# Axioms for modal logics based upon counterfactuals

## What are the axioms of modal logic?

Some characteristic axioms of modal logic are: Lp ⊃ p and L(p ⊃ q) ⊃ (Lp ⊃ Lq). The new rule of inference in this system is the rule of necessitation: if p is a theorem of the system, then so is Lp. Stronger systems of modal logic can be obtained by adding additional axioms.

## What are the types of modal logic?

Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth: alethic (“necessarily”), epistemic (“it is known that”), deontic (“it ought to be the case that”), or temporal (“it is always the case that”) among others.

## What is modal proposition in logic?

Any proposition at least one of whose constituent concepts is a modal concept is a modal proposition. All other propositions are nonmodal. Any modal proposition can be represented in our conceptual notation by a wff containing one or more modal operators, e.g., “•”, “0”, etc.

## What is a counterfactual statement?

COUNTERFACTUAL statements may be identified as statements. that ” If p were true, then q would be true “; i.e. assertions. whose antecedent and consequent are known or assumed to be. false, and whose truth or falsity is determined independently of. that fact.

## What does axiom mean in math?

In mathematics or logic, an axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful. “Nothing can both be and not be at the same time and in the same respect” is an example of an axiom.

## What is the modal ontological argument?

The best-known modal ontological arguments are basically of this form: (1) It is at least possible for God to exist. (2) If God’s existence is possible, then necessarily, God does exist. (3) Therefore, necessarily, God exists. As noted, even most atheists will initially agree to (1).

## Where is modal logic used?

However, the term ‘modal logic’ may be used more broadly for a family of related systems. These include logics for belief, for tense and other temporal expressions, for the deontic (moral) expressions such as ‘it is obligatory that’ and ‘it is permitted that’, and many others.

## What is modality logic?

modality, in logic, the classification of logical propositions according to their asserting or denying the possibility, impossibility, contingency, or necessity of their content.

## What is S4 modal logic?

The flavor of (classical) modal logic called S4 is (classical) propositional logic equipped with a single modality usually written “□” subject to the rules that for all propositions p,q:Prop we have.

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## Do counterfactuals have truth value?

Counterfactuals are not truth-functional.

## What is the problem with counterfactuals?

The problem of counterfactuals

Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true.

## What are counterfactuals economics?

Counterfactuals are what ifs, thought experiments, Gedankenexperimenten, alternatives to actual history; they imagine what would have happened to an economy if, contrary to fact, some present condition were changed; in the philosophical literature therefore they are known also as ‘contrary-to-fact conditionals’.

## What are counterfactuals in econometrics?

In history counterfactuals are posed by “what if” questions, such as “what would the U.S. economy have been like in 1890 had there been no railroads?”, Fogel (1964). In economics alternative counterfactuals (hypothetical states of the world) are considered in decision making under uncertainty.

## What is an example of counterfactual thinking?

Counterfactual thoughts spell out what people think caused an outcome. For example, the thought “If I had not eaten so many potato chips, I wouldn’t feel ill right now” implies eating too many potato chips caused the person to feel sick.

## How is positive economics different from normative economics?

While positive economics is based on fact and cannot be approved or disapproved, normative economics is based on value judgments. Most public policy is based on a combination of both positive and normative economics.

## What is macroeconomics and microeconomics?

Microeconomics is the study of how individuals and companies make decisions to allocate scarce resources. Macroeconomics is the study of an economy as a whole.