This is a critical point in understanding the reformed view. Our logic usually is flawed when it comes to concluding upon such premises.
Eg1: When I say, "All tall men were permitted into the room" - a flawed assumption is that the short men weren't. But "Some short men too could have been permitted". I didn't use the word "only".
Eg2: When I say, "If a flower is red, it will be used in decoration" - a flawed assumption is that the yellow flowers, white flowers etc are not used in decoration. But while the condition comments on red flowers, it makes no distinction on the other colors at all. We can then only conclude, that "if a flower is not used in decoration, it definitely is not red in color".
Eg3: Taking the same premise, "If a flower is red, it will be used in decoration" - a flawed assumption is that the reason this flower is used in decoration is because it is red. Maybe its being 'red' is only an indicator of the actual true basis , which could be something entirely different - perhaps the actual basis was that any flowers which were grown in a flower bed treated with a particular fertilizer must be used in decoration, and it so occurs that only 'red' flowers were grown in that flower bed - here the true basis is the fertilizer and not the 'red' color, which is only used as a reference parameter.
Eg4: When I define a rule, "If any man completes the marathon, he will receive $1000 for doing so" - a flawed assumption is that not one of those who haven't completed the marathon end up receiving any money. It seems strange not to assume that way, but it is so by the rules of mathematical logic. As seen in the above Eg2, we are only permitted to conclude, that "if a man does not receive $1000, it is because he has not completed the marathon" - we cannot conclude upon whether he did actually receive any money from the given data. What if the sponsors of the marathon decided to charitably distribute $1000 to some of those who didn't complete too - the difference being the one who completes the marathon merits the $1000 and can claim it under the rules while the one who doesn't complete can stake no claim of merit at all.
OK
And now what if the same sponsors who charitably decided to distribute the $1000 to those who would not complete - what if they decided to display their charity not in directly giving the money but in giving an energy tonic that would make these cross the line, thereby upholding the rule AND still making it their charitable contribution to which these still have no claim of merit at all, since they're no longer under the rule?
How about this,
There are two runners in a race, they have to run the race, they have no choice in this matter. The rules say that whoever finishes the race within the 10 seconds gets a $1000. The distance of the race is set so that neither runner can finish in 10 seconds. Their natural ability will not allow them to do this.
So the one who initiated the race, chose the runners in the race, and made the rules provides one runner with an energy tonic so that runner could finish the race in the 10 seconds. That runner wins the $1000.
Or,
There are two runners in a race, they have to run the race, they have no choice in this matter. The rules say that whoever finishes the race within the 10 seconds gets a $1000. The distance of the race is set so that neither runner can finish in 10 seconds. Their natural ability will not allow them to do this.
So the one who initiated the race, chose the runners in the race, and made the rules provides both runners with a written rule book. That rule book explains the race, the rules, and tells both runners how they can win the race.
The message in the rule book is quite clear, they can't win it by their own abilities, they must drink the energy tonic in order to win the race. The initiator also provides instructors to help them understand what the rule book says. But most importantly the initiator is able to prick both men's conscious' (by the Holy Spirit, John 16) and the rule book commands, Repent, drink the energy tonic. The initiator provided the man with an intellect that is able to understand a simple message of drink the energy tonic and you win, if you don't you lose.
So the initiator provided the race (He didn't have to), He provided the reward, He provided the men with everything they need to understand the race and how to win. He holds out the energy tonic and says drink (He draws). The men have to drink by faith. They have to trust that what the initiator says is true.
So what I believe to be true is that man must first believe there is a God who is the Creator. (Romans 1)
I believe that the Holy Spirit convicts all men of unbelief in Christ (John 16), preparing them to receive the Gospel message. The Lord will draw them but not all will respond. I believe that if the Lord did not do this, no man could be saved.
Joh_6:44 No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.
Joh_12:32 And I, if I be lifted up from the earth, will draw all men unto me.
Jas_4:8 Draw nigh to God, and he will draw nigh to you. Cleanse your hands, ye sinners; and purify your hearts, ye double minded.
God gives an invitation to win the race, drink the energy tonic. Not all men will believe there is an initiator of a race, or that there is a race, or that they must be a runner in the race, or that they need the energy tonic in order to win the race.
Mat 22:3 And sent forth his servants to call them
that were bidden to the wedding: and they would not come.
Mat 22:4 Again, he sent forth other servants, saying, Tell them which are bidden, Behold, I have prepared my dinner: my oxen and my fatlings are killed, and all things are ready: come unto the marriage.
Mat 22:5 But they made light of it, and went their ways, one to his farm, another to his merchandise: (the Jews)
Mat 22:8 Then saith he to his servants, The wedding is ready, but they which were bidden were not worthy.
Mat 22:9 Go ye therefore into the highways,
and as many as ye shall find, bid to the marriage.
Mat 22:10 So those servants went out into the highways,
and gathered together all as many as they found, both bad and good: and the wedding was furnished with guests.(Jew and Gentile)
Mat 22:11 And when the king came in to see the guests, he saw there a man which had not on a wedding garment:
Mat 22:12 And he saith unto him, Friend,
how camest thou in hither not having a wedding garment? And he was speechless.
Mat 22:13 Then said the king to the servants, Bind him hand and foot, and take him away, and cast him into outer darkness; there shall be weeping and gnashing of teeth.
Mat 22:14
For many are called, but few are chosen.
I don't see that the call to the wedding was given any differently to any of the guests. Why was the man not chosen? Because he did not put on Christ, he showed dishonor for the King.
Now, applying such mathematical logic to our interpretation of Scripture - we find that if one does not receive $1000, it is because he hasn't completed the marathon. But if one does end up receiving $1000, it could either be because he completed the marathon OR because of a completely different reason(Eg3) where the true basis is the charity of the sponsor in contributing the $1000 but through the means of the recipient completing the marathon. ["completing the marathon"="believing in Christ" ; "$1000"="eternal life"]. One could refer Deut 9:5 for this concept of the bad half alone being merited by man while he has absolutely no claim of merit to the good half.
In my scenario of the race, there is no completing the marathon without the charity (love, grace, mercy) of the initiator of the race.
So my belief about election goes something like this. By grace, through faith, the gift of salvation is given. It was not any different in the OT. Those who believe God (faith) whether it was because God spoke to them directly, or because they believed what the prophets said about the Messiah, or because they heard the Word of God and didn't close their eyes and block their ears, they were preserved until the day the Messiah would come and suffer the cross for their sin. To those who would seek the one true God, God said they could find Him.
Deu 4:28 And there ye shall serve gods, the work of men's hands, wood and stone, which neither see, nor hear, nor eat, nor smell.
Deu 4:29 But if from thence thou shalt seek the LORD thy God, thou shalt find him, if thou seek him with all thy heart and with all thy soul.
Deu 4:30 When thou art in tribulation, and all these things are come upon thee,
even in the latter days, if thou turn to the LORD thy God, and shalt be obedient unto his voice; ( that voice which is calling, Come repent)
Deu 4:31 (For the LORD thy God is a merciful God;) he will not forsake thee, neither destroy thee, nor forget the covenant of thy fathers which he sware unto them.
They were aware of the presence of the Holy Spirit and their need. David cried out in his remorse,
Psa_51:11 Cast me not away from thy presence; and take not thy holy spirit from me.