LOGIC IS BEDROCK

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posthuman

Senior Member
Jul 31, 2013
27,897
8,509
113
Discrete Mathematics can show this..... and @posthuman can check it if he likes ;)

  • If I did all the suggested exercises, then I got an A+
  • I got an A+
  • Therefore, I did all of the suggested exercises.
s denote >> "I did all of the suggested exercises" and a denote >>>> "I got an A+."
The premises are therefore sa and a and the conclusion is c.
To show this argument is invalid, we find truth values to make all of the premises true, but the conclusion false.
If we set s=F and a=T, we have saFTT and aT, and so the premises are true.

However, the conclusion is sF so the conclusion is invalid.

(credit Carleton U)

hooray math!

i found the source you quoted from; here it is with a little more context:


Not all arguments are valid! To show an argument is invalid, find truth values for each proposition that make all of the premises true, but the conclusion false.
This works because proving an argument is valid is just showing that an implication is true. Therefore, to show an argument is invalid, we need to show that the implication is false. An implication is false only when the hypothesis is true and the conclusion is false. Since the hypothesis is the conjunction of the premises, this means that each premise is true and the conclusion is false.
  • Consider the argument:
    • If I did all the suggested exercises, then I got an A+
      • I got an A+
      • Therefore, I did all of the suggested exercises.
    • Let ss denote "I did all of the suggested excerises" and aa denote "I got an A+." The premises are therefore s→as→a and aa and the conclusion is cc. To show this argument is invalid, we find truth values to make all of the premises true, but the conclusion false. If we set s=F s=F and a=Ta=T, we have s→a≡F→T≡Ts→a≡F→T≡T and a≡Ta≡T, and so the premises are true. However, the conclusion is s≡Fs≡F, and so the argument is invalid.

the symbols don't copy-paste into the forum well for the math at the bottom of the quote, but it's kind a rubbish explanation ((@ Carleton U, you can write that more beautifully, for sure)) anyway.

the important bit is at the top of the quote: it's when premises are true but conclusions are false that you have an invalid argument. it's proven invalid by contradiction: the premises lead to a conclusion that contradicts the premises. this tells you, you were using bad logic.

here's the example he gave in a little clearer terms, i hope:

  • Consider the argument:
    • If I did all the suggested exercises, then I got an A+
    • I got an A+
    • Therefore, I did all of the suggested exercises.
  • Let:
    • X = {do all the exercises}
    • Y = {get an A+}
  • The premises are:
    • X → Y
      • read this as "X implies Y" or "if X, then Y"
  • the conclusion is:
    • Y → X
to prove this isn't valid, you would find a case in which X is true but Y is not. that is, you got an A+ but you didn't do all the work. the author of the quote just assumed such a scenario exists; he said:

  • suppose that X is true and Y is false.
  • then:
    • {X = T} ⇒ Y = T, since X → Y
      • read this as 'X is True. it follows that Y is true, since X implies Y'
    • {Y = T} ⇒ F = T, since Y = F
      • read this as 'the fact that Y is true implies false is True, since we know Y is false
      • really should have stopped there =\
    • {F = T} ⇒ X = F, since we know X = T
      • he concludes X is false, contradicting that X is true, on the basis that false is the same as true.
      • this is extraneous at this point, we knew what we were looking at was invalid the moment we got Y is true, because that contradicted the premises. the author of this proof was noob at the time he wrote it, IMO. or very tired, more likely, from staying up for days to write that webpage, and missed that he made the same argument twice when he only needed it once.
anyhoo, the gist is, you know you have a bad argument when your argument predicts something according to some conditions, but you can find the same conditions being true somewhere yet the something-predicted not being true. in the example, the fallacy was assumed to exist: to wit, if you can still get an A+ without doing all the work, then just because if you do the work you get an A+ does not imply that you must have done all the work if you did get an A+
you might have done extra credit.
the teacher might drop the lowest grade, and maybe you did all but one homework, and got A + on all you did but a zero on the one you didn't do, however the zero was dropped & didn't count.






and here's a bonus: a more beautiful proof, in a more beautiful form:

  • let TRUE = 1, FALSE = 0
  • let E = the collection of events e1 . . eN where each event ek is the doublet {Xk, Yk}
  • the premise X → Y can then be encoded as:
    • X + Y > X
  • hypothesis: Y → X
    • ⇒ Y + X > Y
  • suppose that there exits an event in E: ei = {1, 0}
    • X + Y = 1 > 0 = X
      • the premise holds
    • Y + X = 1 = X
      • the hypothesis fails
  • therefore the hypothesis is invalidated if e ∈ E, e = {1, 0}
 
U

UnderGrace

Guest
hooray math!

i found the source you quoted from; here it is with a little more context:


Not all arguments are valid! To show an argument is invalid, find truth values for each proposition that make all of the premises true, but the conclusion false.
This works because proving an argument is valid is just showing that an implication is true. Therefore, to show an argument is invalid, we need to show that the implication is false. An implication is false only when the hypothesis is true and the conclusion is false. Since the hypothesis is the conjunction of the premises, this means that each premise is true and the conclusion is false.

  • Consider the argument:
    • If I did all the suggested exercises, then I got an A+
      • I got an A+
      • Therefore, I did all of the suggested exercises.
    • Let ss denote "I did all of the suggested excerises" and aa denote "I got an A+." The premises are therefore s→as→a and aa and the conclusion is cc. To show this argument is invalid, we find truth values to make all of the premises true, but the conclusion false. If we set s=F s=F and a=Ta=T, we have s→a≡F→T≡Ts→a≡F→T≡T and a≡Ta≡T, and so the premises are true. However, the conclusion is s≡Fs≡F, and so the argument is invalid.
the symbols don't copy-paste into the forum well for the math at the bottom of the quote, but it's kind a rubbish explanation ((@ Carleton U, you can write that more beautifully, for sure)) anyway.

the important bit is at the top of the quote: it's when premises are true but conclusions are false that you have an invalid argument. it's proven invalid by contradiction: the premises lead to a conclusion that contradicts the premises. this tells you, you were using bad logic.

here's the example he gave in a little clearer terms, i hope:

  • Consider the argument:
    • If I did all the suggested exercises, then I got an A+
    • I got an A+
    • Therefore, I did all of the suggested exercises.
  • Let:
    • X = {do all the exercises}
    • Y = {get an A+}
  • The premises are:
    • X → Y
      • read this as "X implies Y" or "if X, then Y"
  • the conclusion is:
    • Y → X
to prove this isn't valid, you would find a case in which X is true but Y is not. that is, you got an A+ but you didn't do all the work. the author of the quote just assumed such a scenario exists; he said:

  • suppose that X is true and Y is false.
  • then:
    • {X = T} ⇒ Y = T, since X → Y
      • read this as 'X is True. it follows that Y is true, since X implies Y'
    • {Y = T} ⇒ F = T, since Y = F
      • read this as 'the fact that Y is true implies false is True, since we know Y is false
      • really should have stopped there =\
    • {F = T} ⇒ X = F, since we know X = T
      • he concludes X is false, contradicting that X is true, on the basis that false is the same as true.
      • this is extraneous at this point, we knew what we were looking at was invalid the moment we got Y is true, because that contradicted the premises. the author of this proof was noob at the time he wrote it, IMO. or very tired, more likely, from staying up for days to write that webpage, and missed that he made the same argument twice when he only needed it once.
anyhoo, the gist is, you know you have a bad argument when your argument predicts something according to some conditions, but you can find the same conditions being true somewhere yet the something-predicted not being true. in the example, the fallacy was assumed to exist: to wit, if you can still get an A+ without doing all the work, then just because if you do the work you get an A+ does not imply that you must have done all the work if you did get an A+
you might have done extra credit.
the teacher might drop the lowest grade, and maybe you did all but one homework, and got A + on all you did but a zero on the one you didn't do, however the zero was dropped & didn't count.







and here's a bonus: a more beautiful proof, in a more beautiful form:

  • let TRUE = 1, FALSE = 0
  • let E = the collection of events e1 . . eN where each event ek is the doublet {Xk, Yk}
  • the premise X → Y can then be encoded as:
    • X + Y > X
  • hypothesis: Y → X
    • ⇒ Y + X > Y
  • suppose that there exits an event in E: ei = {1, 0}
    • X + Y = 1 > 0 = X
      • the premise holds
    • Y + X = 1 = X
      • the hypothesis fails
  • therefore the hypothesis is invalidated if e ∈ E, e = {1, 0}

Been a while since I studied Discrete Mathematics.... need to put my thinking cap on again, amazing how much one forgets over time :(

Thanks for finding the link I knew it was from Carelton U, however not really known for their Mathematics Department though, yours does look much more elegant!!

Hold on @Dino246 still looking for a better argument to support my premise....
.jpg
 

CharliRenee

Member
Staff member
Nov 4, 2014
6,073
6,637
113
So on the edge of my chair, as I can not imagine you finding an example.

I am so intrigued though.
 

Roughsoul1991

Senior Member
Sep 17, 2016
4,778
1,917
113
hooray math!

i found the source you quoted from; here it is with a little more context:


Not all arguments are valid! To show an argument is invalid, find truth values for each proposition that make all of the premises true, but the conclusion false.
This works because proving an argument is valid is just showing that an implication is true. Therefore, to show an argument is invalid, we need to show that the implication is false. An implication is false only when the hypothesis is true and the conclusion is false. Since the hypothesis is the conjunction of the premises, this means that each premise is true and the conclusion is false.

  • Consider the argument:
    • If I did all the suggested exercises, then I got an A+
      • I got an A+
      • Therefore, I did all of the suggested exercises.
    • Let ss denote "I did all of the suggested excerises" and aa denote "I got an A+." The premises are therefore s→as→a and aa and the conclusion is cc. To show this argument is invalid, we find truth values to make all of the premises true, but the conclusion false. If we set s=F s=F and a=Ta=T, we have s→a≡F→T≡Ts→a≡F→T≡T and a≡Ta≡T, and so the premises are true. However, the conclusion is s≡Fs≡F, and so the argument is invalid.
the symbols don't copy-paste into the forum well for the math at the bottom of the quote, but it's kind a rubbish explanation ((@ Carleton U, you can write that more beautifully, for sure)) anyway.

the important bit is at the top of the quote: it's when premises are true but conclusions are false that you have an invalid argument. it's proven invalid by contradiction: the premises lead to a conclusion that contradicts the premises. this tells you, you were using bad logic.

here's the example he gave in a little clearer terms, i hope:

  • Consider the argument:
    • If I did all the suggested exercises, then I got an A+
    • I got an A+
    • Therefore, I did all of the suggested exercises.
  • Let:
    • X = {do all the exercises}
    • Y = {get an A+}
  • The premises are:
    • X → Y
      • read this as "X implies Y" or "if X, then Y"
  • the conclusion is:
    • Y → X
to prove this isn't valid, you would find a case in which X is true but Y is not. that is, you got an A+ but you didn't do all the work. the author of the quote just assumed such a scenario exists; he said:

  • suppose that X is true and Y is false.
  • then:
    • {X = T} ⇒ Y = T, since X → Y
      • read this as 'X is True. it follows that Y is true, since X implies Y'
    • {Y = T} ⇒ F = T, since Y = F
      • read this as 'the fact that Y is true implies false is True, since we know Y is false
      • really should have stopped there =\
    • {F = T} ⇒ X = F, since we know X = T
      • he concludes X is false, contradicting that X is true, on the basis that false is the same as true.
      • this is extraneous at this point, we knew what we were looking at was invalid the moment we got Y is true, because that contradicted the premises. the author of this proof was noob at the time he wrote it, IMO. or very tired, more likely, from staying up for days to write that webpage, and missed that he made the same argument twice when he only needed it once.
anyhoo, the gist is, you know you have a bad argument when your argument predicts something according to some conditions, but you can find the same conditions being true somewhere yet the something-predicted not being true. in the example, the fallacy was assumed to exist: to wit, if you can still get an A+ without doing all the work, then just because if you do the work you get an A+ does not imply that you must have done all the work if you did get an A+
you might have done extra credit.
the teacher might drop the lowest grade, and maybe you did all but one homework, and got A + on all you did but a zero on the one you didn't do, however the zero was dropped & didn't count.







and here's a bonus: a more beautiful proof, in a more beautiful form:

  • let TRUE = 1, FALSE = 0
  • let E = the collection of events e1 . . eN where each event ek is the doublet {Xk, Yk}
  • the premise X → Y can then be encoded as:
    • X + Y > X
  • hypothesis: Y → X
    • ⇒ Y + X > Y
  • suppose that there exits an event in E: ei = {1, 0}
    • X + Y = 1 > 0 = X
      • the premise holds
    • Y + X = 1 = X
      • the hypothesis fails
  • therefore the hypothesis is invalidated if e ∈ E, e = {1, 0}
o_O math.... the killer of my academic grades....
 

Roughsoul1991

Senior Member
Sep 17, 2016
4,778
1,917
113
hooray math!

i found the source you quoted from; here it is with a little more context:


Not all arguments are valid! To show an argument is invalid, find truth values for each proposition that make all of the premises true, but the conclusion false.
This works because proving an argument is valid is just showing that an implication is true. Therefore, to show an argument is invalid, we need to show that the implication is false. An implication is false only when the hypothesis is true and the conclusion is false. Since the hypothesis is the conjunction of the premises, this means that each premise is true and the conclusion is false.

  • Consider the argument:
    • If I did all the suggested exercises, then I got an A+
      • I got an A+
      • Therefore, I did all of the suggested exercises.
    • Let ss denote "I did all of the suggested excerises" and aa denote "I got an A+." The premises are therefore s→as→a and aa and the conclusion is cc. To show this argument is invalid, we find truth values to make all of the premises true, but the conclusion false. If we set s=F s=F and a=Ta=T, we have s→a≡F→T≡Ts→a≡F→T≡T and a≡Ta≡T, and so the premises are true. However, the conclusion is s≡Fs≡F, and so the argument is invalid.
the symbols don't copy-paste into the forum well for the math at the bottom of the quote, but it's kind a rubbish explanation ((@ Carleton U, you can write that more beautifully, for sure)) anyway.

the important bit is at the top of the quote: it's when premises are true but conclusions are false that you have an invalid argument. it's proven invalid by contradiction: the premises lead to a conclusion that contradicts the premises. this tells you, you were using bad logic.

here's the example he gave in a little clearer terms, i hope:

  • Consider the argument:
    • If I did all the suggested exercises, then I got an A+
    • I got an A+
    • Therefore, I did all of the suggested exercises.
  • Let:
    • X = {do all the exercises}
    • Y = {get an A+}
  • The premises are:
    • X → Y
      • read this as "X implies Y" or "if X, then Y"
  • the conclusion is:
    • Y → X
to prove this isn't valid, you would find a case in which X is true but Y is not. that is, you got an A+ but you didn't do all the work. the author of the quote just assumed such a scenario exists; he said:

  • suppose that X is true and Y is false.
  • then:
    • {X = T} ⇒ Y = T, since X → Y
      • read this as 'X is True. it follows that Y is true, since X implies Y'
    • {Y = T} ⇒ F = T, since Y = F
      • read this as 'the fact that Y is true implies false is True, since we know Y is false
      • really should have stopped there =\
    • {F = T} ⇒ X = F, since we know X = T
      • he concludes X is false, contradicting that X is true, on the basis that false is the same as true.
      • this is extraneous at this point, we knew what we were looking at was invalid the moment we got Y is true, because that contradicted the premises. the author of this proof was noob at the time he wrote it, IMO. or very tired, more likely, from staying up for days to write that webpage, and missed that he made the same argument twice when he only needed it once.
anyhoo, the gist is, you know you have a bad argument when your argument predicts something according to some conditions, but you can find the same conditions being true somewhere yet the something-predicted not being true. in the example, the fallacy was assumed to exist: to wit, if you can still get an A+ without doing all the work, then just because if you do the work you get an A+ does not imply that you must have done all the work if you did get an A+
you might have done extra credit.
the teacher might drop the lowest grade, and maybe you did all but one homework, and got A + on all you did but a zero on the one you didn't do, however the zero was dropped & didn't count.







and here's a bonus: a more beautiful proof, in a more beautiful form:

  • let TRUE = 1, FALSE = 0
  • let E = the collection of events e1 . . eN where each event ek is the doublet {Xk, Yk}
  • the premise X → Y can then be encoded as:
    • X + Y > X
  • hypothesis: Y → X
    • ⇒ Y + X > Y
  • suppose that there exits an event in E: ei = {1, 0}
    • X + Y = 1 > 0 = X
      • the premise holds
    • Y + X = 1 = X
      • the hypothesis fails
  • therefore the hypothesis is invalidated if e ∈ E, e = {1, 0}
Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry. — K. Shegel
Oh how do I wish I could understand its ancient language.
 

PERFECTION

Active member
Aug 14, 2019
222
63
28
you do have a gift for trying to create a reason for a person who did not say what you say they did, to get on the defensive

but instread, let's take a closer look at your manipulating what I said and you changing what you said

here we go :giggle:

here is what you posted and what I responded to:

Your THINKING is totally flawed. You are not the first to try and explain how you mind works when exposed to Gods word.
If you think we settle into some logical coma that makes perfect sense try reading the book of Jermiah.
In the mean time tell me about what spiritual growth you have achieved through the trials in your life.
These trials are what offer the opportunity to increase your faith.
Start talking about what has happened in your life that has brought you to your knees before God.


And yes you are the person who tied me to the steak as a witch and burned me.

that was actually a post to the op, but since I agree with the op, I responded...this is an open forum and anyone can respond

you do not address what was posted in the op, instead you create an ad hominem attack, which in case you do not know, is an attack upon the PERSON rather than the subject. you tell the op his thinking is flawed, accuse him of things he never said...you create an entire personal attack and then you create criteria that God Himself does not say we need to prove anything and end your post with an obscure reference to being burned at the stake

so I wrote what I did because I consider what you posted immature and unreasonable as you attack a poster rather than address the fact you obviously disagree with the position reflected in the op. are you not able to illustrate why you disagree or, do you usually simply attack people because that is what you do?

frankly I do not care about your little story of faith you have above which appears to be fiction. this thread is not about that. I can give my own TRUE stories regarding faith and even lack of faith and the faithfulness of God

you are simply bloviating and hoping no one will notice

further you are in no place to now try to teach scritpure since you have already shown you are good at attacking as your first go to

you mention being qualified. you have not shown any indication of being qualified as you do not give any sort of response that indicates you understand what is being discussed here

I don't believe, at this moment, that I will respond to you again because you do not address the op and simply create a response to take the topic off line
Sorry for causing you so much stress. I will admit my lack of understanding in posting sometimes steps on peoples nerves and obviously I have stepped on yours. It was not intentional I can assure you.

However, with that being said , I would suggest you seek counseling about your anger issues.
 

oldhermit

Senior Member
Jul 28, 2012
8,800
443
83
66
Texas
I can't say that time is a product of those events because nothing suggests that it is, time is the perception that resulted as mortal man claimed to be created by an eternal God. Since a good tree cannot bring forth evil fruit, then can an eternal God create and eternal man if the eternal is distinguished from the mortal nature by having always existed? A very simple question that answers itself, but feel free to give what you believe the answer is if you disagree.


But to answer your question, based upon my observations I would say that the natural world has about the same possibility to tell us all the truth about reality as the Bible has to tell us all the truth about reality. So do believe that the Bible will guide you into all truth?
Looking back over this thread, I noticed this response to my previous post. I am sorry, I must have completely overlooked this post and it is certainly worthy of an answer.

I think we can agree that there is a difference between time and eternity. Time is relative only to the material world, and like everything else in the material would, time is a created factor. We can see the beginning of time and the organization of temporal measurements in the creation account of Genesis 1. Scripture always presents God as existing beyond and outside of time. Scripture also demonstrates the fact that time responds to the will of God.

As to you first question, "...can an eternal God create and eternal man if the eternal is distinguished from the mortal nature by having always existed?" The answer is of course, yes! I think Eccl 3:10-11 answers the question quite well. "I have seen the task which God has given the sons of men with which to occupy themselves. He has made everything appropriate in its time. He has also set eternity in their heart, yet so that man will not find out the work which God has done from the beginning even to the end." God created man as an eternal being. Only man's mortal existence is measured by time.

As to your second question, "Do believe that the Bible will guide you into all truth?" I think we need to understand that when it come to the acquisition of truth, "all" is a relative term. There is truth that man is simply not privileged to know. This is the lesson of the tree of knowledge of good and even in the garden. There are simply things man is not given to know. The Bible is a document of revealed truth but clearly, God has not revealed all truth to man in the pages of scripture. He has only revealed truth that is relative to man's need for salvation and his relationship with the Creator.

Jesus promised the apostles that the Holy Spirit would guide them into all truth. In turn, they delivered this truth in the form of scripture through the guidance of the Holy Spirit. In this respect, yes, the Bible is man’s only guide to all revealed truth.

There are truths we can understand from our observation of the natural world, but there are also truths that cannot be ascertained from man’s observation of the natural world. An appeal to logic will only take one so far. It is impossible for logic to breech the threshold into the eternal dimension of God. That requires the element of faith. Let me offer you an example from scripture to demonstrate this point.

When Abraham acquiesced to offer Isaac, he did not conclude that God could raise Isaac from the dead based on any logical exercise. There is nothing in the world of man that could possibly lead man to conclude through any logical process that someone could be raised from the dead to rejoin the living. Abraham had to look beyond logic to conclude the possibility of a resurrection. Logically, the facts are as follows,
1. Knife to the throat = an absolute outcome - death.
2. Fire to the flesh = absolute outcome – total destruction of the flesh.
These have always produced irreversible results – the death and total thermal consumption of the victim.

Abraham's experience with offering sacrifices tells him that sacrifices do not survive the ordeal; not ever! Human logic based on human experience says, “If I do this my son will be irretrievably dead and gone.” Something is going to have to happen in Abraham's reasoning processes that transcends the logic of the human experiential index. Abraham faced a logical dilemma - If Isaac is dead, how will the promise be fulfilled. Abraham based his decision not on any logical assumptions but upon the faithfulness of God. Abraham’s conclusion reached beyond the boundaries of applied logic – “God is able to raise one even from the dead.” This is certainly not a logical conclusion. How could Abraham possibly know this? The text never says that this knowledge was ever revealed to Abraham. He has never had a sacrifice get up off the altar and follow him home after the ordeal. He has had no experience with the dead being raised to life. The only thing Abraham’s experience can confirm to him about death is that logically, it is always decisive and irreversible. This is the limit of the logical approach. The Hebrew writer confirms for us that faith was the only factor that drove Abraham’s conclusion and moved him to honor God's demand to sacrifice Isaac. The result of this was that God acknowledged Abraham as faithful, not logical.
 

oldhermit

Senior Member
Jul 28, 2012
8,800
443
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Texas
I have been thinking a great deal over the past few days about man's use of logic and its relation to biblical faith. What we learn from examples in scripture is that precise logic is contrary to biblical faith. We use logic all the time in our interactions with other people, with nature, and with the universe. That is well and good and is as the Creator intended. Logic is part of our created nature and it emerges from our experiences as we transact with temporal realities. So, I suppose we could call this transactional logic. However, human transactional logic does not and cannot explain the biblical concept of faith. Biblically defined faith, constitutes a spiritual transaction with the Almighty, not a logical one. Numerous biblical examples demonstrate that one cannot live by faith while relying upon transactional logic. Here are just a couple of examples from scripture to demonstrate this point.

1. The evil report at Kadesh-Barnea in Numbers 14
Human transactional logic would insist upon logical impossibilities. The assessment of the spies in Numbers 14 is a perfect example of this. After the 40-day reconnaissance of Canaan, a faithless representation that was totally dependent upon transactional logic was put into evidence by 10 of the spies. Based on the evidence of their reconnaissance, these men were convinced that conquest of Canaan was a logical impossibility. More than that, they used the logical argument to convince the rest of the people that this would never work and that they were all going to end up dead. The problem was that their observation of all available material facts and evidences did not tell them all the truth about the situation. Personal observation invariably leaves us with very vivid impressions, and human nature being what it is, would insist that these impressions require a logical response. Faith, on the other hand, calls us to reason beyond impressions, and this is not logical. Whether or not God can be trusted with our well-being is not a matter of logic, it is a matter of faith. The logical response to the circumstances by Israel proved to be a faithless act and 15,000 people, including all ten of the faithless spies died as a result.

2. Genesis 16 is another perfect example of an epic fail in the use of transactional logic.
When Abraham and Sarah were faced with the dilemma of producing a son, they approached the situation with a purely logical mind and came up with a purely logical solution. They used logical to fill a gap in the logical sequence of their situation. What is the logical sequence for producing an heir? Abraham + Sarah + fertility + time = desired result – an heir. What are the discontinuities in this logical sequence?

a. They are too old. Abraham is 85 and Sarah is 75.
b. Sarah is too barren, 11:30
These two factors represent a physiological discontinuity.
c. Time was against them – This is a discontinuity of physics. We have a tendency to make the same mistake in measuring the promises of God against time.
d. Hagar was the logical solution to a logical problem.
This is a perfect example of the proper application of logic to solve a perfectly logical situation. The problem was, it required the abandonment of faith in God to fulfill his promise. The only element of continuity in this situation was the power of God to overturn the limitations of physics and physiology. Rather than relying on the promise and the power of God, Abraham and Sarah opted for the logical approach.
 

Dino246

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Jun 30, 2015
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I have been thinking a great deal over the past few days about man's use of logic and its relation to biblical faith. What we learn from examples in scripture is that precise logic is contrary to biblical faith. We use logic all the time in our interactions with other people, with nature, and with the universe. That is well and good and is as the Creator intended. Logic is part of our created nature and it emerges from our experiences as we transact with temporal realities. So, I suppose we could call this transactional logic. However, human transactional logic does not and cannot explain the biblical concept of faith. Biblically defined faith, constitutes a spiritual transaction with the Almighty, not a logical one. Numerous biblical examples demonstrate that one cannot live by faith while relying upon transactional logic. Here are just a couple of examples from scripture to demonstrate this point.

1. The evil report at Kadesh-Barnea in Numbers 14
Human transactional logic would insist upon logical impossibilities. The assessment of the spies in Numbers 14 is a perfect example of this. After the 40-day reconnaissance of Canaan, a faithless representation that was totally dependent upon transactional logic was put into evidence by 10 of the spies. Based on the evidence of their reconnaissance, these men were convinced that conquest of Canaan was a logical impossibility. More than that, they used the logical argument to convince the rest of the people that this would never work and that they were all going to end up dead. The problem was that their observation of all available material facts and evidences did not tell them all the truth about the situation. Personal observation invariably leaves us with very vivid impressions, and human nature being what it is, would insist that these impressions require a logical response. Faith, on the other hand, calls us to reason beyond impressions, and this is not logical. Whether or not God can be trusted with our well-being is not a matter of logic, it is a matter of faith. The logical response to the circumstances by Israel proved to be a faithless act and 15,000 people, including all ten of the faithless spies died as a result.

2. Genesis 16 is another perfect example of an epic fail in the use of transactional logic.
When Abraham and Sarah were faced with the dilemma of producing a son, they approached the situation with a purely logical mind and came up with a purely logical solution. They used logical to fill a gap in the logical sequence of their situation. What is the logical sequence for producing an heir? Abraham + Sarah + fertility + time = desired result – an heir. What are the discontinuities in this logical sequence?

a. They are too old. Abraham is 85 and Sarah is 75.
b. Sarah is too barren, 11:30
These two factors represent a physiological discontinuity.
c. Time was against them – This is a discontinuity of physics. We have a tendency to make the same mistake in measuring the promises of God against time.
d. Hagar was the logical solution to a logical problem.
This is a perfect example of the proper application of logic to solve a perfectly logical situation. The problem was, it required the abandonment of faith in God to fulfill his promise. The only element of continuity in this situation was the power of God to overturn the limitations of physics and physiology. Rather than relying on the promise and the power of God, Abraham and Sarah opted for the logical approach.
You make some good points, from the perspective of the unregenerate mind (not meaning you, of course). To me, a right understanding of God, His nature, and His word are fundamental to logical analysis. Therefore, obedience to His direction is perfectly logical.

That said, Scripture doesn’t reveal whether God told Abraham not to try to make things happen.

As an aside, I’ve always found it curious that Abraham is said to be old (implying he was no longer able to sire children) but that he had several children with Keturah years after these events.
 

oldhermit

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You make some good points, from the perspective of the unregenerate mind (not meaning you, of course). To me, a right understanding of God, His nature, and His word are fundamental to logical analysis. Therefore, obedience to His direction is perfectly logical.

That said, Scripture doesn’t reveal whether God told Abraham not to try to make things happen.

As an aside, I’ve always found it curious that Abraham is said to be old (implying he was no longer able to sire children) but that he had several children with Keturah years after these events.
Precisely how would you use logic to understand the nature of God?
 

Dino246

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Precisely how would you use logic to understand the nature of God?
Perhaps you're seeing this 'backwards' of how I see it. I accept the nature and purposes of God as revealed in Scripture. With that understanding in hand, I apply it to understanding His actions, and I see that they are logical in light of Who He is.
 

oldhermit

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Perhaps you're seeing this 'backwards' of how I see it. I accept the nature and purposes of God as revealed in Scripture. With that understanding in hand, I apply it to understanding His actions, and I see that they are logical in light of Who He is.
Perhaps that is true. Logic. however will never enable us to comprehend the nature of God. The only reason we understand what little we do about the nature of God is not through logic but because those things are revealed to us in scripture. We do not accept that revelation as truth by logic but by faith. Logic is dependent upon things that can be proven or measured. Faith is acceptance of those things we cannot proven. We accept it because scripture says it is so, and by faith, we accept scripture as the word of God.