Limited Atonement and Perseverance of the Saints in Light of 1 Corinthians 8:11 (Calvinism) The acronym T.U.L.I.P summarizes five core doctrines of Calvinism concerning salvation. I hope I've summarized them accurately enough for the question's purpose.

T. Total Depravity — The doctrine that fallen man is 'dead in trespasses and sins' to the point of not even being able to accept salvation where such an offer thereof to be said to be possible or made possible in Calvinism.
U. Unconditional Election — The doctrine that God's election is, for lack of a better word, arbitrary, or not based on a condition on the creature—everyone saved is just as worthy of it: that is to say, not worthy at all.
L. Limited Atonement — The doctrine that since the grace of God is irresistible and is beneficial without exception to its recipients, this necessitates that Christ died only for such recipients, whose technical term are the elect.
I. Irresistible Grace — The doctrine that those whom God has elected to receive His grace, cannot resist it—according to Calvinism, any notion of 'resist' it would imply that His grace wasn't powerful enough in the first place, since grace means an action God does to someone, and not a spiritual help (which would naturally be able to be refused).
P. Perseverance of the Saints — The doctrine that if God has elected you, you are not among those that are damned, but of the infallibly saved: therefore it is impossible that you will be lost.


In light of these, how do Calvinists answer the objection that 1 Corinthians 8:11 (among other verses, of course) disproves in a marked way the Limited Atonement and Perseverance of the Saints (but also all of T.U.L.I.P since each point can be said to rely on the truth of the others)?
Here is 1 Corinthians 8:10-11 (NA28; my translation):

ἐὰν γάρ τις ἴδῃ σὲ τὸν ἔχοντα γνῶσιν ἐν εἰδωλείῳ κατακείμενον, οὐχὶ ἡ συνείδησις αὐτοῦ ἀσθενοῦς ὄντος οἰκοδομηθήσεται εἰς τὸ τὰ εἰδωλόθυτα ἐσθίειν; ἀπόλλυται γὰρ ὁ ἀσθενῶν ἐν τῇ σῇ γνώσει, ὁ ἀδελφὸς δι’ ὃν Χριστὸς ἀπέθανεν
For if someone sees you, who know better, sat eating in the temples of idols, will not his conscience, being weak, be emboldened to eat things sacrifices to idols? For by your knowledge he that is weak has been destroyed: a brother for whom Christ died.

This appears to me to invalidate both Limited Atonement and Perseverence of the Saints, since scandal is described as destroying one for whom Christ died.
In the same context, St. Paul writes the following to the church at Rome (Romans 14:14-15, 20: NA28; my translation):

οἶδα καὶ πέπεισμαι ἐν κυρίῳ Ἰησοῦ ὅτι οὐδὲν κοινὸν δι’ ἑαυτοῦ, εἰ μὴ τῷ λογιζομένῳ τι κοινὸν εἶναι, ἐκείνῳ κοινόν· εἰ γὰρ διὰ βρῶμα ὁ ἀδελφός σου λυπεῖται, οὐκέτι κατὰ ἀγάπην περιπατεῖς· μὴ τῷ βρώματί σου ἐκεῖνον ἀπόλλυε ὑπὲρ οὗ Χριστὸς ἀπέθανεν. ... μὴ ἕνεκεν βρώματος κατάλυε τὸ ἔργον τοῦ θεοῦ. ...
I know and am fully convinced in the Lord Jesus that nothing is unclean of itself, but that to him who considers anything to be unclean, for him it is unclean. For if by food your brother is offended, you are no longer walking according to love: do not destroy for the sake of food him for whom Christ died. ... Do not destroy the work of God for the sake of food. ...

Thanks in advance.
The answer to Paul's question :


  Shall the weak brother perish ? (I Corinthians 8:11 - KJV - απολειται ο ασθενων αδελφος)


is ... no he shall not perish.

The reason that the weak brother will not perish is :


  ... for whom Christ died. (I Corinthians 8:11 - KJV - δι ον χριστος απεθανεν)


The brother will not perish (or 'be destroyed') because Christ died for him and Jesus Christ loves him and Jesus Christ will not permit the sin of one brother to cause the other - weak - brother to be overcome and to be cast away.

Thus He sends a messenger to instruct both the 'strong' brother and the 'weak' brother - and we have the documented record of the messenger's epistle, proof positive that Jesus Christ is risen, and ascended, and ministers as a Priest at the right hand of the Father in the heavens.

And thus Paul addresses the errant - 'strong' - brother (so full of his superior knowledge and so sure of his own 'strength') and questions him. Because of you and your superior knowledge, will you damage your brother ? 

Will you cast a stumbling block - a 'scandal' - in his path ? Will you trust in your own strength of knowledge and care nothing for the weaker composure of your brother who will be tempted to do what is - actually - against his own conscience ?

For the weak brother might be emboldened to follow suit but, afterwards, his conscience will smite him (for his knowledge is not strong) and he will be overcome of guilt.

And Paul questions him to the ultimate - because of you and your attitude, will this brother ultimately perish ? Will he commit sin against his own conscience and be overcome of guilt and be destroyed ?

But the question of that weak brother's ultimate destiny is not up to the errant 'strong' brother. 

Nor is up to the weakness of himself (else would we all perish).

It is ultimately a matter of what God, in Christ, will or will not do.

For the Lord (I Peter 3:9) is not slack ... but is long-suffering to us-ward (that is to say to the 'them', also, who have obtained like precious faith with 'us' - see I Peter 1:1) not willing that any should perish, but that all should come to repentance.

[And I do respect what (I think) prompts the OP question - that repentance is necessary, else we perish. And I do not respect the attitude of those who think that a knowledge of doctrine is carte blanche to commit sin.]

The Lord is not slack. He sees every sparrow which drops to the ground in the forest, Matthew 10:29. He knows the number of the hairs of the head of them that seek him, Luke 12:7. He is aware of every single thought - not one is withheld from him, Job 42:2.

And he will not let one single one perish, for whom sacrifice was made and for whom righteousness has been satisfied . . . it cannot be. 

Otherwise, righteousness would be no more righteousness.



Note : I do not subscribe to 'tulip' myself. Jack Glass, in Glasgow, conveyed it to me fifty years ago when I was seventeen but I found it to be not a sufficiently spiritual expression of the gospel for me to embrace it. But I have answered the question as one who believes that the sufferings and death of Jesus Christ are effectual and are not dependent on the works of men to supplement them.

But I do believe that all for whom Jesus Christ suffered and died shall be brought to repentance and shall be brought to faith and that they shall be fully justified and, ultimately, glorified.

And in that, some might call me a follower of John Calvin and I would not disagree.

I would say that the argument of the posed question falls down because the argument has left Jesus Christ out of the process and has considered only the two brothers and their relevant 'strength' and 'weakness'.

It is the Lord who is above all.