Following that question : How to justify the use of logic?

I'm looking for references of the justification of the use of Logic (the question above didn't ask explicitly for resources but rather for a direct answer).

I'm especially interested in the concepts involved in that text : Are logical foundations circular ?, the philosophy behind the use of meta-logic/meta-language/meta-theory in Logic, the circular nature of the foundation of Logic and such.

I'm not sure about which concepts exacly are invovled so I'm not against some enlightenment.

  • Maybe relevant : Ian Rumfitt, The Boundary Stones of Thought ; An Essay in the Philosophy of Logic, Oxford University Press (2015). – Mauro ALLEGRANZA Dec 28 '16 at 9:36
  • do you want justification of logic, or justification of the use of logic? big difference. – user20153 Dec 28 '16 at 21:30
  • @mobileink What's the difference ? I think I'm looking for the justification of the rules of Logic and its use. – Boris E. Dec 29 '16 at 11:43
  • For example, Brouwer thought the Law of Excluded Middle was totally unjustified. But mathematicians use it all the time anyway. Its use can be justified for their purposes, even if it cannot be justified on intuitionist grounds. Also note there's a difference between "logical foundations" (of something other than logic) and Foundations of Logic. – user20153 Dec 29 '16 at 16:35
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    As I see it, the idea that you avoid the paradox of the foundation of logic by being concrete is that you provide a solid foundation for logic by providing good evidence of what is a valid logical implication, and you do this by exhibiting actual instances of implications involving concrete situations, instances of implications that most people intuitively take to be true, such as Aristotle's syllogism to the effect that Socrates is mortal, or the implication "If it is true that it rains and that I am hungry, then it is true that it rains", etc. Like physics, logic is an empirical science. – Speakpigeon Jan 15 at 11:48

Some references on the justification of logic:

Quine's critique of the idea that logic can be derived from the concept of analyticity can be found in his papers "Truth by Convention", "Two Dogmas of Empiricism" and "Carnap and Logical Truth". These can be found in his collections The Ways of Paradox, and From a Logical Point of View.

Putnam argues that we may have reason to accept that logic is empirical in his paper "Is Logic Empirical?" Boston Studies in the Philosophy of Science 5 (1968).

Michael Dummett argues that the justification of deductive reasoning must be found in a theory of meaning, in "The Justification of Deduction" (1974, in his collection of papers Truth and Other Enigmas).

Laurence BonJour defends the view that a priori knowledge of logic stems from rational insight, independently of experience in his book, In Defense of Pure Reason, Cambridge University Press (1998).

Paul Boghossian attempts to restore the concept of analyticity as a source of a priori knowledge in "Knowledge of Logic" In Paul Boghossian and Christopher Peacocke (eds.), New Essays on the A Priori (2000).

Other useful papers include:

Crispin Wright, "Intuition, entitlement and the epistemology of logical laws" Dialectica 58 (1):155–175 (2004)

Sinan Dogramaci, "Knowledge of Validity". Noûs 44 (3):403-432 (2010).

Hartry Field, "Epistemological Nonfactualism and the A Prioricity of Logic". Philosophical Studies 92 (1/2):1-24 (1998)

Corine Besson, "Logical Knowledge and Ordinary Reasoning". Philosophical Studies 158 (1):59-82 (2012)

William Hanson. "Logic, the a Priori, and the Empirical". Theoria 18 (2):171-177 (2003)

Julien Murzi and Florian Steinberger. "Is Logical Knowledge Dispositional?" Philosophical Studies 166 (1):165-183 (2013)

Timothy Williamson. "Understanding and Inference". Aristotelian Society Supplementary Volume 77 (1):249–293 (2003)

Mark Jago, "The Content of Deduction". Journal of Philosophical Logic 42 (2):317-334 (2013)


Firstly, I think science itself is self Justified and mathematics is tools (or a part of science).

This is the core main reason that the writer found circular events in his experience. In fact there are circular events in difference science and mathematics domain. (Similar as dictionary).

However, it is not the main point of science or mathematics. The main point of them is the evidence of those two domains normally contains a simple base line. "The actual world".

Any science theory is the evidence which is observed from the actual world, and mathematics is used to predict the circumstances which is not possible to be observed.

It is also what exactly dictionary trying to explain to the user, they explained a word by other sentences. Note here that: the object (the word to be explained) is something you expected to know. While the explanation is just tools, it can be pictures or any other things (in this case it is not circular anymore, but it is meta physically it is still a dictionary). I think just because word is usually a better manifestation for human to understand, thus most of the dictionary is copied by using sentences.

Then you may ask, is the real world also full of circular or self justified circumstances. This is another question which may not related to this question. But according to the general rule of chaos theory, any single existing event is just a subset which contain very similar properties of its super set. It is why the chaos is created.

For example When a single event is inflated many times to its infinite, the chaos is created and you already unable to determine the initial stage (it is another philosophical issue rather an object has initial point). Then you ask about the inflated object (logical foundations), is it circular? The answer is no, but it is truth that there is many other events (rather the next stage or the previous stage of inflation of this chaos set) can explain this object (as the core properties [the formula of the propagation of the set] is the same).

  • It doesn't answer my question but it's an interesting view. – Boris E. Dec 28 '16 at 23:42

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