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- เผยแพร่เมื่อ 6 ต.ค. 2024
- Anybody with an interest in philosophy is aware of the problem of induction. But there are philosophers who have suggested that deduction is equally vulnerable to a skeptical attack.
Susan Haack's paper, "The Justification of Deduction", is available online here: www.as.miami.ed...
Carroll's "What the Tortoise Said to Achilles": courseweb.sttho...
Thomson's "What Achilles Should Have Said to the Tortoise": www.math.dartmo...
Regarding the points discussed around 26:00 - 27:11, cf. for example: en.wikipedia.or... & Belnap's paper "Tonk, Plonk, & Plink": www.pitt.edu/~b...
I'm so grateful for this goldmine of a channel. Best philosophy channel on youtube. no contest
Totally agree
solution 3 looks good to me. The meaning of the connective. The operation that the connective represents allows you to infer B from A and A>B, but it does not allow you to infer A from B and A>B. MP is valid in virtue of its adherence to the logical rule and MM is invalid in virtue of its lack of relationship to the operation of the conditional connective
Exactly what I was thinking. Using the modus morons rules of inference, it seems, "A -> B" is just a goofy way of writing "B -> A", since it follows all the same structural rules.
The fact that MP and MM are different, specifically the 1st if valid and the 2nd is not, isn't a matter of English language. It's a matter of Math which provides the exemplification of these logical schemata.
For example:
MP
If N is even number, then it's a number.
2 is an even number
So, it's a number.
(True)
MM
If N is even number, then it's a number.
5 is an even number
So, it's an even number.
(Not true)
So; we don't know how we know!
it's very deep problem; for me it has no solution
it's the incompleteness of human reason !
we can't isolate the reason from everyday life ;"reality" .
reasoning isn't " a close system"
or
as kane said in the end of the video we take them as fundamental ; as axioms
we take them because we take them !
thanx for the video its very interesting and useful
I find it strange how so few actually brings up the problem of deduction. I have for a decade now always understood intuitively that deduction is just induction with a few extra steps, really. But it seems no one else gets it. It's so sad that in the philosophy of logic of all places, people just assert deduction to be valid, and don't really question why it is.
Should they attempt to, they will quickly realise that whatever justification they're using, cannot be using deduction, since that would be circular. And thus, all they have left is induction, the very thing the religious deduction fanatics call so unreliable and weak. Ironic.
It seems the problem arises from the assumption that deduction must deductively be proven valid. I don't think modus ponens is capable of being doubted; and modus morons is incapable of being accepted or believed. What people say counts for little, since I can say I am not self-identical and each magnitude is greater than itself, etc. I have never encountered anyone who claimed the ability to doubt deduction, nor have I encountered an argument which even seemed to disprove modus ponens which was the least bit compelling.
With that reasoning, then the problem of induction exists because we assume that induction must be proved by induction. By dismissing the problem of deduction so easily, then I too can dismiss away the problem of induction as well.
very interesting! The last argument really resonated with me. Since we can never really know anything about the real world, we have to use models to describe it (which all of us intuitively already do). Logic is simply one of those models and it has MP as one of its axioms. Then, just like with any other model, we justify the application of this model to reality with induction. This removes the need to justify MP itself and shifts the problem to establishing that the model of logic is actually applicable to reality. And for that, induction is a strong enough justification, provided you accept it. If you don't, then we have just reduced the problem of deduction to the problem of induction, which is also a nice result imo.
The cost of justifying deduction inductively is massive. In that case, no matter how strong any argument is, it will always remain just probably true. In other words, we would no longer be able to say that the truth of the conclusion is guaranteed by the truth of the premises. That's not a result any of us want to have, right?
Love this guy
1. The Carol presentation of "The problem of Deduction", is remarkably similar to G.E. Moore's "Naturalistic Fallacy" of Ethical Reasoning. This is the presentation of ethical reasoning as type of deduction that is a "causitry" presentation of Aristotle's Ethics of "a good" and virtuous act in a situation by an virtuous man is its deduction from "The Good": a principle. importantly Moore notion of natural fallacy here is not just a criticism of naturalism but more a criticism of the idea of a Universal definition to connect compel or cover all cases and all contexts. Pritchard made a similarly structured argument against duty i think as a hierarchy of duties and stations determining a single exclusive duty and so station (identity) for a person in a situation.
2. Here then, while structural similarities can be presented between Induction and Deduction, I would claim there are similarities here between Ethics and Morality, when these are conceived as activities like deduction, for example in the Natural Law traditions that took over The Ancient Greek and Roman Personal "Character" "identity" focus of Virtue and Duty, with a certain conception of legalistic reasoning.eg Aquinas, that became a project to increasingly present ethics and morality as the structure and the gap as a problem of the character of the individual. This allowed the people using and making the the scheme to manufacture sin and guilt of those under the scheme, a priori. The notion of Reason became the definitions and structure of those managing the schema. Whether they themselves follow their own schema (rule of law that the law applies to the law makers) is not sufficient a criteria for its Rationality constancy completeness and decidability.
3. There is with this schema a similarity between the deduction and the Syllogism and the legal political structure of the state or Holy Roman Empire. With the Universal major premise, as the executive, the particular minor premise and the legislative, and the conclusion as the judge in a case. (In this i am inspired by discussions of Kant on Hobbes where this similarity is made* I will try and find the reference.). What is interesting is that the rule of law now only has the semblance of the law makers being under the law "empirically" that disguises or makes covert that they make and inhabit the Semblance of it being Formal structure as whole.
4. This then shifts the question of the problem of deduction from being a formal problem needing a formal type of solution, to a puzzle that needs a diagnosis and then a dissolving. In this later Wittgenstein approach the problem of deduction an antinomy, is not to be solved, this project comes too late. Rather ethics and morality are shown to have a reality beneath its the Deductive Surface appearance or ideology. So in the example of a Truth Table schema we see this is just a heuristic a technology to give the appearance of closed reasoning,. However this was introduced, by early Wittgenstein, only from within the wider context of a "picture theory of meaning". This view I would claim is about irreducible real context of a fact, in contrast to empiricism and deductive rational that attempts to surreptitiously make the fact a abstract singularity. The error of deduction then lies in its problem is really that the structure attempts at arriving at a abstract singular given case with no context (I am inspired here by J.L. Austin "Truth" (1950) discussed in Goldstein, Brennan, Deutsch and Lau "Logic: Key Concepts in Philosophy (pg.s 66-70) )
5. I would claim that Kant's Ethics and Morality has similarly been mis-appropriated as a deduction in the natural law tradition, where in fact Kant merely presents it through that apparent form to "show" that it a is a mere surface appearance of a depth of reality beneath. I then would place Kant as a Critical Philosopher not "justifying" deduction and natural law as it is but showing from its terms and problems a deeper reality to these questions that shift the project away from questions of "gap closing" and "infinite regress halting".
So we must move the issue away from natural law problematics as the image of reasoning as external to the person, indeed as well as this project trying to manufacture a reality reality of abstracts subsumable cases by closing down our environments to remove concreteness and ambiguity of contexts it also is a project directed at the persons to make them an abstract ideal singularity. the image of though as deduction then tries "implicitly" and for the most past unconsciously to make all cont4exts and situations the same and all people the same, in its attempt to close the gap and halt what it sees as excuses. Thus the real meaning of natural law and deduction as a notion a project progress i akin to the logic of Hegel as a sublation of context and difference towards Absolute Actuality as a Deductive State Reason of Universal Right and The General The whole. This requires ironically manufacturing sameness and identity of place and people. it is a tragic irony that this deductive model of logic and reason in its 20th century form was set up in opposition to Hegel but has as a project and in praxis become structurally the same.
6. the kind of re-presentation of deduction then in Kant mirrors the re-presentation of natural law deduction in his morality. The key point is that of the "Schematism" in which he show Deduction is secondary and General Logic a logic of Truth is impossible. the project of a General Theory of truth then is rejected as an erred project, and through the syllogism and form of relational inference (Categories of Relation) we are to re-orientate ourselves to judgement as a unity of the manifold in a situation though the 12 Categories as special and temporal heuristics not deductions. This brings into view the subject as active and responsible and agent, in contrast to the deductive model that want as to eliminate the subject and create anonymity for those who construct and run the schema truth table and Universal and Existential Quantifiers of records and risk assessments of those under it.
7. You may see a certain structural parallel here between what i am doing and Foucault and Derrida, but rather while they deconstrued the image of the state and law back in the day their followers are now constructing a new deductive system that has the same structure with their own privileged content. They increasingly work with law as seen though content generated by Bayesian Risk that while represented as an alternative to deduction actually in practice the "use" of its content is deductive. the content itself also suffers form errors of abstraction of single series homogeneous probability fields. Errors akin to the myth of single differential fields of exchange in supply/demand differential calculations. That is the assumption of a constant necessity for a fixed possibility field that is the apparent single ground for a probability. This becomes even absurd when modelled as a axiomatic modal Theory in antinomy with Quantification a mix up of dynamic and static representations. Now Deleuze expresses the dissatisfaction with these surface problem of deduction a Axiomatic quantification and Axiomatic Modality, in "Difference and Repetition" but rather in order to exploit the subterranean ground for a radical evolutionary political praxis from within the terms of liberal capitalism and transitivity commutativity ect. However he views Kant as within the same "preserving or conservative traditions, that Kant's Transcendental Philosophy is merely justification of the deductive representations. That is "conditions of possibility" just ground our traditional structures of deduction, rather than may view that they make explicit a depth that dissolves the deduction problem of justification to be on the same or similar levels as deduction as General Logic of Truth. i imagine he has in mind the post World War Two Analytic Interpretations of Kant's Transcendental Deduction of the Categories, that work in the terms and problematics of Strawson's view as Kant is justifying "uncritically" a pre Critical view of logic metaphysics and epistemology, whereas Kant is rather radically reorienting the metaphysical tradition not justifying it as it is. (reference Deleuze "Difference and Repetition" (1968) especially Chapter 4.)
Many thanks Kane B for the Problem of Deduction discussion as always the very best accounts are to be found here.ction discussion
B1. It is interesting to see what happens to the Deduction Schema when negations are brought in, as one model of proof is to employ strategies of avoiding contradiction. This is not Modus Ponens as equivalence or symmetry of strategy or consistency of strategy leading to affirming as valid to a MP fallacy. The thing is though the negation strategy, involvers placing negation as "everything else" other than what is affirmed. This conflates intention and reference and responsibility equally to the unaffirmed. This i view as the problem of Hampel's Paradox: the logical equivalence of truth as assertion to, the assertion of the falsity of everything else. This negation problem in general was already approached historically with tacit reference to action and the "ought" in relation to the "is" as a relation of imagination to truth and fact. This was the existence of the unicorn unicorn discussions between Russell and the pre-phenomenology context form Mineong and Brentano. The issue of negation here assumes no temporal relation between is and ought (transitive etc. Leibnitz put this in terms of possible world as modal factual existences and sub moral existences s a different space to negation, but still removing relations of temporal reach (proof) and human action mediating is and ought.
2. The consequence of this view of negation is that what works to assume or arrive at contradiction can be expressed in terms of reach between is and ought, is and not. The logic disjunctive spaces are separate but in some sense have to be equivalent. This becomes problematic when we think of "being in the law and being outside the law, or against the law. places action and intentions i a strange space where now all action can be view as potentially or possibility or probability wise towards being against he law. People might say of a illegal act that it is potentially or possibly leading to a legal act, but only through behavioural retraining or "rehabilitation, or some kind of educational program to become in accord with the law. This forgets the non reversibility of time and habit, or that the learning of first language is the same as learning a second language. second. or there is a basic number series.
3. its interesting that the legal political ontology in Quine etc. has it that the negation of the Universal Quantifier is the Existential Quantifier and the negation of the Existential Quantifier is the Universal Quantifier. It seems to me that if we recognise the legal and political shape of these Logics to be constructive at their base, then the UQ stands for the instituional meaning of Right and the EQ stands for the objects posited as Right. If we say this as the Universal is Hegelian (post war Universal legal right ), then the existential is Kierkegaard. the semantics here are radically different as opposition to being related as negation of each other. this is odd since the universal legal right as law and the individual post is the same or simultaneous. anyway rights are, in their negative sense law prohibiting and determining the application of laws, they are only derivative then posits of those people as posits under the law already. meaning the space of action is closed under law to be either positive or negative, but now the negative is intentional derivative of the negation of bei9gn against law. it is not in itself space of action excepts as a probity to be against the law.
4. I think if we look at the context of the work being done on this logic in Germany and Poland and Austria between WW1 and WW2, it sees to me to be a mode of tacitly covertly addressing the rise of powerful legal states. the logic is the logic of the State Quantifiers predicate tables, reference by positive predications (definite descriptions) unique reference and identity of indecearnables and to its legal expression. (see also Peter Suter on Russell paradox of sets, meta-languages and constitutional Rights law).
5. its not that sate try and reproduce logic though institutions and technologies rather, these are the home of logic and we get a better understanding of it when looking at logic in its instituional and technical use, the symbols are after the fact of the practice meaning. Look at the early criticisms of probability eg by Popper on Reichenbach (Sellars and Feigl "Readings in Philosophical Analysis ) Also Quine's interviews and discussions of 1994. He comes right out and says the fundamental reason for his view on extension over intension was because of witnessing racism and anti Semitism.)
I don't understand how the argument for deduction applies just as well for counterinduction. It would seem to me that the counterinduction argument would only work if we know something about the set, for instance the set of Fs contains Fs that are Gs and Qs. Then it would be reasonable to assume that the next F will not be G. If there is no prior knowledge of the set I find that the most reasonable thing to assume in line with induction until proven otherwise.
I think it's because induction says "this has been the case so far, so it _should_ continue to be the case". But this leaves the negative case still possible, so you have two choices of possibility; it is the case, it is not the case. Therefore, we can just as well choose the "it is not the case" option for all future observations
Deduction assumes that premises would be valid all the time and continue to be valid, which itself is an induction. If empirical proof is used to validate the conclusion, then that makes empricism even stronger and more infallible.
If born with horns -> animal
A is born with horns
Therefore, A is an animal.
Which doesn't have to be true. A human can be born with horns due to mutation and Alien species can be born with horns who are neither humans nor animals.
C.K.Raju explains problem of deduction and that of 2-valued logic.
What if you are talking about non-temporal things though? mathematics is a stateless language.
What a beautiful problem
Wait… so deductive logic isn’t sound ?
Maybe deductive inference rules are not propositions that ought to be justified but rather imperatives of the formal language. So, modus ponens is not: ''[ (A-->B), A therefore B]; but more like: If you have A and A-->B, then INFERE B. This does not require a justification.
How did I get here from a cat video?
Kane, would you be interested in doing a Discord Voice Chat AMA with our philosophy group? We have 4k members now!
Sure, that would be cool. Send me the link and let me know what times would be best for you.
Strangely enough we run 24/7, im here around 15 hours a day personally, but the admins are more than capable. We stream 24/7 and record all convos as well. discord.gg/9fGw5uR
PHD Alex Malpass is in here now
Thanks for the link, I will check it out sometime over the weekend.
@@mrfamousgetfamous7885 Is there a way to hear any of these recorded discussions?
An if-then argument requires you to visualize the sequence of reasoning as a whole rather than separate convictions. When you say modus ponens is the argument you assume that no error has been made in the structure of the argument and from that point are lost in a web of symbols that do not accurately represent the logic or the reasoning. If the tortoise doesn't accept that Socrates is mortal, then he does not accept that all men are mortal. Despite the claim that "A" was accepted it clearly wasn't. The bigger problem of deduction is the reality of our temporal perception that keeps us from being able to predict the future. If "a" usually happens under "x" conditions, then this combination will cause the same result in the future has no more weight than implying that because it happened in the past it wont happen again because the reality is that we cant take affirmation and attribute the success of a prediction as the result of the logical method by which the confirmed conclusion had been derived from alone. The method is a way to understand the situation but ultimately probability of specific convictions and hope are the best we can achieve as humans. If you agree that experience lead to knowledge and wisdom. Then the statement that some people have a lifetime of experience but show very little intelligence will strike you as dull and without respect to the point of view that you have presented. At this point saying that specific experiences combined with the aspects of hope, diligence and luck will lead to growth intellectually and logically doesn't make the first statement wrong. But it makes it lacking in scope. When A is assumed to be comprehensive of an opinion is becomes impossible to use the method of deduction to derive a conviction through reasoning. It is not the method but the improper use of terminology.
Z Ro DMG god bless my grammar. please take the entirety of what I am saying into consideration despite the difficulty of having to sift through poor syntax.
Z Ro DMG
You didn't address the actual point of the argument, however flawed you may think the *example* given was.
thats the good stuff
Ahhhh the problem with using reasons to prove reasons
Wtf... A problem of deduction.. Really?
Skiesc
I am 100th liker
The problem of deduction is not analogous to the problem of induction; they are fundamentally different. The problem of induction represents a failure of inductive reasoning to make guarantees about its conclusions. The problem of deduction represents a failure in communicating ideas between people who use the medium of communication in different ways. As long as you don't try to present your deductive arguments to anyone, the problem of deduction cannot arise.
In part 3 this is made very clear because the only way MM can apply is if the conditional connective is allowed to have a different meaning, and you'll never have two different meanings for the connective unless at least two people are trying to interpret it. Ultimately the only solution to the problem of deduction must lie in convincing people to not have alternative interpretations of connectives.
Suppose Achilles said, "La pomme est rouge." The tortoise might look at the apple and declare Achilles statement to be false because the apple is not green. When Achilles made his statement he intended for "rouge" to mean red, but the tortoise has its own ideas. The problem arises because the tortoise has chosen a different meaning for that word, much as MM chooses a different meaning for the conditional connective. Obviously there is nothing we could say to the tortoise to prove that it is wrong about the meaning of the word or the connective; the issue is social, not logical.
By using a nonstandard version of French the tortoise is making it impossible to communicate. Our job is simply to explain all the negative consequences of doing so and ask the tortoise to please acquire a dictionary and start using it because everything will become much easier. Either that, or the rest of the world can start using the tortoise's version of French. By whatever means, once we are all reading from the same rulebook the problem of deduction disappears.
If deduction works, then you should be able to prove that claim. That is the problem (the same one as induction). The only solution is to say that it’s true because it’s true as an axiom.
@@SkillUpMobileGaming Saying that it is true as an axiom is the correct solution. The whole problem of deduction comes directly from failing to respect the purpose and meaning of axioms and rules of inference. There can be no problem if we all simply use the relevant axioms and rules of inference. The problem of deduction demands a proof for something which should not be proven. It would be like asking us to prove that bachelors are unmarried. It's not the sort of thing that one should even attempt to prove: it's an axiom. That's all the justification that we should want if we understand the purpose of axioms and why we need them.
To put this another way, the problem of deduction raises the question: How do we prove that modus ponens is valid? The answer is that it cannot be proven, and yet it still must be valid because it is a rule of inference, and all the rules of inference are valid and impossible to prove. So then we have the question: How do we prove that all the rules of inference are valid? The answer is that it cannot be proven, and yet it must be true because it is an axiom, and all axioms must be true. How do we prove that all axioms must be true? We can't, because the truth of all axioms is also an axiom.
So the real question is why do we need axioms when they behave so strangely and contrary to the usual rules of reasoning? For almost any claim we expect some sort of argument or evidence to justify our belief, so why make an exception for axioms? The answer is that axioms serve a critical role in logical reasoning, and to do without axioms means doing without logic. Consider how deduction breaks down in the problem of deduction when someone demands proof for modus ponens. Without deduction, logic is pointless, so we have axioms to allow us to avoid that problem.
Think of how to people with radically different worldviews can accidentally talk past each other because they each misunderstand the context of what the other is saying, so that they misinterpret each other's words. In order to understand each other they need some common ground where their worldviews overlap, and that can become a foundation for communication. The utility of axioms is that they can serve as common ground. Even when we agree on little else, we can at least agree that modus ponens is valid.
+Ansatz66 I don't know for sure why, but axioms work in every single situation they are in, and if you count these confirming instances as "evidence," then there is an infinite amount of evidence supporting every axiom we use. In addition, there is zero evidence against the axioms we use. I believe that infinite supporting evidence and zero disconfirming evidence (not even in a hypothetical situation!) should make us extremely confident in trusting our axioms.
@@SkillUpMobileGaming "I believe that infinite supporting evidence and zero disconfirming evidence (not even in a hypothetical situation!) should make us extremely confident in trusting our axioms."
That would be getting our confidence from the wrong place. We should be confident in trusting our axioms, but that confidence should come from an understanding of the nature of axioms, not from evidence that cannot possibly be real. For example, consider the fact that bachelors are unmarried. We could do a total survey of all the bachelors in the world, and that survey would confirm that every one of them is unmarried, but that's not really evidence of anything. That's just a consequence of the meaning of the word _bachelor._ In other words, bachelors being unmarried is an axiom and all this "evidence" that we've supposedly gathered is just a misunderstanding.
In the same way we could do a total survey of every instance of modus ponens and confirm that it has been valid every time, but such a survey is totally pointless. The "evidence" that it would gather is just a misunderstanding of the nature of modus ponens. We don't accept modus ponens as a rule of inference due to every instance being valid; every instance is made valid by the fact that modus ponens is a rule of inference. It's just the same as how all bachelors are unmarried due to the meaning of the word _bachelor._
+Ansatz66 Again, I don't know if I'm right here, and I want to hear what you have to say. I understand your reasoning, but if axioms are just rules we decide on, then how can we know that the rules are applicable to the world we live in? We could decide to use any axioms we wanted to. The axioms we use are technically true, as you've shown, because they are "definitions" or "rules" that work because we've said they work. By definition they work. Although that's the truth, don't we only use the axioms we use because they apply to our world? I thought that the reason we believe they are applicable to the real world was because they always work.
We could, if we decided to, come up with axioms for a hypothetical universe (with whatever axioms we wanted to by whatever definitions we came up with), but they wouldn't apply to our world. Isn't the reason that we agree that the axioms we have chosen are applicable to our world because they work in every instance and never fail? Otherwise, we could come up with any axioms we wanted to and it wouldn't matter how applicable or relevant to our world they would be. Axioms are useful only so far as they are applicable to our world. How can we know that they apply to our world? Because they work every time and never fail.
LOL this is what happens when they don't teach you Aristotle in school, you get deluded into thinking your "acceptance" is a prerequisite for logic to be real.
Could you elaborate? As a mathematician who's still quite unfamiliar with philosophy, I'd appreciate it if you could explain how Aristotle fits into this discussion. Thanks!
@@jitsekuilman2492the first example in the video which is supposed to be a refutation of deduction elevates the hypothetical tortoise's acceptance of 2+2=4 as somehow tangential on its truthfulness or correctness. It's the enchrochment of vulgar linguistics upon the foundations of our knowledge, but only as a way to doubt certainty, often in service of the status quo or some ideology. At any rate "west centric math", or the kind of math that works, the kind of math that makes airplanes fly, compells us to accept the transcendent nature of logical and mathematical statements as essential parts of what grants coherence to all language. We are beseached by people who will publish papers in which the necessity for the coherence of all language is put to question but when it comes to their paychecks and grants and tenured positions suddenly they're "stupid essentialists" like the rest of us.
@@jitsekuilman2492 he basically introduced the concept of deduction
Use truth-table to justify MP, problem-solved.