Our most basic axioms

Author: secularmerlin

Posts

Total: 1,302
#1261
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
It's only "true" in the context of the hypothetical.
Ergo “under those circumstances”.
Valid but NOT Sound.

Valid (only true conditionally or hypothetically) but NOT Sound (demonstrably true and or logically-necessary).

A Valid statement MIGHT BE "true", but it is NOT "demonstrably true and or logically-necessary" unless it is both Valid and Sound.
Topic's author
#1262
secularmerlin
secularmerlin's avatar
Debates: 0
Posts: 7,093
3
3
3
secularmerlin's avatar
secularmerlin
3
3
3
-->
@3RU7AL
A Valid statement MIGHT BE "true", but it is NOT "demonstrably true and or logically-necessary" unless it is both Valid and Sound.
Well stated 
#1263
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@3RU7AL
unless it is both Valid and Sound.
Which is always.
#1264
zedvictor4
zedvictor4's avatar
Debates: 22
Posts: 11,354
3
3
6
zedvictor4's avatar
zedvictor4
3
3
6
-->
@Tarik
Typically, you paid attention to the bits that suited your argument and ignored the bits that didn't.


In short:
Sound is sound but not necessarily sound.

And valid is not necessarily synonymous with sound.


Such is the eccentricity and variability of the English language.
#1265
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@zedvictor4
Typically, you paid attention to the bits that suited your argument and ignored the bits that didn't.
Did I ignore this too?


Check synonyms under the second definition for adjectives.



#1266
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
Valid (only "true" conditionally or hypothetically) but NOT Sound (empirically demonstrable and or logically-necessary).
#1267
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@3RU7AL
I read that the first time you posted it, you reposting it doesn’t make it valid/sound.
#1268
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
I read that the first time you posted it, you reposting it doesn’t make it valid/sound.
Are all dogs blue?
Topic's author
#1269
secularmerlin
secularmerlin's avatar
Debates: 0
Posts: 7,093
3
3
3
secularmerlin's avatar
secularmerlin
3
3
3
-->
@3RU7AL
Are all dogs blue?

Imperical (and adorable) evidence that ALL dogs are not blue.
#1270
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@3RU7AL
No and that’s neither valid or sound.
#1271
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
No and that’s neither valid or sound.
Do you believe a logical statement can be valid without being true?
#1272
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@3RU7AL
What do you think? Absolutely not
#1273
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
(IFF) all dogs are blue

This premise is provably false (not sound).

A logically sound statement requires every premise be provably true.
#1274
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@3RU7AL
Theirs no certainty in regards to what ifs so proof isn’t necessary.

#1275
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
Theirs no certainty in regards to what ifs so proof isn’t necessary.
Every AXIOM is an implicit conditional statement.

Every PREMISE is an implicit conditional statement.

Every VALID logical statement is comprised of PREMISES.

Every VALID logical statement is comprised of AXIOMS.

SOME AXIOMS ARE LOGICALLY NECESSARY.

SOME AXIOMS ARE NOT LOGICALLY NECESSARY.

SOME PREMISES ARE LOGICALLY NECESSARY.

SOME PREMISES ARE NOT LOGICALLY NECESSARY.
#1276
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@3RU7AL
SOME AXIOMS ARE NOT LOGICALLY NECESSARY.
Once you add “IF” to the equation even the impossible is possible making anything logically necessary under that “IF” circumstance.
#1277
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
SOME AXIOMS ARE NOT LOGICALLY NECESSARY.
Once you add “IF” to the equation even the impossible is possible making anything logically necessary under that “IF” circumstance.
HYPOTHETICAL LOGICAL-NECESSITY and ACTUAL LOGICAL-NECESSITY are NOT the same.

A HYPOTHETICAL LOGICAL-NECESSITY IS VALID BUT NOT SOUND.

AN ACTUAL LOGICAL-NECESSITY IS BOTH VALID AND SOUND.
#1278
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@3RU7AL
HYPOTHETICAL LOGICAL-NECESSITY and ACTUALLOGICAL-NECESSITY are NOT the same.
I didn’t say they were, if your arguing that the term valid is only limited to hypotheticals then that’s not true, it applies to EVERYTHING that’s true, your never going to find in any dictionary valid being defined by hypotheticals.
#1279
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
if your arguing that the term valid is only limited to hypotheticals then that’s not true,
i agree.

All sound statements are necessarily valid.

HOWEVER.

Not all valid statements are necessarily sound.
#1280
FLRW
FLRW's avatar
Debates: 0
Posts: 5,178
3
4
8
FLRW's avatar
FLRW
3
4
8
-->
@3RU7AL
Yes, not all valid statements are necessarily sound.

From Validity and Soundness - rintintin.colorado.edu:

So, an argument is valid if it has the proper form. An argument can have the right form, but be totally false, however. For example:
1. Daffy Duck is a duck.
2. All ducks are mammals.
3. Therefore, Daffy Duck is a mammal.
The argument just given is valid. But, premise 2 as well as the conclusion are both false. Notice however that, IF the premises WERE true, then the conclusion would also have to be true. This is all that is required for validity. A valid argument need not have true premises or a true conclusion. On the other hand, a sound argument DOES need to have true premises and a true conclusion:

#1281
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@3RU7AL
i agree
Then why’d you say

Valid (only "true" conditionally or hypothetically)
#1282
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@FLRW
Yes, not all valid statements are necessarily sound.
Not according to the dictionary which defines valid as (of an argument or point) having a SOUND basis in logic or fact; reasonable or cogent.

#1283
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
Valid [but not sound] = (only "true" conditionally or hypothetically)
It is possible for an argument to be BOTH (VALID) (AND) (SOUND).

It is possible for an argument to be ONLY (VALID) (BUT NOT) (SOUND).
#1284
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@3RU7AL
Not according to the dictionary which defines valid as (of an argument or point) having a SOUND basis in logic or fact; reasonable or cogent.

#1285
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
You've confused a colloquial (GENERAL) dictionary with a jargon term specific to the discussion of LOGIC ITSELF.

#1286
FLRW
FLRW's avatar
Debates: 0
Posts: 5,178
3
4
8
FLRW's avatar
FLRW
3
4
8
-->
@Tarik

Validity (logic)
From Wikipedia, the free encyclopedia

In logic, more precisely in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed by means of sentences called well-formed formulas (also called wffs or simply formulas). The validity of an argument—its being valid—can be tested, proved or disproved, and depends on its logical form.
In logic, an argument is a set of statements expressing the premises (whatever consists of empirical evidences and axiomatic truths) and an evidence-based conclusion.
An argument is valid if and only if it would be contradictory for the conclusion to be false if all of the premises are true. Validity doesn't require the truth of the premises, instead it merely necessitates that conclusion follows from the formers without violating the correctness of the logical form. If also the premises of a valid argument are proven true, this is said to be sound.


#1287
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@3RU7AL
If that’s the case then why was I able to find it in a general dictionary?

#1288
Tarik
Tarik's avatar
Debates: 1
Posts: 2,397
3
3
5
Tarik's avatar
Tarik
3
3
5
-->
@FLRW
Doesn’t matter my credible definition still says otherwise.
#1289
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
Not according to the dictionary which defines valid as (of an argument or point) having a SOUND basis in logic or fact; reasonable or cogent.
USE THAT SAME DICTIONARY TO COMPARE AND CONTRAST THE DEFINITIONS OF "VALID" AND "SOUND".
#1290
3RU7AL
3RU7AL's avatar
Debates: 3
Posts: 13,684
3
4
9
3RU7AL's avatar
3RU7AL
3
4
9
-->
@Tarik
Doesn’t matter my credible definition still says otherwise.
Please use your magical dictionary to help you understand the full meaning of the term, "JARGON".