This question comes from two false premises.
- That the claim that Calvinists depend on a logical fallacy when they point to the particularized language of the Bible.
- That the Calvinist argument for "limited atonement" depends exclusively on such inferences.
First, let's address the alleged fallacy. When exegeting scripture, it is not enough to treat the verses in an isolated fashion apart from any context or subtext.
Example 1: "Coffee is in the lobby."
Technically speaking, this is just telling you the location of coffee. Now suppose I give some context: You're at a car dealership for an oil change. Now it's clear that it's not just information, it's an offer for complimentary coffee. Even if the pot had a sign that said "free coffee" on it, there is is a subtext: It's only free coffee for customers to drink while they wait for their cars. If you were a drunkard who stumbled into the dealership and poured yourself a cup of coffee and started lounging on the furniture, you would be asked to leave. You would not be able to say, "Ha! You have committed the objective logical fallacy of informally known as the 'negative inference fallacy'! You didn't actually say that the free coffee was only for customers!"
Example 2: Englishman #1: "How have you been?" Englishman #2: "I've been better."
How is Englishman #2 doing? Absolutely horrible! How do you know? Because it's common for Englishmen to say, "Just fine" under virtually any circumstances. If he can't say he's doing fine even to this most insincere inquiry, he must be doing exceedingly poorly.
In both of these two examples, just a little bit of information about the backstory changes the meaning completely. So it is with so much of the particularized language of the New Testament.
When Jesus speaks of laying down his life for his sheep (John 10:15), we cannot divorce this from the immediate context of Jesus' sayings nor from the Old Testament context of "sheep" language.
- Jesus is disputing with Pharisees after being accused after healing a blind man.(John 9:40)
- Jesus argues that the sheep hear his voice and the gatekeeper opens the door when he calls, calling himself both the shepherd (10:11) and the door to the sheepfold (10:9). He is the shepherd, the savior (10:9), owner (10:12), protector (10:15), and feeder of the sheep (10:9). he is the door as the only right and proper way into the sheepfold (10:1).
- Jesus has other sheep outside of Israel who he will gather (10:16).
- The Pharisees are not his sheep (10:26).
The point of the parable is that he is distinguishing between those who are in and those who are out. He is especially distinguishing between the true and false people of God. It is in that context where Jesus says he lays down his life for the sheep.
Think of how strained this interpretation would be:
"I lay down my life for the sheep (but also for everyone else). The sheep come and enter the sheepfold and I feed them and keep them safe. Those who are not my sheep who try to come in are my enemies. Either way, I've still died for all of them, whether or not they are my sheep and whether or not they have entered through the door." It just does violence to the passage.
Old Testament Context: The Identity of the Sheep
Jesus is invoking a familiar biblical metaphor when he refers to the sheep, but giving it a prophetic twist. Israel was a nation of shepherds traditionally. It is why even when they first came to Egypt they were first despised by the Egyptians on the grounds they were shepherds and allowed to settle in the land of Goshen (Genesis 46:32-47:6). As biblical history unfolded, the metaphor grew to liken the people of Israel to be the sheep and God's anointed, David, to be the shepherd (2 Samuel 5:2). Even more so this language grew in the prophetic (Isaiah 53:6) and poetic literature (Psalm 23).
In the context of John 10, Jesus is drawing upon the analogy of God's people to sheep, but using it subversively. He draws a distinction between the literal, visible Israel, and the true people of God. This is why he rejects the literal Israelite, the Pharisee, who presumed that his pedigree (not his faith in Jesus) made him one of God's sheep and turns around and calls him a wolf.
Jesus is making the point that the true child of Abraham is the one who has faith like Abraham. This is exactly the point that Paul makes in Romans 4:1-13 and Galatians 6:15-16, where Paul identifies the true Israel as those who are righteous by faith.
Therefore, in John 10, Jesus intends to draw a distinction between the true sheep for whom he died and the false sheep who are simply biological descendants of Jacob or Judah. The argument is that Jesus' saving work is particular to his people.
Likewise Jeremiah 31:1 works perfectly with this interpretation.
“At that time, declares the LORD, I will be the God of all the clans of Israel, [the people of faith from all nations] and they shall be my people.”
Otherwise, Jesus words of John 10 cannot be true. If Jeremiah 31:1 were speaking only of biological Israel, the Pharisee would have been one of Jesus' sheep, yet Jesus said explicitly to him, "You are not my sheep."
Limited Atonement Not Depending on this Inference
The logic of Limited atonement (or particular atonement, which is more correctly termed) can be proven on the simple fact that Jesus' death actually paid for the forgiveness of sins. If the atonement were not particular, then there are people whose sins were paid for through the blood of Christ who ultimately end up going to Hell for their sins. While weeping and gnashing their teeth, they cry out, "At least Jesus died for my sins!"
For a more Biblical perspective, you get an affirmation of all five of the so-called, "Five Points of Calvinism" in Ephesians 1 & 2.
- Total Depravity (Eph 2:1)
- Unconditional Election (Eph 1:4-6)
- Limited Atonement (Eph 1:7 blood atonement understood in the context of the aforementioned election)
- Irresistible Grace (Eph 1:7, graciousness understood in terms of predestination before the foundation of the world)
- Perseverance of the Saints (Eph 1:13, sealed by the Holy Spirit)
Finally, as stereotypical of a Calvinist passage as it is, Romans 9 directly states that certain people were predestined for non-election and hardening (Romans 9:14-24).