"Without Christianity, there is no purpose to anything"
"Unless there is a God, there can be no real ethics"
"All people need hope, and the only real hope comes through Jesus"
All three statements, and many others that could be made like them are, I think, true. I would still be happy to make them and to stand by them. The problem is where they fit into our argument. Let's take the statement about ethics. It is often used as if it could be formulated thus:
Major premise: only the existence of God could create objective ethics.
Minor premise: there is such a thing as objective ethics.
Conclusion: therefore, God exists.
Well, that won't do. Anyone can happily deny the minor premise. And they regularly do. Sure, you can push people into admitting that they do think that one thing or another is 'just wrong', but that is just their feeling or preference as far as they are concerned.
What about hope? I've often heard something a bit like:
Major premise: only Christianity offers ultimate hope for individuals and the cosmos.
Minor premise: we all need hope.
Conclusion: therefore, Christianity is true.
But that is not even a valid syllogism! It is a valid question whether our need for hope, especially in the face of death, is not in fact a product of our Christian heritage. Even if hope is a universal human desire - and I don't see how you could prove it - that doesn't show that it is a valid desire. I hope for many things that don't come to pass.
Arguments like these have their place. What they demonstrate, if presented properly, is that 'it would be nice if Christianity were true'. That sounds like a pretty weak conclusion, but actually I think it is one of the things that my contemporaries need to hear. Christianity is attractive; faith in Jesus makes sense of the world. These arguments are important because many people have already decided that Christianity is intellectually, ethically and aesthetically barren. We need to show them that it is not so. We also need to point out, by use of these sorts of arguments, that they ought not to be content to swallow the nonChristian worldview without careful thought - after all, it deprives you of hope, ethics etc. Maybe those things are illusory, in which case we'll have to do without, but you ought to at least check. In this way, positively and negatively,we win a hearing for the gospel.
That would be the first step. But that is as far as any of these arguments can take you. Even here, your argument needs to be qualified: if Christianity is true, there is also the reckoning with the wrath of God against sin, which is frankly unattractive. That tells me that even here these arguments cannot be allowed to control.
Everything hinges on this: is it true? By which we mean: did the man Jesus die and rise?