (Y) follows from a false statement (X)"—although maybe "everything follows from a false statement" sounds better. This is precisely why an inconsistent logic can prove everything. This principle is sometimes also called ex falso quodlibet (https://en.wikipedia.org/wiki/Ex_falso_quodlibet https://en.wikipedia.org/wiki/Ex_falso_quodlibet). Of course, giving it another name doesn't make it any more (or less) true, but it may make it sound more familiar and less dodgy! I know I muffed up the first statement pretty badly, which doesn't inspire confidence; but, as a mathematician, I'm pretty sure about this one. :-)

dragonwriter 11y ago

Laws are not claims, so "inconsistency implies falsity" is irrelevant in the context of law, however accurate it might be in terms of the truth values of a collection of claims. (And, anyhow, what actually is being discussed isn't actual consistency or inconsistency in the law, but the ability to construct a consistent set of principles supporting the law that is more general than the specific laws that the principles support. The issue isn't that the laws at issue are actually inconsistent, is that the author feels that the specific laws should be justified by more general principles than the laws themselves, and that (for the laws in question) those principles should address only the degree of danger of the activity, and the more general principles the author infers from each of the laws in question, based on the premise that the justifying principle must consider only safety, are when taken together, are inconsistent. This isn't really about consistency, its about whether the actual content of the law fits a particular preference of the author which involves more than just logical consistency.)