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2016-10-18
sufficient condition and necessary condition
Since 1998 I carry out independent research on the logic operators and in particular of "if then" and "if and only if then". Given my difficulty when a student, and the difficulties of my students to understand mainly the operator "if then" and the concepts of sufficient condition and necessary condition in it implicit, and given my passion for logic, neuroscience and psychology, I spent over 20 years researching how these concepts arise in reality, and how our minds create their abstract models.
The study of the 4 cards test of Peter Wason (1966), is an excellent didactic example to explain the logical infrastructure of sufficient condition, and always use with my students. But in spite of literary research, not having met a specimen, equally excellent in explaining the necessary condition, I started a thorough study on the issue that has led me not only to devise a new specific test for the necessary condition, but also to find out what I think is a millenary gap in on the operators "if then", "if and only if then" and on the concepts of sufficient condition and necessary condition. I subjected for years to many professors, some researchers, professionals and students of different academic areas my observations and my tests, including last month one of the collaborators of the same Peter Wason. Not having met in years of serious studies and trials of the arguments, someone has proven wrong them, I wish I had the honor and pleasure to be able to present in more large-scale, the results of research and meet someone who is interested in deepening together the topics and publish an article. I availability, to present, talk and answer questions of those interested.
Thanks for the attention.

2016-10-26
sufficient condition and necessary condition
necessary = what must be concludedsufficient  = what will lead to the conclusion

so if a implies b,  b is necessary for a  and a is sufficient for b. 
alternative locution   a only if

2016-10-26
sufficient condition and necessary condition
Do you have a bio?

Also, search for on the Internet and read my works on logic, where I think I address a number of your concerns:

www.academia.edu

https://sites.google.com/site/yourmindshomepage/documents



Then, get back to me.

2016-10-31
sufficient condition and necessary condition
It is a pleasure to receive your comments.
 
 Good! As classical literature, Robert points out that the operator "if P then Q"
 is also expressed in the form "only if P then Q" and even "Q only if P" and "P implies Q",
 and there are also other.
 
 For the discussion and illustration of the results of my research with all of you, I would
 proceed for small steps, well-structured and clear, in order that the exchange of ideas and
 concepts either simple and consistent. And in case of doubt or differences of interpretation
 of a concept, this can be isolated, treated and resolved without creating confusion in the
 flow of our ideas.
 
 It's a good place to start the analysis of the etymology of the term "implication" with which
 the operator "if then" is named, defined and also represented in the "P implies Q" form.
 
 Implication: It is a derivation of the term to imply that originates from the Latin 'implicàre' and
                    from the Greek 'emplekèin'. It means fold together, wrap, envelop.
    
    
 The set-theoretic representation of the implication operation - always from classical literature -
 it's the following: 

    P implies Q  =  P included - equals Q

  -----------------
|   ------      Q  |
|  |        |         |
|  |  P    |         |
|  |        |         |
|   ------           |
 -----------------

The concept is expressed: the knowledge that an element belongs to P is sufficient to know that even belongs to Q and as is also evident from the graphical representation, Q is to "wrap", "include" P itself, and not the opposite as  'the expression "P implies Q" in its lingustic interpretation he says.    
    
In my intuition the concept of implication is instead perfectly adherent to the case of the definition and representation of the "necessary condition". We all know that - as in classical literature, but on this It will go later to propose some other considerations - when a proposition P is composed with the operator "If then" with a proposition Q (note that no longer use the concept of implication, do not say more when a proposition P implies a proposition Q), P is the sufficient condition  to Q and Q is the necessary condition to P, and revisits the previous graphical representation is correct to declare that  Q is a necessary condition to P as follows: "Q implies P". Because The concept is expressed: know that an element belongs  to Q is a necessary cause can also belong to P, being Q that "wraps", "contains" P coherently to the meaning to imply.

The notion of sufficient condition that is: to know that um element belongs to P is sufficient to know that even belongs to Q always keeping in mind the graphical representation, in my intuition wants to mean that by the knowledge that an element belongs to PI know for sure, that I can ensue, inferred with certainty that belongs Q. Here we proceed from P to Q with a concept of "derivation" so it seems to me correct that:

if P then Q:
                     P is a sufficient condition for Q = P derives Q
                     Q is a necessary condition P = Q implies P

NOTE: in the sense proposed by me now P derives Q would mean the P implies Q of classical literature and Q implies P would mean the concept of necessary condition of Q to P.

Please do your thoughts and comments so far, before it goes on, proposing new concepts on the sufficient condition boarding and other critical aspects that I have detected.

Thank you all for your attention.




2016-10-31
sufficient condition and necessary condition
You say:
Q is a necessary condition P = Q implies P

So, 

Being male is a necessary condition for being a bachelor

= being male implies being a bachelor ?

My wife is going to be surprised by this startling news.

2016-11-01
sufficient condition and necessary condition
Hello Karl, thank you for your intervention that gives me the opportunity to clarify for all of us
the above concepts.

Karl, the meaning of the term implication, referring to its etymology clearly indicates the
concept of wrapping, that when we say that something A implies a second thing B is emerging
- As clarified by the set-theoretic representation - that is A that wraps B.

 ------------------
|   ------       A  |
|  |        |          |
|  |  B   |          |
|  |        |          |
|   ------            |
 ------------------

So far I've managed to be clear?

Now Karl, let's consider an implication in the sense proposed by the classical literature:

P implies Q equivalent to that if P then Q

I make the following question: how associate P and Q, respectively, with A and B?

If you take any logic manual where it encounters the representation set-operator "if then",
You meet the following representation:

 ------------------
|   ------       Q  |
|  |        |          |
|  |  P   |          |
|  |        |          |
|   ------            |
 ------------------
Figure 1

Now I ask you - on the basis of the etymological definition of the term implication of what our eyes
and brains are observing in Figure 1 - between P and Q, who wraps whom?

It seems clear that P implies Q always according to the etymological definition would be to say that P is enveloping Q,
but this is not what our eyes and brains are watching, rather! is the opposite! Q is enveloping P.

Agree with me that in classical literature is used the term implications in an improper sense in respect of its significance?

What I have proposed is simply to properly use the term implication that is perfectly adherent
to the concept of necessary condition and not to the sufficient condition according to the use of classical literature.

So when I say A implies B, ie A wraps B, it seems consistent observing Figure 1 affirm Q implies P, it should be easy now to understand the following:

Being male is a necessary condition for being a bachelor

A: being male
B: a bachelor

according to the consistent use of the etymology of the term "implies" that perfectly defines the concept of a necessary condition

I write A implies B    =     Being male "implies" being a bachelor, where "implies" no longer assumes the significance of classical literature that confused your ideas and surprised your wife.

Karl, I managed to explain myself?

Any other questions, comments or clarification rest at your disposal to discuss it together.
Thanks again for everyone's attention.

Soon be back on the concept of derivation and many more who still want to offer and I hope to receive your comments.


2016-11-01
sufficient condition and necessary condition

Fabrizio,

There are still people who argue “awful” really means “awe-inspiring” and not “bad or unpleasant”, and I don’t see how your argument that implication is really set-theoretic wrapping is in principle any different than that.

Sure, the Venn diagram for “all bachelors are male” will show the set of bachelors included in (or “wrapped by”, to use your idiom) the set of males, but I fail to see any pragmatic value in switching to your preferred sense of “implies” as set-theoretic wrapping. But note that the concept of bachelor is a complex concept analysable as the concept of <unmarried&male & adult>, so the concept of <bachelor> includes (or “wraps”, if you like) the concept of <male>. And using that analysis, “X is male” is implied by (in the standard sense) and can be derived (in standard first-order logic) from “X is a bachelor”.

 So you can still have an etymologically inspired notion of wrapping if you want, albeit differently located; nothing else needs to change as regards necessary conditions, sufficient conditions, implication, etc. as ordinarily understood.

Cheers,

Karl


2016-11-02
sufficient condition and necessary condition
Set  inclusion  is  equivalent to Material Implication.  There are other forms of implication  which are stronger.  For example: entailment.  Also Strong Implication  which say  a +=> b (strongly implies) if and only if it is logically necessary that if a is true then b must be true.  
In material implication which is weak  a materially =>  b  if and only if it is not the case that a is true and b is false.  

entailment and strong implication indicate that the premise is linked to the conclusion by a logically necessary relation and  not just because it is not the happenstance that a true and b false is not the case. 

Bob Kolker

2016-11-02
sufficient condition and necessary condition

Hi Karl

thank you very much for your attention and for your precious incentives to develop the result of my research content.

I just started to show the first concepts that I want to propose, for this, at this moment are not yet clear theoretical positions that I am Proposing.

I propose this reflection: on the basis of the etymological interpretation of the term to imply I have called

the condition sufficient "if P then Q" as "P derives Q"    (just to remember clearly that here in classical literature using P implies Q)

and the necessary condition "Q if P" as "P implies Q"       (in the classical letetratura never met in no manual, a name)

I ask you the following: in classical literature I have not found a term that defines the necessary condition similar to that It happens with the sufficient condition which is precisely called implication. Certainly you have more knowledge than me and can help me,
what's his name?

But regardless of the name, I come to the pragmatic aspect.

I suggest to all of you the following reflection:

I studied in dozens of formal logic professional texts, historical and modern, and all have internet, although some sources are not fully trusted there is a lot of material on which to reflect, the minimum clear set of elementary logical operators that you find in any manual or tutorial of logic, I think you will all agree with me that it is as follows:

 Not P
 P And Q
 P Or Q
 Or P or Q
 If P then Q
 If And Only If P then Q

So far we all agree?

Someone notices something strange in the formulation of these operators?

Karl, I apologize for my idiom I was born in a country different from yours, and maybe I did not have all the resources and opportunities that you have had in life, to stand here and be able to converse with you I'm helping with an online translator. But for any questions or concerns, they are available to help clarify content that I think you will agree with me is the important thing here.

Thank you so much for your attention.


2016-11-02
sufficient condition and necessary condition

 

You say:

the condition sufficient "if P then Q" as "P derives Q"

I reply:

Why “derives”? Derivation in logic means that you can get from P to Q by using a set of logical rules of inference. Whether this is possible depends on the nature the propositions involved. 

You say: 

the minimum clear set of elementary logical operators that you find in any manual or tutorial of logic, I think you will all agree with me that it is as follows: …..

I reply:

Your list is redundant. There are 16 possible binary propositional connectives ( here is Wittgenstein’s list from the Tractatus:

http://readingwittgenstein.blogspot.com.au/search/label/Tractatus%20Logico-Philosophicus%205%20to%205.101 )

Basically you only need one truthfunction; “neither…nor…” can be used to define the other 15; “not both… and…” can also be so used.

You say:

and the necessary condition "Q if P" as "P implies Q"       (in the classical letetratura never met in no manual, a name) ... I ask you the following: in classical literature I have not found a term that defines the necessary condition similar to that It happens with the sufficient condition which is precisely called implication.

I reply:

The connective “only if” can serve as a term that names (in the sense of always introduces) a necessary condition if you want such a term.

But “P only if Q” just says that without Q you don’t have P, i.e. “if not-Q then not-P” which is logically equivalent to “if P then Q”.

You should also take Robert Kolker’s last remarks above into careful consideration. The truthfunctional “if…then…” of propositional logic only takes the truth values of the component propositions into account. The truthfunctional “if…then…” (aka the material conditional) is often misleadingly called “material implication” for no good reason other than that was what Russell called it. But ordinarily when we say “P implies Q”  there is some relationship (e.g. semantic, causal) between the content of P and the content of Q that goes beyond mere truth values.

I hope this helps.

K

 


2016-11-07
sufficient condition and necessary condition

Hello Karl, Bob,

your contributions are always very valuable to me.

The goal of my research and my proposals was born and has the purpose of
clarify and highlight the "scaffolding" that support the concepts that certainly after many studies
and individual insights become clear, but in classical literature contain in my opinion - and
especially for students who are boarding for the first time these concepts - many aspects
very little developed and very little light in books and manuals. And as you know, when a student
does not mean anything, first of all loses interest, and worse creating a gap that, in respect of
not only cultural and professional resources, but psychological, that logic provides, constitutes
a fundamental problem for the educational institutions. Not to mention that the result is we,
people by goods of social, political and economic systems that exploit our ignorance.

Karl
 
I used Derive precise basis of the concepts you mentioned, "Derivation in logic That means you can get from P to Q by using a set of logical rules of inference"
two propositions dates P, Q, NOT composed, and atomic, the operator "if, then" is an operation, an atomic rule to go from P to Q.
It is also consistent from the etymological point of view. This is why I propose:

for the sufficient condition "if P, then Q" the conceptual definition "P comes Q"

and

for the necessary condition "if Q then P" the conceptual definition "P implies Q"

What do you think?

The connective "only if" can serve as a term That names (in the sense of always Introduces) A Necessary condition if you want such a term.

I ask you to reflect on the fact that when you teach, you do need to definitional terms and etymologically consistent to expose the concepts.
I think even you, in front of the manuals and presential logic classes have made several efforts to interpret and understand
the matter.

When present the concepts of sufficient condition and necessary condition for the first time to the students, one speaks of the concept of
implication, a term that sums - as already said not etymologically coherent form - the operation and the operator that you are presenting.
You do not have the same opportunity for the necessary condition. These two aspects: the etymological inconsistency and lack of a term definitional
for the necessary condition, are aspects that over the years I found recurring in my classes of students, and in my experimental lessons,
integration proposed by me, responds positively in terms of clarity, completeness and consistency of concepts.

For this I am here to discuss with you all.

Now, according to your following observations:

"Entailment implication and strong That indicated the premise is linked to the conclusion by a logically Necessary relations ..."

"But" P only if Q "just says without Q That you do not have P, i.e." If Not-Q then not-P "Which is logically equivalent to" if P then Q ""

Abstract in the truth tables:

P | Q | Not P | Not Q | if P then Q | if Not Q then Not P | only if Q then P
-----------------------------------------------------------------------------------------------
V | V |  F       |   F      |     V            |        V                     |        V
V | F |  F       |   V      |     F            |        F                     |        F
F | V |  V       |   F      |     V            |        V                     |        V
F | F |  V       |   V      |     V            |        V                     |        V

Based on all this, I propose the following reflection:

You can propose your own teaching model, a clear explanation and without dark sides or conventions of logical form "if then"?

Please do not propose the classic examples that are encountered in the books and tutorials, and that you yourselves also know for your personal experience when you met them for the first time in your studies, you do not have clear ideas.

I ask you a justification of the results of the third column that comes from a real experience and
reproducible that helps a person to understand clearly and to fix in the mind the concepts it represents.

P | Q | if P then Q
------------------------
V | V |     V      
V | F |     F      
F | V |     V      
F | F |     V

I ask this because in my opinion, "if P then Q" and "only if Q then P" are equivalent is, but I think hide critical aspects
I want to discuss with you.

I await your answers.

Thank you so much for your attention and valuable contribution.


2016-11-07
sufficient condition and necessary condition

I apologize for the error here *
for the sufficient condition "if P, then Q" the conceptual definition "P comes Q"  * error

for the sufficient condition "if P, then Q" the conceptual definition "P derives Q" * correct



2016-11-07
sufficient condition and necessary condition
Regarding your remarks:
"  I ask you a justification of the results of the third column that comes from a real experience and
reproducible that helps a person to understand clearly and to fix in the mind the concepts it represents.

P | Q | if P then Q
------------------------ 
V | V |     V       
V | F |     F       
F | V |     V       
F | F |     V 

I ask this because in my opinion, "if P then Q" and "only if Q then P" are equivalent is, but I think hide critical aspects
I want to discuss with you."

OK, Fabrizio, here is an ordinary example:

• Suppose someone sincerely asserts S, namely ‘If the lit match is dropped into the pile of oily rags, the pile will ignite’.

• Consider the corresponding material conditional (MC): ‘the lit match is dropped… → the pile will ignite’.

• Clearly, if S were true, we would expect the pile to ignite when the lit match is dropped into it; so the 1st line of the truth table for MC is uncontroversial.

• Clearly, if we dropped the lit match and the pile did not ignite, we would regard S as false; so the 2nd line of the truth table for MC is uncontroversial.

• Some people balk at the 3rd and 4th lines.

• However, if we did not drop the lit match, but the pile ignited anyway due to spontaneous combustion, this would still be compatible with S’s being true. So line 3 is vindicated.

• Likewise, if we did not drop the lit match, and the pile remained unignited, this would also be compatible with S’s being true. So line 4 is vindicated.

Karl




2016-11-08
sufficient condition and necessary condition

Hi everybody

Karl, thanks for your quick response.

You have submitted an excellent example to make a detailed analysis:

I beg you to analyze well my observations and questions

.1 you think I could put myself with a box of matches, a notebook and a pencil in front of a pile of oily rags and do the following test?
  
   .light a match
   .dropping him well lit on the pile of rags
   .verify that the match has reached the pile of rags without shutting down
   .if the match will go off, discard this sequence and start again
   .if the match is it is not switched off in the fall, observe what is happening
    and make note on the notebook the statement S result (true or false)
   .repeat the process from start until finish all the matches
   .wait for a time the possible spontaneous combustion of rags (we are assuming that this
    can happen with a good frequency and that the phenomenon is observable in a finite time,
    and small enough to verify in the time dedicated to testing.
   .observe in the notebook the veracity of the operator's table "if then" being able to verify
    the four cases described by you.

Thank you all for your attention and participation
I'm learning a lot and I hope that a few crumbs of my experiences helpful to you.

Fabrizio

2016-11-08
sufficient condition and necessary condition

I apologize for my mistakes:

below the correct version of what I wanted to say in the previous post in these lines:

[INCORRECT VERSION: I have highlighted in bold incorrect points]
for the sufficient condition "if P, then Q" the conceptual definition "P comes Q"

and

for the necessary condition "if Q then P" the conceptual definition "P implies Q"

[CORRECT VERSION]
for the sufficient condition "if P then Q" the conceptual definition "P derives Q"

and

for the necessary condition "only if Q then P" the conceptual definition "Q implies P"

thank you and forgive me.



2016-11-08
sufficient condition and necessary condition
All bachelor is male but some male is bachelor
Then
bachelor implies male but male do not implies bachelor.

2016-11-08
sufficient condition and necessary condition
Fabrizio,

Here are a couple of sources that address some of the subtleties involved that may help you to work out your position.

http://philpapers.org/archive/GOMANA.pdf

http://plato.stanford.edu/entries/necessary-sufficient/

K

2016-11-09
sufficient condition and necessary condition


Hi Piotr

thank you so much for your attention and your contribution.

Likewise the example of the matches of Karl, I proceed to propose the following:

Given a group G, for example 100 people selected randomly for natural sex (therefore exclude all optional cases
which for our purposes may be confusing) and civil status.

Based on your propositions:
        S1 = if a person of the group G has a bachelor of civil status, then it is a male.
        S2 = only if a person of the group G is a male then He has bachelor civil status.

Correct me if I made errors of interpretation or formulation of the propositions.

I beg you to analyze well my observations and questions

.1 Piotr you think I could put myself with a notebook and a pencil in front of the group G and do the following test?
  
   .ask a person of the group G to show me his identity document (we are assuming that
    the identity document indicates sex and civil status of the person)
   .if not in possession of identity document, discard this sequence and start again
   .verify that in the identity document is indicated bachelor civil status
   .if bachelor is bachelor, observe the sex indicated in the document
    and make notes on the notebook the statement S1 result (true or false)
   .repeat the process from start until finish all the peolple of the group G
   .observe in the notebooks the veracity of the operator's table "if then" to check the four cases
    similar to those presented by Karl but in the context of the case you proposed.

Thank you all for your attention and participation

Fabrizio


2016-11-10
sufficient condition and necessary condition
Hi,

S1 is from smaller notion to larger notion in respect of range
S2 is from larger nation to smaller notion in respect of range

I make mistake bachelor implies that person is male

I based on notion. You based on institutional and biological facts. From biological fact that he is a male you deduce institutional fact that he is a bachelor, but not all male is bachelor and not all bachelor is male from definition, if we change definition of bachelor and male will be different. Relation from bachelor to male is relation based on range of notions, male include bachelor, and bachelor is contain in male.

In test you see that he is bachelor from identity document and sex from identity document, this test is algorithm

Operator "only if" is needful to deduce from larger to smaller. If we want to deduce from smaller to larger we have to first deduce from larger to smaller based on definition.

"only if a person of the group G is a male then He has bachelor civil status." We said about bachelor in civil sense not in sens used in army.

"Only if" is needfull to prescribe status of person in this test, because group G coul contain male, female and not only bachelor.

If we mix notions that female is male then range of notions will be too same but it will be different language.

In how sense operator could be false, false could be relationship included by operator, then non sequitur.


2016-11-10
sufficient condition and necessary condition
Hi,

One more.

Necessary condition in logic:

Ex, (x => y) => Ey
Ea, ((a=>b)=>Eb)=> Ea ^ Eb iff a=a ^ b=b

Sufficient condition based on operator "could" |If a then could b| Maybe in modal logic We could formalize that.

2016-11-10
sufficient condition and necessary condition
Hello to all,

Karl, I analyzed the two texts you have indicated, I met some of the elements that I found in my research,
but, in both, it is not present a satisfactory and conclusive interpretation, and remains confirmed - in my view -
the millenary gap on the operator "if then".

I do not know your beliefs about the results of these two texts or any other your interpretive theories.
In fact they remain open my questions regarding your examples with matches and bachelors. I think it would be very useful
give your opinions and continue along our discussion in order to be able to present my conclusions and receive
your criticisms which are always extremely constructive and help me to understand better.

Thank you all.

Fabrizio

2016-11-10
sufficient condition and necessary condition
The modal interpretation comes from the fact that there is a problem of interpretation at the base of the standard connective "if then".

Fabrizio




2016-11-11
sufficient condition and necessary condition

Hi everybody

I think that to avoid any question of interpretation, can I make for you my question in this way:

I beg you to analyze well my observations and questions

.1 Given the P and Q events of any kind you want, but that you have in fact absolutely certain that they can
   It is properly described by the logic form  S: if P then Q, I ask:
   you think I could put myself with a notebook and a pencil in front of a sequence of events P and do the Following algorithmic test?

   .wait for a time a P event (we are assuming that this can happen with a good frequency and that the phenomenon is observable in a finite time,
    and small enough to verify in the time dedicated to testing.
   .observe what is happening in respect of the occurrence of Q
   .make note on the notebook the statement S result (true or false)
   .repeat the process from start a finite number of times
   .observe in the notebook the veracity of the operator's table "if then".

Please ask me any further questions other clarifications.

Thanks again to all of you

Fabrizio


2016-11-14
sufficient condition and necessary condition
Hello everybody,

please, if I wrote something wrong or unclear correct me, or ask me questions, if what I propose does not make sense let me know.
If on the contrary I have put a proper question, I think for intellectual honesty, if you do not have a definite answer, however, it is not proper to abandon a discussion, and to have the humility to admit they do not have a definite answer distinguishes a serious professor, a true philosopher, an honest researcher, a professional by whom has the illusion of possessing all the knowledge.
I do not have the illusion they claim to possess superior knowledge to anyone, after many years of sacrifice and commitment to understand concepts that are passionate I still submit my reflections and ideas to high-level professionals who can help me to understand and to verify whether some
of my theoretical proposal can be useful. I proposed here my ideas, just to have the opinion of professionals as you all.
Help me understand if my ideas are not good, or allowing me to develop them through our discussion, if recognizing a value, we collaborate to write an article, for me it would be the realization of a dream.

Thanks to all and forgive my provocation.

Fabrizio

2016-11-15
sufficient condition and necessary condition

It looks like you’re no longer really after truthtables for conditionals in propositional logic, Fabrizio, but something essentially involving quantifiers, since your Ps and Qs are now standing for descriptions of particular instances of types of occurrences.

But okay, let’s proceed your way. I’m walking down a lane and notice a pebble now and again (i.e. meeting your conditions of good frequency and finite time):

If I see pebble #1 then it is still observable 2 seconds later.

If I see pebble #2 then it is still observable 2 seconds later.

If I see pebble #1000 then it is still observable 2 seconds later.

Assuming that none of the pebbles that I see disappear from sight before 2 seconds are up, these 1000 conditionals, with true antecedents and true consequents, are true. This accords with line 1 of the truthtable.

But now suppose instead that pebble #47 and only pebble #47 disappears after 1 second. Then the proposition

If I see pebble #47 then it is still observable 2 seconds later.

is false and its antecedent is true and its consequent false. This accords with line 2 of the truthtable. (Note that the truth of the other 999 propositions is not affected.)

What about all the pebbles I could have seen at a particular time but failed to see? Well, some of them may have been observable 2 seconds after my failure but since I didn’t see them I cannot verify or falsify whether they were still observable 2 seconds later. So for those pebbles we would have conditionals with false antecedents and true or false consequents. Are those conditionals true or false? Their truth would be in accord with lines 3 and 4 of the truthtable.

But consider pebble #5097, one of the many I failed to notice:

If I see pebble #5097 then it is still observable 2 seconds later.

The antecedent is false and the consequent may or may not be true. In everyday English we might balk at regarding this proposition as true for either possibility. But cf. “If I had seen pebble #5097 then it would have still been observable 2 seconds later.” Perhaps it can be regarded as probably true on inductive grounds?

So ordinary English conditionals (of which there are several types) may not generally be truthfunctional (although some folks have advanced subtle arguments to the contrary). But the truthfunctional material conditional may serve other important purposes, such as testing for validity.

Anyway, Fabrizio, I don’t think I can say anything more about these matters without going in circles.   <:‑|

 

 

 


2016-11-23
sufficient condition and necessary condition


My observations:

.1


There is no ordinary language; there are people who do not know the language, so make it an intuitive functional ordinary use for the purposes of basic social interactions.

 

.2


The concept, truth function, psychologically / axiomatically arises from observation and description in a sentence of a natural language or formal system of phenomena, events that the human brain identifies of the same nature and characteristics always the same except for his present, his senses, not constantly, then evaluated, or better, in this sense can be defined as "true" when it presents itself, "false" when it does not occur. Therefore say event or, truth function, it says the same thing.

 

.3

Regardless of your observation "since your Ps and Qs are now standing for descriptions of Particular instances of types of occurrences" what you are experiencing is the same phenomenon on different objects, in the case of matches and rags, the phenomenon is the burning, if of the pebble their observability in two-second distance, the two phenomena considered to equal initial conditions.

.4


 "Assuming that none of the pebbles That I see disappear from sight before 2 seconds are up, 1000 These conditionals, with true antecedents and consequents true, are true. This accords with the first line of the truthtable. "


This is not correct, we have the same conditional related to observability phenomenon after 2 seconds applied to 1000 different stones, if you write:


A: If I see pebble # 1 then it is still observable 2 seconds later.
B: If I see pebble # 2 then it is still observable 2 seconds later.

You are describing the observable phenomenon preached by the two propositions A and B on two different objects (pebble # 1, # 2 pebble) but of the same nature and subject to the same laws implied in the assumptions. In my formulation with matches or bachelors, you proposed, I have called for clearer shape, the conditions (assumptions) start and I formulated all through an algorithm with clear instructions and clearly defined in order not to run into interpretations, and your in If the pebble, is quite naive.

 

.5


"If I see pebble # 47 then it is still observable 2 seconds later.
is false and its antecedent is true and its consequent false. This accords with the second line of the truthtable. (Note That the truth of the other 999 propositions is not affected.) "

Are you sure of this that affirms?

Think about the situation of matches or the bachelor of which I report the descriptive passages:


 ".if The match is it is not switched off in the fall, observe what is happening
    and make notes on the notebook the statement S result (true or false) "


"That .verify in the identity document is indicato civil status bachelor
   .if bachelor is bachelor, observe the sex indicato in the document
    and make notes on the notebook the statement S1 result (true or false) "


Now:


"I am at the pebble number 47 of your example, I see, I wait two seconds, and I check if I can still see it .... Now observe what is happening  and make notes on the notebook the result (true or false) "


I say that I could write in the notebook false in this case and that the rest of the 999 propositions is unaffected by this.

.6

“ What about all the pebbles I could have seen at a particular time but failed to see? Well, some of them may have been observable 2 seconds after my failure but since I didn’t see them I cannot verify or falsify whether they were still observable 2 seconds later. So for those pebbles we would have conditionals with false antecedents and true or false consequents. Are those conditionals true or false? Their truth would be in accord with lines 3 and 4 of the truthtable. ”

 

Here there is another very naive observation, third and fourth lines of the logical form of involvement where the antecedent is false and the consequent is true, based on what you assess true?


In algorithmic model that I have proposed, I reject cases:

.if the match will go off, discard this sequence and start again

.if not in possession of identity document, discard this sequence and start again

And I would go even to discard:

“If I not see pebble #N discard this sequence and start again”

 

That is the case where the antecedent of the implication is false, and I do not by mistake or naivete.


My purpose is:

 

I ask you a justification of the results of the third column that comes from a real experience and reproducible that helps a person to understand clearly and to fix in the mind the concepts it represents.

P | Q | if P then Q
------------------------
V | V |     V      
V | F |     F      
F | V |     V      
F | F |     V


Or how you justified, psychologically and axiomatically, someone the logical form of the implication.
It 'quite evident that my thesis on the theoretical gaps and the deep understanding of the concept of implication is true.

Even professionals of your caliber manifest cognitive presence of these gaps, and with this I do not intend neither to offend nor to judge anyone, because I am here to learn and to propose to your criticism the results of my own studies for all of us always have new opportunities to grow, as I think all of you as the philosophers, professors, great professionals, certainly share with me, that in my small way I am also a professional.

To justify psychologically and axiomatically the implication the algorithm I proposed is sufficient and solves all the cases of the four rows of the truth table, although apparently it seems like you've highlighted karl does not treat lines 3 and 4.

 

But still no one answered me:

You think I could put myself with a notebook and a pencil in front of a sequence of events (truthfunction, proposition) P and do the algorithmic test I proposed?

The nature of the concept of implication and those of sufficient condition and necessary condition still today hide aspects which maybe for the longest time I have devoted to studying and above experiment and justify them I was able to throw a faint light.

Maybe even my studies in psychology and neuroscience have contributed a lot to this to arrive at a deeper understanding of these concepts.

 

In the algorithm and in the proposed questions you can find important tips, the same that led me a step forward in understanding.

 

There is still much to discover and discuss, we are only at the tip of the iceberg and not imagine how much I would like to personally meet you, discuss with you around a table and looking into his eyes.

 

If only I had more resources I would invite you to reunite and discuss and produce an article perhaps, epochal.

 

Please, correct me if I made erros, ask me any further questions other clarifications and forgive any provocation and misunderstanding.

 

Thank you all for your attention and participation

Fabrizio




2016-12-07
sufficient condition and necessary condition


Hi everybody

await your precious observations

Fabrizio

2016-12-08
sufficient condition and necessary condition
My proposition to translate for ordinal language. By the way this could be definition of modal operators.

P | Q | if P then Q
------------------------
V | V |     V   - necessary   
V | F |     F   - unnecessary   
F | V |     V   - possible    
F | F |     V   - imposible

Fabrizio.

Abaut peebles We could use P -> Q ^ L observer, observable Q ^ L in this same time, but this depend on his cognitive abilities. Imagine that You ride a car and take steering wheel and change gears, also look at ride. Then if You has cognitive abilities You can observe some number of peebles. If You take amphetamine or something like that, your cognitive abilities going up.

Also

(P -> Q ^ R) -> (P -> Q) ^ (P -> R) in this same time. Phisics they called it values coupled

P. A. Grabowski.