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LOGICAL OPERATORS:
Let’s preserve our philosophical innocence!!
You can build up many kinds of logics, like relativistic logic, or relevance logic.
”Nobody has ever died from drinking coffee at Mustasche, Pete is currently drinking a coffee at Mustasche, so Pete will not die from this.”
What is wrong with this statement?
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It looks reasonable
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The conclusion is plausible from the premises
However it is not deductively valid.
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The premises do not provide an absolute, unavoidable, guarantee for the conclusion.
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It is important to remember that it is possible to imagine a different case without contradicting oneself
-It is basically about ”100% guarantee”, however this in reality just means that it only really works for abstract categories.
Regarding inductive reasoning however
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it acts from past to future
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from a number of specific cases to all cases
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not deductively valid
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(usually) reliable
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Empirical science is usually inductive
Scientific division of labor
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deductive reasoning → logic
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inductive reasoning → statistics
”Does there exist a situation” =/ whether I can imagine a situation in which an argument is not valid
(Non-)existance: ”objectively” valid
Imagine: too subjective
→ drives need for a more formalised mathematical approach to logic
If a situation in which an argument is false exists, it will be apparent.
That is why we formalise logic, we use it as a heuristic to find these cases immediately.
Validity has to do with formal structures, and not at all to do with content.
All F are G
n is F
so n is G
- Every argument that instantiates the above form is valid.
Most G are H
most H are K
so there exist G that are K
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An argument like this is not deductively valid (depending on the content funnily enough).
”One error and you’re out!”
Validity and Soundness
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An argument is valid if and only if there is no possible situation in which all premises are true and in which the conclusion is false.
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What is meant by ”possible situation”?
Logical possibility
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What can be thought coherenctly, without contradicting oneself
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The weakest, most inclusive kind of possibility
eg.
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Whatever is physically possible, is logically possible as well
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Whatever is financially possible, is logically possible as well
Validity: Is all about ”logical possiblity”!!
Necessity: Is the same as saying ”it is not possible that x is not the case”.
Stays the same for all kinds of possiblity.
Possiblitity is however about being true in at least one situation
Logical possibility is the weakest kind of possibility;
However, logical necessity is the strongest kind of necessity → very few things are logically necessary.
Deductive validity:
An argument is valid if and only if it is necessary that the if the premises are true, then the conclusion is true as well.
Validity = necessary truth preservation, yet still independent of de facto truth!!!
Validity flows from the premises to the conclusion.
Premises and conclusion are both called propositions!
In classical logic, a proposition is a kind of thing that can either be true or false in a given case.
Don’t make the categorical mistake of thinking that an argument is a proposition. They are valid or invalid, propositions are true or false.