The debate between Intralapsarianism and Suprelapsarianism concerns the logical order of God's decrees. God as the sovereign Ruler plans for everything, and thus the various decrees of God are God's directives to cause various and diverse things to happen in space-time. Thus, there is the decree of creation, which results in the creation of this universe, and the decree of the incarnation, where the Son willingly came down and was born of a woman into this world, which is part of the overall decree of redemption. Since in eternity (past) time doesn't really exist, the order of the decrees must be logical, not temporal. In other words, what is the best way we can understand how God's decrees relate to each other?
In the Supralapsarian scheme, the decree of election and reprobation comes before (thus "supra-") the decree of the Fall. Thus, the order is (1) the decree of election and reprobation, (2) the decree to cause the Fall, and (3) the decree to create. Whereas, in the Infralapsarian scheme, the decree of election and reprobation comes after (thus "infra-") the decree of the Fall. Thus, the order would be (1) the decree to create, (2) the decree to cause the Fall, (3) the decree of election and reprobation. It is to be noted that the logical order of the decree is just that: logical. It therefore does not concern the execution of the decrees in space-time, one thing which we need to take note when we look at the Reformed Confessions none of which have dealt specifically with anything other than the execution of the decrees.
Charles Hodge in pages 318-319 of volume 2 of his Systematic Theology lists down his objections to Surpralapsarianism. I think them singularly unconvincing and would like to provide a response to his objections.
Hodge's first objection is that Supralapsarianism involves a contradiction because the objects of the decree of election and reprobation need to exist, for nothing can be determined of a non-entity. This objection however is to confuse the idea of a logical order with the execution of that order in space-time. Individuals can be thought of before they have existed, in fact they must be for after that this is how any piece of fiction is made: One conceives of the plot and the characters before writing them down. One does not (at least in a good plot) introduce a character without any idea of what that character would be doing in the story, so how much more are individual humans before the Creator God, the Author of the greatest story ever told?
The second objection argues from the principle that "where there is no sin there is no condemnation" to show that foreordination unto death must contemplate its objects as being already sinful. But this fails to distinguish between the aspects of preterition (passing-by) and condemnation. Reprobation in the orthodox scheme is never equivalent to election. Election is God's active work to save sinners, while reprobation is God's passive work in leaving sinners in their sin. [Note: the use of the word "sinners" here is the language of the execution of those decrees]. The decree of reprobation therefore includes their preterition, and then only after that, their subsequent condemnation. No reprobate is ever condemned apart from consideration of his sins, and thus, while we agree that where there is no sin there is no condemnation, we disagree that this has anything to say about the decree of reprobation, which is primarily about preterition, which does lead to damnation but is not damnation per se.
Hodge's third objection is that the language of Romans 9:9-21 is that the "'mass' out of which some are chosen and others left, is the mass of fallen men" (2:318). But this again confuses the logical order of the decree with the execution of that order, which, as the scholar Robert Reymond has pointed out, is always the inverse of the logical order of the decree. His fourth objection is that creation in the Bible is never represented as a means to execute the purposes of election and reprobation, but that to me is a strawman. Creation has its own penultimate telos, but we are talking about how these decrees relate to each other logically, not whether these decrees have legitimate penultimate purposes different from each other. The decrees of God are not just towards one goal only, but many goals, all of which are non-exclusive. After all, the desire to glorify the Son is not mutually exclusive to the desire to save some sinners to eternal life in Christ. Similarly, the desire to manifest His glory in Creation is not mutually exclusive from the desire to glorify Himself through redemption.
The final objection given is that Supralapsarianism is inconsistent with the portrayal of God as a God of mercy and justice, since in Supralapsarianism individuals are condemned to "misery and eternal death" as "innocents." First of all, this confuses preterition and condemnation. Secondly, since in the Infralapsarian scheme, God permitted or passively caused the Fall which affects all subsequent "innocents," the Infralapsarian scheme is not superior to the Supralapsarian scheme in dealing with the topic of theodicy ("Why evil exists").
Hodge of course supports the Infralapsarian position. But if that is treated as the logical order of God's decrees, then it seems that election and reprobation only come about because of sin, and therefore they are contingent upon sin occurring. In the Supralapsarian scheme, the allowance of sin serves the purposes of election and reprobation, whereas in the infralapsarian scheme, election and reprobation are reactions to sin. This seems to me troubling because of what that implies for our understanding of God's desire to save us. To put it practically and somewhat simplistically for simple believers, are we saved because God has always desired to save us (Supralapsarianism), or that God desires to save us only when it appears we are falling away (Infralapsarianism)?
I mentioned that we need to decide on the best way we are to understand God's decrees as they relate to each other. The best way to relate them is to look for the ultimate purpose of God, which is His own glory, and then locate each decree in the order towards the promotion of God's glory. After all, God desires to glorify Himself, and therefore the best way to relate them is to put them in an order towards that same goal. Before time began, God who works all things for His own glory will plan for that to happen, thus we perceive the logical order of God's decrees accordingly. God of course will execute these decrees in "time," and thus in the execution we see the election and reprobation of sinners after they have sinned in Adam. Thus, we understand a logical order, and an order of execution. All of these intellectual exercises are for us to be consistent in our theology, and thus make us understand that God has always desired to save us, which did not begin only after Adam and Eve fall.