Question

What time is it? proposition or not

Answer 1

a proposition is a statement that is capable of being true or false.
proposition:

Abraham lincoln was president of USA.

Answer 2

this is either true or false.

Answer 3

"what time is it" <----does it make sense to ask if this statement is true or false?

Answer 4

ok imagine this scenario:
Imagine there is an all knowing computer that knows everything, but the computer can only answer true or false. thats the only thing this computer can do, answer true or false.

so a question that an all knowing computer can answer using true or false, is a proposition.

Answer 5

input :
Abraham lincoln was president of USA.

computer output: True

input: 3 is a prime number

computer output : True

input: 5 is an even number

computer output: False

input: What is your favorite color?

computer output: ... (no answer)

Answer 6

so any statement for which an all knowing computer is capable of saying true or false, that is a proposition

Answer 7

input: What time is it?

computer output: ...

remember the computer can only answer true or false, thats the limitation of this computer

Answer 8

if this all knowing computer can answer true or false, then your statement is a 'proposition'. if the computer just waits and says nothing, then its not a proposition

Answer 9

its gud, not a proposition

Answer 10

Is this question "What time is it?" a proposition or not?

Answer 11

right, thats the question

Answer 12

this computer can only answer 'true' or 'false'

Answer 13

this has implications for computer science, so its not a trivial thing

Answer 14

this is actually a 'meta' question, asking what questions are valid to be asked within a logical system

Answer 15

heres a more challenging one

input : This statement is false.

try to figure out the computer output

Answer 16

input: The Riemann hypothesis is true:

output : (to be determined)

this is one of the famous open problems in mathematics.

Answer 17

thats really a challenging question to think about, how about this one :

input : This statement is true.

Answer 18

since the statement has no 'content' , i dont think the computer would say anything

Answer 19

it should attempt to evaluate the truth value since it looks more like a proposition right ?

Answer 20

or it could be true, since the statement is about the statement

Answer 21

self referential statements are tricky

Answer 22

Well, honestly, I don't know. I'd say it it's not a propositional in propositional logic because it cannot have a truth value of 0 or 1.

Furthermore, it's a question and not a statement, so it's not a proposition in that greater linguistic sense. But honestly without more context, I would be reluctant to answer that question

Answer 23

proposition in propositional logic*

Answer 24

yeah

if "this statement is true" is true ===> then the statement evaluates to true
if "this statement is true" is falst ===> then the statement evaluates to false

we have a biconditional right ?

Answer 25

true true
false false

Answer 26

In propositional logic, all propositions under a given interpretation has a truth value of 0 or 1. And you can't assign 0 or 1 to the question What time is it?

Answer 27

At least, when we take the conventional understanding of time as being on a continuum of values

Answer 28

right, `what time is it?` is not a proposition based on my past 1 hour knowledge on the subject

Answer 29

lol, ''1 hour''

Answer 30

Oh biconditional just means equivalence... so that's not a biconditional
biconditional is p if and only if q
so you have the implication in both directions p implies q and q implies p

Answer 31

But analyzing what you said ...

Answer 32

Just think of it this way
P = "This statement is true"
P is the propositional atom
v(P) = 1. Or v(P) = 0.

where v is the interpretation function, the interpretation function assigns truth values to propositions in the propositional logic

Answer 33

this is a meta-logic question though

Answer 34

ganeshie, did you feel it was true?

Answer 35

If you cannot define the interpretation for some supposed proposition P, then it's safe to say that this P is not a proposition because by definition all propositions P can be defined by an interpretation function.

I mean this is to be contrasted with the situation where the interpretation of the proposition is free to be whatever values possible say to meet satisfiability
This is a meta-logical statement which says, there's no way to actually define an interpretation for this supposed proposition P

Answer 36

But also I don't want to confuse syntax with semantics though. Just so its clear. The interpretation function is the semantics of the logic. And the propositions P and the well formed formulas are the syntax.

But whatever the syntax, in a logic, you should be able to define the semantics, if you can't, the syntax must not be in the logic

Answer 37

so we would have to exclude these statements ?

Answer 38

... there is an issue of how to write down the English sentence "What time is it?" in propositional logic. And depending on how you write it down. What interpretation to give it that would be linguistically meaningful

If you just regard the sentence as a collection of words without regard to their linguistic meaning, then you could give it an interpretation, but that would be meaningless
towards how we normally think of it.

Answer 39

Yes I think the point though is that ...
Truth in propositional logic is 0,1
And the statement "What time is it?" has a continuum of answers
so it doesn't really work in that logic

Answer 40

need at minimum something like fuzzy logic or better

Answer 41

There are temporal logics too ofc

Answer 42

ok

Answer 43

do you think the all knowing computer analogy works, to distinguish propositions from non-propositions. at least, for simple propositions

Answer 44

Hm. I'm not sure if you're referring to some specific argument which defines an "all knowing computer." However, in the sense that all of human intellect is computation, then, yes, since I am a human and I compute. I was able to decide if this statement was a proposition or not in the given logic.

If you're asking if a Turing machine could decide if this statement is a proposition or not.

Answer 45

I don't think so, and if you're asking about deciding in propositional logic the validity of a proposition, then that problem is semi-decidable

it's all the entscheidungs problem
fundamental to comp sci and computability theory

Answer 46

i was just looking for a way to distinguish between propositions and non propositions

Answer 47

semi-decidable meaning that there's always a finite proof that a propositional is valid, but there's not always a finite proof that a proposition is invalid, so you could potentially wait an infinite amount of time to decide if a proposition is valid or not

Answer 48

Ah, okay, well... i think this is the issue of syntax then

Answer 49

right

Answer 50

logicians make these ideas more precise than i presented it

Answer 51

So if you disconnect from english language statements all logics are based on formal languages and formal languages by definitions have an unambiguous way to decide if a formula is well-formed formula and hence part of the syntax - this is true

Answer 52

That's why they are formal languages and not say... english :)

Answer 53

yes, they do - that's their job

Answer 54

yes

Answer 55

So for propositional logic ...

Answer 56

Well, the point is just that you have a structurally recursive definition of how to construct formulas in the syntax. So it's easy to always decide if a formula is part of the syntax or not

Answer 57

So the set of WFF is the minimal set X. Where A, B, ... are atoms in X. Then if P is proposition in X, then so is ~P in X. (not P). And if P, Q are propositions in X, then P * Q is in X, where * is some logical connective.

Answer 58

the typical functionally complete set of logical connectives for propositional logic is {and, or, implies} Uhm and atoms are just propositions with no simpler substructure

Answer 59

ok

Answer 60

So if you get some mess
P V P ~~~~~~Q
or something it's always in principle easy to decide if this is in the set of WFF
I believe it's probably even linear time or better but don't quote me on that

Answer 61

so can you do logic without appealing to real world truth checking, syntactically

Answer 62

i mean, we can decide if a statement is a valid wff without finding a concrete example of it in the real world , by our recursive rules

Answer 63

yes, the logic is just a formal system with syntax, semantics, and certain rules of inference... the way you connect it to reality well that's up to you. Of course, we design different logics to model different real world things

Answer 64

the interesting thing is when you design a logic to model some real world phenomena, and then properties inside the logic inform you about properties about the world

that's the really cool thing

Answer 65

so its difficult to define a valid proposition in english, because of the ambiguities in language

Answer 66

i mean to define a 'wff' say in english, that would be pretty difficult

Answer 67

you would have to define grammatically correct sentences ,

Answer 68

yea

Answer 69

the grammar in english is not absolute and fixed

Answer 70

or unambiguous

Answer 71

right

Answer 72

and english has the ability to be self referential, which leads to problems

Answer 73

Self reference is a problem, but it's not limited to english. Logic can self reference

Answer 74

right

Answer 75

This is essential to the proof of Goedel's incompleteness theorems
so-called Goedel sentences

Answer 76

so if we could hypothetically define a grammatically correct english set of wffs, we would have to exclude questions, directives , exclamations.

Answer 77

but sometimes a question is actually a statement, such as
"Who is the boss here?", that can be a question or a statement, depending on the tone

Answer 78

if the boss is speaking, then its a statement

Answer 79

hm yes that sounds about right

Answer 80

english is gnarly :)

Answer 81

Although I am pondering the possibility of implementing a question in logic, I never really thought about it before... what that would mean in terms of semantics

Answer 82

I think the issue with questions it that
you would not implement a question like a statement in logic

A question is basically an algorithm. You'd identify the question as equivalent to its answer. And the answer is computed by an algorithm. So insofar as you can encode algorithms in logic, you can encode questions - Which is not a problem, you can reduce any computer language to a logic.

But it's not entirely satisfactory because, one is limited then to the results of computability theory... what is decidable, what isn't, etc

That's my take on it anyway

Answer 83

questions always not proposition :)