25

We will suppose for the sake of argument that there do exist an infinite number of parallel universes. The question then becomes "Which universe are we in?". We observed these events, so we know we're in the subset of the universes in which they happen. Within that subset, there are some universes in which these events were deliberately designed, ...


7

Thinking in terms of parallel universes shouldn't do much to change the way we assess which of two explanations is more likely. For example, if we're playing poker, and I know I'll win unless you have the other two aces in your hand, I can ask, which is more probable? That you have those aces, or that you're bluffing recklessly? If we think in terms of all ...


6

These rules are intuitionistically valid, but... Intuitionists accept modus tollens in the form given (2), but not {¬q→¬p, p} ⊢ q, see Can one prove by contraposition in intuitionistic logic? A contradiction out of ¬q only gives us ¬¬q, and removing the double negation is something they reject. This is because p → q is interpreted as "given a proof of p a ...


5

I'd be tempted to say that logic is not a model that we use to reason. It's a model, a representation, of how we reason (or should reason). People don't need to learn the rules of classical logic to make inferences, but logicians are interested in how people make inferences, this is where the models of logic come from. This might apply to some extent to ...


5

If we inhabited every parallel universe simultaneously, then the antistatistic argument might have merit. But we do not, and events in one parallel universe can have no effect whatsoever on any of the other universes. Testing the antistatistician's world view requires him or her to 1) establish the reality of parallel universes and 2) devise some way to make ...


4

Well, here is one very non-statistical, informal answer. I don't think explanations using multiple worlds or "parallel universes" do any work. Kant once remarked, in reference to the ontological proof of God, that "existence is not a predicate," meaning that it adds nothing to the statements, and the same can be said of such fundamentally ...


4

It's the difference between absolute certainty and reasonable certainty. We are not 100% sure that an exceedingly-unlikely event won't happen (or that an event didn't have an exceedingly-unlikely cause). We are only reasonably sure of this. We assume exceedingly-unlikely events don't happen because they are exceedingly unlikely, thus we would statistically ...


3

The parallel universes talk is a red-herring. The philosopher could just as well say that "it's possible for this to be a case of sheer luck which just happened to come true". And well... so what? How exactly does this refute statistical inference? Doesn't he have any further grounding for his belief? The claim he makes could be made for pretty ...


2

The following description of the two criteria in the OP's post may not be accurate: The chapter starts with asserting that every rule of inference must satisfy two criteria: Note that it is not that every rule of inference must satisfy the two criteria, but the set of rules of inference as a whole must satisfy those two criteria. Some sets of rules may ...


2

If you refute statistical reasoning, it becomes practically impossible to reason about anything occurring in the natural world. The example you gave involved unlikely coincidences, but we use similar inductive reasoning for all the "normal" events in our life as well. Every time someone walks behind a barrier and then reappears on the other side, ...


2

Short Answer Induction and deduction are relatively artificial subsets of reasoning. Human reasoning is very complex and defeasible. A third form of reasoning recognized is that which is abductive generally considered equivalent to inference to best explanation. Is it "legal" to reduce various aspects of an argument into components? Yes, certaintly,...


2

"If a argument is deductively valid we don't care if premises are true or not right?" Well, valid means that if the premises are true, the conclusion is guaranteed to be true as well (one way of describing logical validity is that if you have some premises P and a conclusion Q, then the statement P -> Q is a tautology). Note his comment "to ...


1

Short Answer There is no royal road to a strong argument. It takes a lot of diligence and mastery of a number of subject matters including mastery of the facts of the domain of discourse, formal and informal logic, linguistics, argumentation theory, and having a good range of argumentation examples. Professional philosophers spend their whole lives trying to ...


1

The common sense philosopher and the anti-statistical philosopher are working with different definitions of "knowledge," so it is highly likely that they will come to different opinions on the matter. The common sense philosopher is arguing that at some point, its best to just give up and accept a "truth" about the universe because you'...


1

You are misreading the "sufficient (but not necessary)" comment of page 22. We have to consider also the following parenthetical comment : (As we shall see in Ch.4, we obtain a complete characterization of logical consequence by omitting the restriction to sentential interpretations). Consider now Ch.4 : General Theory of Inference, page 68 : ...


1

Tacit inference is the norm, not the exception. In a real sense, language is merely pointing with words, and we all have to infer referents from the inherently ambiguous symbols that others provide for us. Consider our interactions with young children: a young child will point and make a grasping gesture with a hand, and say (perhaps) "Gagrlagaaagah"; we are ...


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