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12

I don't think you can do any mathematics at all without axioms, or principles which are equivalent to axioms. Consider the statement "3 is prime". There are two definitions embedded here: 3 is the successor of the successor of the successor of zero. a positive integer is prime if it has exactly two divisors. The notion of the 'successor' is usually ...


9

When it comes to justification there is indeed a symmetric problem of deduction. But forming general opinions or laws is not part of deduction, it is abductive (or in older terminology inductive), when it comes to science it is the "hypothetical" part of the hypothetico-deductive method, see Are “if smoke then fire” arguments deductive or inductive? for more ...


8

What fallacy is it when someone says "this is true/it happened, therefore there are good reasons for it"? There is no fallacy described here. The argument uses the Principle of Sufficient Reason. The Principle of Sufficient Reason is simply stated: “For every fact F, there must be an explanation why F is the case” (Melamed and Lin 2016, §1). The ...


7

Mathematics goes through periods of accumulation of facts of interests and axiomitisations which orders and organises these facts. Although traditionally in European curricula mathematics is held to have begun properly with Euclids axiomitisation of Plane Geometry, this would not have been possible without the prior accumulation of facts about Plane Geometry,...


6

Not enough reputation for comment so I'll give an answer: The fact that a number is prime or not depends of the ring (i.e. axioms) to which is considered to belong. For instance 3 is prime if seen as an integer, but not if seen as a rational number (it is invertible). Also 5 is prime as an integer, but not as a Gaussian integer (of the form a+b*i, with a,b ...


6

Heidegger's idea here is actually not difficult to make out, unlikely as that might appear, if we trace the quotation to its source and check the context. Gavin Rae, 'Overcoming Philosophy: Heidegger, Metaphysics, and the Transformation to Thinking', Human Studies, Vol. 36, No. 2 (Summer 2013), pp. 235-257 : 247 : In The Word of Nietzsche: 'God is Dead,' ...


6

"Everything happens for a reason" is usually used in a different context, as a way to cope with senseless tragedies caused by random disasters. It is a case of pathetic fallacy, ascribing human reasons to inanimate things. "The statement that everything happens for a reason does not explain away randomness, and in fact it dismisses important truths about ...


5

I know the problem : you either get books on the science vs faith theme or you find books trying to vindicate the rationality of (usually Christian) faith. Something less polemical or 'apologetic' and more conceptual is required. Try any or all of these : Basil Mitchell : How to Play Theological Ping-Pong: And Other Essays on Faith and Reason Published by ...


4

You appear to be referring to self-selection bias. This is a well-known phenomenon in statistics, whereby self-selection into a category is correlated with other characteristics, and hence, inclusion in that category is not statistically independent of those other characteristics. This means that every field of expertise would be expected to attract a ...


4

David Blomstrom's answer is detailed and deeply informative. I am going to offer something shorter - shorter only with a view to the basic explanation you need to give to your son. ▻ DEDUCTION A deductive (or deductively valid) argument is one in which it is impossible for the conclusion to be false if the premises are true. The truth of the premises, if ...


4

The philosopher J. L. Austin, in his 1957 paper "A Plea for Excuses", makes a distinction between justifications and excuses. Contrasting these notions, he writes: In the one defence, briefly, we accept responsibility but deny that it was bad: in the other, we admit that it was bad but don't accept full, or even any, responsibility. (p. 2) In one of his ...


4

It seems you don't understand the terms. The essence of deductive reasoning: If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true. https://en.wikipedia.org/wiki/Deductive_reasoning Inductive reasoning, on the other hand: Inductive reasoning is a method of ...


4

tl;dr– Sounds like the basic premise behind conservativism (as opposed to liberalism). In general, both conservatives and liberals favor intelligent consideration when able; but, when it's unclear if a tradition has due motivation, more conservative positions weight the tradition's possible wisdom more heavily while more liberal positions weight the ...


4

Yes, this is a valid argument - if the premises were true, the conclusion would also be true. However, premise 1 is not true, so the argument is unsound.


3

Within contemporary philosophy, "logic" is narrower than "reason." We can waste our time in etymology, but the key is how the terms are used in the discipline. In most* contemporary philosophy, "logic" refers to sentential logic, truth-predicate logic, modal logic, deontic logic, and other variations on the formalization and evaluation of arguments in this ...


3

I typically present 'The Problem of Deduction' as a the following analogy to the better known 'Problem of Inductioon': One of the workhorses of deduction surely is Modus Ponens ... but why do we trust Modus Ponens? Is there a proof for Modus Ponens? Well, to demonstrate the validity of Modus Ponens, we typically do the following. We say that a truth-...


3

Not clear ... This is not a syllogism. Having said that, the statement: "if A, then B and if (A and C), then not-B" is not a contradicition. If the student does not get 85/100 at maths test, both conditionals are TRUE, and thus the conjunction is TRUE. But also if A and B are both TRUE, the conjunction is still TRUE, provided that C is FALSE.


3

In one sense we can say whatever we want, the question is to what end. On the shades of meaning associated with "is" see What is the difference between the "is" of predication and the "is" of identity? But the "fault" here does not lie with "is" exactly. It is the substitution play with the "red hat"...


3

Sherrilyn Roush describes epistemic self-doubt as the special case of doubt "where what we doubt is our ability to achieve an epistemically favorable state, for example, to achieve true beliefs". The problem with self-doubt is "one is using one’s judgment to make a negative assessment of one’s judgment". Not only Descartes but also Socrates is known for ...


2

In a certain sense your protagonist is correct. If your starting position is that logic and reason are correct, then applying logic to conclude that logic and reason are correct will always be circular. The trick is to not get all "truthy" about it. Logic is a useful tool for drawing inferences from a set of statements. That's all, nothing more mystical ...


2

When an agent provides "reasons", she stands for, and takes responsibility for her action. It signals that the agent acted (wasn't passive), and acted under favorable circumstances for deliberate action: in clear mind, in possession of one's faculties, in possession of relevant and correct information, not under threat (duress), and without unexpected ...


2

Do you mean : Is all knowledge in the arts based on abductive inference ? Or only that some of it is ? Abductive inference is - what ? - something like this. B needs to be explained; if A were true then B would follow with a high degree of probability; therefore there is some reason to suppose that A is true. Three comments : What of presumptive ...


2

Start with the basics... Deduction begins with a look at "the big picture," then zooms in on more detailed clues before reaching a conclusion. Induction is the opposite, using tiny pieces of evidence in an attempt to grasp the big picture. When using sound logic, deduction is foolproof. Maybe I shouldn't say "foolproof" on a philosophy forum, but let's ...


2

Conditionals like this are not contrary, because many, perhaps most, ordinary English conditionals allow for exception conditions. When we say, If A then B, there is usually an unstated "other things being equal". Adding an extra term to the antecedent is sometimes referred to as 'strengthening' of the conditional, and sometimes, confusingly as 'weakening'. ...


2

Deductive reasoning is "If this, then that." It is very useful in math and science. It's good for exploring the consequences of beliefs. It's essential in writing software (a conclusion arrived at by inductive reasoning). You're being a bit hypocritical by claiming to disdain it and still using the Internet. By claiming that arithmetic is taught through ...


2

A conclusion is sound (true) or unsound (false), depending on the truth of the original premises (for any premise may be true or false). At the same time, independent of the truth or falsity of the premises, the deductive inference itself (the process of "connecting the dots" from premise to conclusion) is either valid or invalid. The inferential ...


2

You summarise what you call deductive reasoning as follows: Deductive reasoning follows from absolute awareness in own intentions and desires. This isn’t what philosophers normally call deductive reasoning. The standard version is more accurately portrayed by your opening joke: start with agreed premises and apply accepted logical argument to arrive at ...


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