With logic we construct a long chain of syllogisms, each producing the premises for the next link in that long, long chain. Also with logic, we construct theologies and all kinds of other extremely intricately interwoven webs. Let one single link be wrong and the entire thing can very quickly unravel faster than a knit sweater in a comedy routine.
A possible analogy could be navigation by dead reckoning. You know where you are starting from, you know your heading, and you know your speed (together, those last two constitute your velocity vector). After a given period of time, you know where you are. Or do you? What about drift due to wind and currents? What about inherent inaccuracies in your compass and compass reading, et al? When we bought our own 17-foot boat, my father took the seamanship courses from the Coast Guard. You sail out of Newport Harbor and head to Santa Catalina Island ("26 Miles Across the Sea"). As he told me, if your heading is off by even one degree, then you will miss the island altogether. In another example, when he was much younger he spent one summer or longer helping a friend mining. They wanted to extend a mine shaft to join up with another mine shaft. They know exactly where that other mine shaft was and how to dig to connect to it. They never found it, even though all their measurements were dead-on accurate. You need only be off by a very little to miss the mark altogether.
In Quartermaster (Navy) training, you use dead reckoning to estimate where you should be, but then you always go out and look at where you actually are (eg, shoot astronomical readings and calculate your position). In USAF tech school, a fellow student was doing flight training and he said that his instructor would have to tell him to pull his head out of the cockpit and look at what was actually out there. Admittedly, a Moody Institute film shown at a private pilots' meeting (my father also had a commercial flight license) gave examples of our senses being fooled when we should instead be trusting our instruments (eg, somehow getting inverted and mistaking the city lights on the ground for the stars). But the main point remains that wherever our logic / dead reckoning leads us, we still need to every once in a while pull our head out of the cockpit and figure out where we really are. There's even a story attributed to Carl Sagan of a toast given about physics and metaphysics, in which the physicist comes up with a promising idea which he then puts to the test in a laboratory and, finding it to be nonsense, drops it, the conclusion of which is that the metaphysicist has no laboratory in which to test his ideas.
You speak of a chain from A to Zed (having listened to the original "Hitchhiker's Guide to the Galaxy" and having viewed the original BBC TV production of that work, I know what "zed" means). That is 26 stages. What is the probability that 26 stages of reasoning will produce a true result? That probability should be
P = p
26, where p is the probability of any single step of being true.
OK, each stage can be true or false. That would imply a 50/50 chance. So what is 0.50
26? 0.000000015, or 1.5 10
-8, or about 15 chances in one billion. In comparison, our chances of willing a state lottery of 5 numbers from 1 to 50 plus one meganumber from 1 to 50 is 7.87 10
-11.
Let's make this extremely friendly and let's arbitrarily assign a 90% probability for each and every stage of A to Zed. That would be 0.065 or 6.5 10
-2. 6.5 chances in 100. Still not that great.
If you are still right by the time you get to Zed then it is likely that your A was correct.
Oh, you can go directly from A to Zed totally regardless of whether A is true or not. We're talking about logic here, not truth nor reality! You can logically construct any number of logically valid constructs of any possible degree of validity, but until you can establish the truth of their premise, they are nothing more than mental masturbation (line from
Miami Rhapsody, "My second favorite kind.").
If logic can tell you anything then there is your start.
Yes, but you must still be extremely rigorous in every step of your logic. And you must be extremely rigorous about the truth of your premises. 26 stages from A to Zed. If you slip up at any one single step, then you have invalidated the entire intricately webbed chain.
Or to return to the Navy navigation problem, what happens when you cannot get a fix? I once worked with a WWII Army Air Corps navigator. They called their aviators' wings "silver leg spreaders", since they gave them access to a lot of intimate female contact -- one psychologist shared with us that the free-wheeling sexual activity of the war years is what led to the sexual repression of the 1950's. During one flight where they were transporting nurses, one nurse was telling him that she had always been partial to navigators, but he was too preoccupied with the fact that the weather had not allowed him to get a proper fix for far too long.
Early in my college career (far longer than that of most), circa 1970 I had become tired of asking why everybody backed off to learn that my Sun was in Scorpio, so I decided to learn about astrology. Sun signs are extremely easy (they're the same each and every year) and are only one tenth of the more complete picture. Indeed, astrology creates a logical web that is as complete and intricate as any theology's. But if its most basic premises are false, then what good is it? The same with the legion of theologies: if their most basic premises are not true, then what good are they?
Logic can still tell us how to test the various theologies. How many are able to withstand the test?
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