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Purpose of This Letter
1 This is now, beloved, the second letter I am writing to you in which I am stirring up your sincere mind by way of reminder,
2 that you should remember the words spoken beforehand by the holy prophets and the commandment of the Lord and Savior spoken by your apostles.

Peter's linking of the prophets and apostles placed them on the same level of authority.
Follow the commandments of the Lord and Savior, and the apostles which are now found in scripture.

The Coming Day of the Lord
3 Know this first of all, that in the last days mockers will come with their mocking, following after their own lusts,
4 and saying, "Where is the promise of His coming? For ever since the fathers fell asleep, all continues just as it was from the beginning of creation."

Conversational Notes:
We see mockers being mockers because they want their sexual sin, and it might be true, but it not usually fruitful in conversation with non-believers to bring this up.
Paul's audience is believers.

Induction, Hume's argument
1. Definition of a Miracle:
Hume defines a miracle as a violation of the laws of nature. These laws are based on uniform and consistent human experience, like gravity, the behavior of light, or the consistency of physical objects.
2. The Balance of Probabilities:
According to Hume, when faced with a claim of a miracle, one must weigh the evidence for the natural law (which is based on consistent experience) against the evidence for the miracle (which is based on the testimony of a witness or group of witnesses). Since natural laws are supported by universal and consistent experience, they are highly probable.
By contrast, a miracle, by definition, is a rare and exceptional event that goes against this established order, making it inherently less probable. Therefore, the evidence for the miracle must be extraordinarily strong to overcome the very high probability that the natural law remains unviolated.
3. Testimony and Human Nature:
Hume argues that human testimony is often unreliable. People can be deceived, misinterpret events, or have motivations like the desire for attention or to support religious beliefs that might lead them to fabricate or exaggerate accounts of miracles.
Furthermore, Hume points out that reports of miracles often originate in "ignorant and barbarous nations," where critical scrutiny of such claims is less likely.
4. The Principle of Diminishing Credibility:
Even if multiple sources independently report the same miracle, Hume suggests that their testimonies do not multiply the probability of the miracle occurring. Instead, they simply add layers of evidence, each of which is still less probable than the natural law they contradict.
Therefore, the more extraordinary the claim (such as a miracle), the more extraordinary the evidence needed to justify belief in that claim.
5. Hume's Conclusion:
Hume concludes that it is never reasonable to believe in miracles based on testimony alone because the improbability of the miracle outweighs the reliability of the testimony. A wise person should proportion their belief to the evidence, and since the evidence for natural laws is overwhelmingly strong, it would be irrational to believe in a violation of those laws without equally strong evidence.

5 For when they maintain this, it escapes their notice that by the word of God the heavens existed long ago and the earth was formed out of water and by water,
6 through which the world at that time was destroyed, being flooded with water. (contrast between formed out of water, and destroyed by water and then fire on Judgment day)
7 But by His word the present heavens and earth are being reserved for fire, kept for the day of judgment and destruction of ungodly men.

You have seen God work!
Peter refers to creation, to show that God has been at work before.
The scoffers deliberately put aside God's Word and then complained that God was not doing anything.

Creation options:
Young Earth Creationist: Our universe was created by God 6,000-10,000
Day age view or standard Old Earth Creationist: The Universe is 14 billion years old, but every day in Genesis was a unique creation event
Intelligent Design or a Theistic Evolutionary model: There are differences in the details, but God set forth the unfolding of our reality with the law that guided it in such a way to bring about the diversity and intelligent humans like us.

Isaiah (66:15–16) and Malachi (4:1) associated fire with the return of the Lord.
WARNING: There will be a Judgment day and there will be destruction of ungodly men.

8 But do not let this one fact escape your notice, beloved, that with the Lord one day is like a thousand years, and a thousand years like one day.
9 The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance.

The words not wanting (mē boulomenos) anyone to perish do not express a decree, as if God has willed everyone to be saved. Universal salvation is not taught in the Bible. Instead those words describe God's wishes or desires; He longs that all would be saved (cf. 1 Tim. 2:4) but knows that many reject Him.

Think about your day and all of the activities you do. If the Lord comes back, what will he catch you doing?

A New Heaven and Earth
10 But the day of the Lord will come like a thief, in which the heavens will pass away with a roar and the elements will be destroyed with intense heat, and the earth and its works will be burned up.
11 Since all these things are to be destroyed in this way, what sort of people ought you to be in holy conduct and godliness,
12 looking for and hastening the coming of the day of God, because of which the heavens will be destroyed by burning, and the elements will melt with intense heat!
13 But according to His promise we are looking for new heavens and a new earth, in which righteousness dwells.
14 Therefore, beloved, since you look for these things, be diligent to be found by Him in peace, spotless and blameless,
15 and regard the patience of our Lord as salvation; just as also our beloved brother Paul, according to the wisdom given him, wrote to you,

The Lord's patience is because of His desire that people come to salvation (cf. v. 9). The seeming procrastination of the Second Coming, far from being negative inaction on God the Father's part is rather a demonstration of His makrothymian ("long-suffering").

16 as also in all his letters, speaking in them of these things, in which are some things hard to understand, which the untaught and unstable distort, as they do also the rest of the Scriptures, to their own destruction.

Peter calls Paul's letters Scripture or at least put them on the same level.

17 You therefore, beloved, knowing this beforehand, be on your guard so that you are not carried away by the error of unprincipled men and fall from your own steadfastness,
18 but grow in the grace and knowledge of our Lord and Savior Jesus Christ. To Him be the glory, both now and to the day of eternity. Amen.

Search the scripture and get God's heart on the issue
Observation
Interpretation
Application
Categories of language
Multiple places where the command is given or that it is followed